id sid tid token lemma pos ajst-9436 1 1 academic academic ADJ ajst-9436 1 2 journal journal NOUN ajst-9436 1 3 of of ADP ajst-9436 1 4 science science NOUN ajst-9436 1 5 and and CCONJ ajst-9436 1 6 technology technology NOUN ajst-9436 1 7 issn issn NOUN ajst-9436 1 8 : : PUNCT ajst-9436 1 9 2771 2771 NUM ajst-9436 1 10 - - SYM ajst-9436 1 11 3032 3032 NUM ajst-9436 1 12 | | NOUN ajst-9436 1 13 vol vol NOUN ajst-9436 1 14 . . PROPN ajst-9436 2 1 6 6 NUM ajst-9436 2 2 , , PUNCT ajst-9436 2 3 no no INTJ ajst-9436 2 4 . . NOUN ajst-9436 2 5 2 2 NUM ajst-9436 2 6 , , PUNCT ajst-9436 2 7 2023 2023 NUM ajst-9436 2 8 12 12 NUM ajst-9436 2 9 wavelet wavelet NOUN ajst-9436 2 10 denoising denoise VERB ajst-9436 2 11 image image NOUN ajst-9436 2 12 processing processing NOUN ajst-9436 2 13 based base VERB ajst-9436 2 14 on on ADP ajst-9436 2 15 matlab matlab PROPN ajst-9436 2 16 xiangyu xiangyu PROPN ajst-9436 2 17 feng feng PROPN ajst-9436 2 18 , , PUNCT ajst-9436 2 19 geng geng PROPN ajst-9436 2 20 liang liang PROPN ajst-9436 2 21 , , PUNCT ajst-9436 2 22 wei wei PROPN ajst-9436 2 23 pei+ pei+ PROPN ajst-9436 2 24 , , PUNCT ajst-9436 2 25 xuying xuying NOUN ajst-9436 2 26 gao+ gao+ PROPN ajst-9436 2 27 school school NOUN ajst-9436 2 28 of of ADP ajst-9436 2 29 north north PROPN ajst-9436 2 30 china china PROPN ajst-9436 2 31 electric electric PROPN ajst-9436 2 32 power power PROPN ajst-9436 2 33 university university PROPN ajst-9436 2 34 , , PUNCT ajst-9436 2 35 beijing beijing PROPN ajst-9436 2 36 , , PUNCT ajst-9436 2 37 china china PROPN ajst-9436 3 1 + + PROPN ajst-9436 3 2 are be AUX ajst-9436 3 3 : : PUNCT ajst-9436 3 4 the the DET ajst-9436 3 5 .third .third ADJ ajst-9436 3 6 * * PUNCT ajst-9436 3 7 authors author NOUN ajst-9436 3 8 abstract abstract ADJ ajst-9436 3 9 : : PUNCT ajst-9436 3 10 this this DET ajst-9436 3 11 article article NOUN ajst-9436 3 12 uses use VERB ajst-9436 3 13 matlab matlab PROPN ajst-9436 3 14 to to PART ajst-9436 3 15 simulate simulate VERB ajst-9436 3 16 the the DET ajst-9436 3 17 wavelet wavelet NOUN ajst-9436 3 18 denoising denoising NOUN ajst-9436 3 19 algorithm algorithm NOUN ajst-9436 3 20 . . PUNCT ajst-9436 4 1 the the DET ajst-9436 4 2 threshold threshold NOUN ajst-9436 4 3 denoising denoising NOUN ajst-9436 4 4 was be AUX ajst-9436 4 5 simulated simulate VERB ajst-9436 4 6 using use VERB ajst-9436 4 7 the the DET ajst-9436 4 8 function function NOUN ajst-9436 4 9 method method NOUN ajst-9436 4 10 , , PUNCT ajst-9436 4 11 triple triple ADJ ajst-9436 4 12 standard standard ADJ ajst-9436 4 13 deviation deviation NOUN ajst-9436 4 14 method method NOUN ajst-9436 4 15 , , PUNCT ajst-9436 4 16 fixed fix VERB ajst-9436 4 17 threshold threshold NOUN ajst-9436 4 18 algorithm algorithm NOUN ajst-9436 4 19 , , PUNCT ajst-9436 4 20 haar haar PROPN ajst-9436 4 21 , , PUNCT ajst-9436 4 22 sym5 sym5 PROPN ajst-9436 4 23 , , PUNCT ajst-9436 4 24 coif3 coif3 PROPN ajst-9436 4 25 , , PUNCT ajst-9436 4 26 and and CCONJ ajst-9436 4 27 db3 db3 PROPN ajst-9436 4 28 wavelet wavelet NOUN ajst-9436 4 29 bases basis NOUN ajst-9436 4 30 . . PUNCT ajst-9436 5 1 the the DET ajst-9436 5 2 simulation simulation NOUN ajst-9436 5 3 results result NOUN ajst-9436 5 4 show show VERB ajst-9436 5 5 that that SCONJ ajst-9436 5 6 using use VERB ajst-9436 5 7 the the DET ajst-9436 5 8 fixed fix VERB ajst-9436 5 9 threshold threshold NOUN ajst-9436 5 10 method method NOUN ajst-9436 5 11 , , PUNCT ajst-9436 5 12 the the DET ajst-9436 5 13 haar haar NOUN ajst-9436 5 14 wavelet wavelet NOUN ajst-9436 5 15 has have VERB ajst-9436 5 16 the the DET ajst-9436 5 17 best good ADJ ajst-9436 5 18 denoising denoising NOUN ajst-9436 5 19 effect effect NOUN ajst-9436 5 20 . . PUNCT ajst-9436 6 1 keywords keyword NOUN ajst-9436 6 2 : : PUNCT ajst-9436 6 3 wavelet wavelet NOUN ajst-9436 6 4 denoising denoising NOUN ajst-9436 6 5 algorithm algorithm NOUN ajst-9436 6 6 , , PUNCT ajst-9436 6 7 threshold threshold NOUN ajst-9436 6 8 denoising denoising NOUN ajst-9436 6 9 . . PUNCT ajst-9436 7 1 1 1 X ajst-9436 7 2 . . X ajst-9436 7 3 introduction introduction NOUN ajst-9436 7 4 wavelet wavelet NOUN ajst-9436 7 5 transform transform NOUN ajst-9436 7 6 is be AUX ajst-9436 7 7 widely widely ADV ajst-9436 7 8 used use VERB ajst-9436 7 9 in in ADP ajst-9436 7 10 signal signal ADJ ajst-9436 7 11 denoising denoising NOUN ajst-9436 7 12 , , PUNCT ajst-9436 7 13 which which PRON ajst-9436 7 14 not not PART ajst-9436 7 15 only only ADV ajst-9436 7 16 preserves preserve VERB ajst-9436 7 17 abrupt abrupt ADJ ajst-9436 7 18 signals signal NOUN ajst-9436 7 19 but but CCONJ ajst-9436 7 20 also also ADV ajst-9436 7 21 preserves preserve VERB ajst-9436 7 22 signal signal ADJ ajst-9436 7 23 spikes spike NOUN ajst-9436 7 24 . . PUNCT ajst-9436 8 1 wavelet wavelet NOUN ajst-9436 8 2 transform transform NOUN ajst-9436 8 3 can can AUX ajst-9436 8 4 be be AUX ajst-9436 8 5 widely widely ADV ajst-9436 8 6 used use VERB ajst-9436 8 7 to to PART ajst-9436 8 8 eliminate eliminate VERB ajst-9436 8 9 noise noise NOUN ajst-9436 8 10 between between ADP ajst-9436 8 11 transient transient ADJ ajst-9436 8 12 signals signal NOUN ajst-9436 8 13 and and CCONJ ajst-9436 8 14 instantaneous instantaneous ADJ ajst-9436 8 15 state state NOUN ajst-9436 8 16 signals signal NOUN ajst-9436 8 17 , , PUNCT ajst-9436 8 18 as as ADV ajst-9436 8 19 well well ADV ajst-9436 8 20 as as ADP ajst-9436 8 21 to to PART ajst-9436 8 22 suppress suppress VERB ajst-9436 8 23 high high ADJ ajst-9436 8 24 - - PUNCT ajst-9436 8 25 frequency frequency NOUN ajst-9436 8 26 noise noise NOUN ajst-9436 8 27 , , PUNCT ajst-9436 8 28 effectively effectively ADV ajst-9436 8 29 distinguishing distinguish VERB ajst-9436 8 30 high high ADJ ajst-9436 8 31 - - PUNCT ajst-9436 8 32 frequency frequency NOUN ajst-9436 8 33 information information NOUN ajst-9436 8 34 from from ADP ajst-9436 8 35 low low ADJ ajst-9436 8 36 - - PUNCT ajst-9436 8 37 frequency frequency NOUN ajst-9436 8 38 noise noise NOUN ajst-9436 8 39 . . PUNCT ajst-9436 9 1 the the DET ajst-9436 9 2 application application NOUN ajst-9436 9 3 and and CCONJ ajst-9436 9 4 development development NOUN ajst-9436 9 5 prospects prospect NOUN ajst-9436 9 6 of of ADP ajst-9436 9 7 wavelet wavelet NOUN ajst-9436 9 8 denoising denoising NOUN ajst-9436 9 9 are be AUX ajst-9436 9 10 promising promise VERB ajst-9436 9 11 . . PUNCT ajst-9436 10 1 nowadays nowadays ADV ajst-9436 10 2 , , PUNCT ajst-9436 10 3 not not PART ajst-9436 10 4 only only ADV ajst-9436 10 5 are be AUX ajst-9436 10 6 there there PRON ajst-9436 10 7 more more ADJ ajst-9436 10 8 and and CCONJ ajst-9436 10 9 more more ADJ ajst-9436 10 10 applications application NOUN ajst-9436 10 11 using use VERB ajst-9436 10 12 wavelet wavelet NOUN ajst-9436 10 13 denoising denoising NOUN ajst-9436 10 14 , , PUNCT ajst-9436 10 15 but but CCONJ ajst-9436 10 16 also also ADV ajst-9436 10 17 the the DET ajst-9436 10 18 application application NOUN ajst-9436 10 19 fields field NOUN ajst-9436 10 20 are be AUX ajst-9436 10 21 constantly constantly ADV ajst-9436 10 22 increasing increase VERB ajst-9436 10 23 , , PUNCT ajst-9436 10 24 such such ADJ ajst-9436 10 25 as as ADP ajst-9436 10 26 mathematics mathematic NOUN ajst-9436 10 27 , , PUNCT ajst-9436 10 28 computer computer NOUN ajst-9436 10 29 science science NOUN ajst-9436 10 30 , , PUNCT ajst-9436 10 31 seismic seismic ADJ ajst-9436 10 32 exploration exploration NOUN ajst-9436 10 33 data datum NOUN ajst-9436 10 34 processing processing NOUN ajst-9436 10 35 , , PUNCT ajst-9436 10 36 signal signal VERB ajst-9436 10 37 analysis analysis NOUN ajst-9436 10 38 , , PUNCT ajst-9436 10 39 and and CCONJ ajst-9436 10 40 image image NOUN ajst-9436 10 41 processing processing NOUN ajst-9436 10 42 . . PUNCT ajst-9436 11 1 studying study VERB ajst-9436 11 2 the the DET ajst-9436 11 3 well well ADV ajst-9436 11 4 - - PUNCT ajst-9436 11 5 developed develop VERB ajst-9436 11 6 centralized centralized ADJ ajst-9436 11 7 wavelet wavelet NOUN ajst-9436 11 8 denoising denoising NOUN ajst-9436 11 9 algorithms algorithm NOUN ajst-9436 11 10 and and CCONJ ajst-9436 11 11 some some DET ajst-9436 11 12 improved improved ADJ ajst-9436 11 13 algorithms algorithms NOUN ajst-9436 11 14 is be AUX ajst-9436 11 15 beneficial beneficial ADJ ajst-9436 11 16 for for ADP ajst-9436 11 17 better well ADJ ajst-9436 11 18 application application NOUN ajst-9436 11 19 of of ADP ajst-9436 11 20 wavelet wavelet NOUN ajst-9436 11 21 algorithms algorithm NOUN ajst-9436 11 22 for for ADP ajst-9436 11 23 more more ADJ ajst-9436 11 24 development development NOUN ajst-9436 11 25 and and CCONJ ajst-9436 11 26 utilization utilization NOUN ajst-9436 11 27 , , PUNCT ajst-9436 11 28 and and CCONJ ajst-9436 11 29 also also ADV ajst-9436 11 30 contributes contribute VERB ajst-9436 11 31 to to ADP ajst-9436 11 32 the the DET ajst-9436 11 33 development development NOUN ajst-9436 11 34 of of ADP ajst-9436 11 35 wavelet wavelet NOUN ajst-9436 11 36 denoising denoising NOUN ajst-9436 11 37 methods method NOUN ajst-9436 11 38 . . PUNCT ajst-9436 12 1 the the DET ajst-9436 12 2 concept concept NOUN ajst-9436 12 3 of of ADP ajst-9436 12 4 wavelet wavelet NOUN ajst-9436 12 5 transform transform NOUN ajst-9436 12 6 was be AUX ajst-9436 12 7 first first ADV ajst-9436 12 8 proposed propose VERB ajst-9436 12 9 by by ADP ajst-9436 12 10 an an DET ajst-9436 12 11 engineer engineer NOUN ajst-9436 12 12 , , PUNCT ajst-9436 12 13 j. j. PROPN ajst-9436 12 14 morlet morlet PROPN ajst-9436 12 15 , , PUNCT ajst-9436 12 16 in in ADP ajst-9436 12 17 1974 1974 NUM ajst-9436 12 18 and and CCONJ ajst-9436 12 19 established establish VERB ajst-9436 12 20 an an DET ajst-9436 12 21 inversion inversion NOUN ajst-9436 12 22 formula formula NOUN ajst-9436 12 23 . . PUNCT ajst-9436 13 1 perhaps perhaps ADV ajst-9436 13 2 due due ADP ajst-9436 13 3 to to ADP ajst-9436 13 4 the the DET ajst-9436 13 5 novelty novelty NOUN ajst-9436 13 6 of of ADP ajst-9436 13 7 this this DET ajst-9436 13 8 concept concept NOUN ajst-9436 13 9 at at ADP ajst-9436 13 10 the the DET ajst-9436 13 11 time time NOUN ajst-9436 13 12 , , PUNCT ajst-9436 13 13 it it PRON ajst-9436 13 14 was be AUX ajst-9436 13 15 not not PART ajst-9436 13 16 recognized recognize VERB ajst-9436 13 17 by by ADP ajst-9436 13 18 mathematicians mathematician NOUN ajst-9436 13 19 at at ADP ajst-9436 13 20 that that DET ajst-9436 13 21 time time NOUN ajst-9436 13 22 . . PUNCT ajst-9436 14 1 several several ADJ ajst-9436 14 2 years year NOUN ajst-9436 14 3 later later ADV ajst-9436 14 4 , , PUNCT ajst-9436 14 5 two two NUM ajst-9436 14 6 other other ADJ ajst-9436 14 7 scholars scholar NOUN ajst-9436 14 8 were be AUX ajst-9436 14 9 curious curious ADJ ajst-9436 14 10 about about ADP ajst-9436 14 11 this this DET ajst-9436 14 12 concept concept NOUN ajst-9436 14 13 . . PUNCT ajst-9436 15 1 one one NUM ajst-9436 15 2 was be AUX ajst-9436 15 3 the the DET ajst-9436 15 4 famous famous ADJ ajst-9436 15 5 mathematician mathematician NOUN ajst-9436 15 6 y. y. PROPN ajst-9436 15 7 meyer meyer PROPN ajst-9436 15 8 , , PUNCT ajst-9436 15 9 who who PRON ajst-9436 15 10 accidentally accidentally ADV ajst-9436 15 11 constructed construct VERB ajst-9436 15 12 a a DET ajst-9436 15 13 real real ADJ ajst-9436 15 14 wavelet wavelet NOUN ajst-9436 15 15 base base NOUN ajst-9436 15 16 in in ADP ajst-9436 15 17 1986 1986 NUM ajst-9436 15 18 , , PUNCT ajst-9436 15 19 and and CCONJ ajst-9436 15 20 cooperated cooperate VERB ajst-9436 15 21 with with ADP ajst-9436 15 22 s. s. PROPN ajst-9436 15 23 mallat mallat PROPN ajst-9436 15 24 to to PART ajst-9436 15 25 establish establish VERB ajst-9436 15 26 the the DET ajst-9436 15 27 same same ADJ ajst-9436 15 28 method method NOUN ajst-9436 15 29 for for ADP ajst-9436 15 30 constructing construct VERB ajst-9436 15 31 wavelet wavelet NOUN ajst-9436 15 32 bases basis NOUN ajst-9436 15 33 multi multi ADJ ajst-9436 15 34 scale scale NOUN ajst-9436 15 35 analysis analysis NOUN ajst-9436 15 36 . . PUNCT ajst-9436 16 1 after after ADP ajst-9436 16 2 that that PRON ajst-9436 16 3 , , PUNCT ajst-9436 16 4 wavelet wavelet NOUN ajst-9436 16 5 analysis analysis NOUN ajst-9436 16 6 began begin VERB ajst-9436 16 7 to to PART ajst-9436 16 8 spread spread VERB ajst-9436 16 9 widely widely ADV ajst-9436 16 10 and and CCONJ ajst-9436 16 11 develop develop VERB ajst-9436 16 12 vigorously vigorously ADV ajst-9436 16 13 . . PUNCT ajst-9436 17 1 in in ADP ajst-9436 17 2 1992 1992 NUM ajst-9436 17 3 , , PUNCT ajst-9436 17 4 donoho donoho NOUN ajst-9436 17 5 and and CCONJ ajst-9436 17 6 johnstone johnstone PROPN ajst-9436 17 7 proposed propose VERB ajst-9436 17 8 the the DET ajst-9436 17 9 wavelet wavelet NOUN ajst-9436 17 10 threshold threshold PROPN ajst-9436 17 11 shrinkage shrinkage NOUN ajst-9436 17 12 method method NOUN ajst-9436 17 13 , , PUNCT ajst-9436 17 14 and and CCONJ ajst-9436 17 15 also also ADV ajst-9436 17 16 provided provide VERB ajst-9436 17 17 a a DET ajst-9436 17 18 threshold threshold NOUN ajst-9436 17 19 of𝛿 of𝛿 NOUN ajst-9436 18 1 = = NOUN ajst-9436 18 2 𝜎 𝜎 NOUN ajst-9436 18 3 2logn 2logn NUM ajst-9436 18 4 , , PUNCT ajst-9436 18 5 proving prove VERB ajst-9436 18 6 the the DET ajst-9436 18 7 advantages advantage NOUN ajst-9436 18 8 of of ADP ajst-9436 18 9 the the DET ajst-9436 18 10 wavelet wavelet NOUN ajst-9436 18 11 threshold threshold NOUN ajst-9436 18 12 shrinkage shrinkage NOUN ajst-9436 18 13 method method NOUN ajst-9436 18 14 ; ; PUNCT ajst-9436 18 15 krim krim PROPN ajst-9436 18 16 et et PROPN ajst-9436 18 17 al al PROPN ajst-9436 18 18 . . PROPN ajst-9436 18 19 used use VERB ajst-9436 18 20 rissanen rissanen PROPN ajst-9436 18 21 's 's PART ajst-9436 18 22 mdl mdl PROPN ajst-9436 18 23 ( ( PUNCT ajst-9436 18 24 minimumdescriptionlength minimumdescriptionlength NOUN ajst-9436 18 25 ) ) PUNCT ajst-9436 18 26 criterion criterion NOUN ajst-9436 18 27 and and CCONJ ajst-9436 18 28 obtained obtain VERB ajst-9436 18 29 the the DET ajst-9436 18 30 same same ADJ ajst-9436 18 31 threshold threshold NOUN ajst-9436 18 32 formula formula NOUN ajst-9436 18 33 as as ADP ajst-9436 18 34 them they PRON ajst-9436 18 35 . . PUNCT ajst-9436 19 1 however however ADV ajst-9436 19 2 , , PUNCT ajst-9436 19 3 a a DET ajst-9436 19 4 threshold threshold NOUN ajst-9436 19 5 selection selection NOUN ajst-9436 19 6 method method NOUN ajst-9436 19 7 proposed propose VERB ajst-9436 19 8 by by ADP ajst-9436 19 9 donoho donoho NOUN ajst-9436 19 10 and and CCONJ ajst-9436 19 11 johnstone johnstone PROPN ajst-9436 19 12 , , PUNCT ajst-9436 19 13 the the DET ajst-9436 19 14 universal universal ADJ ajst-9436 19 15 threshold threshold NOUN ajst-9436 19 16 method method NOUN ajst-9436 19 17 , , PUNCT ajst-9436 19 18 has have AUX ajst-9436 19 19 been be AUX ajst-9436 19 20 studied study VERB ajst-9436 19 21 due due ADP ajst-9436 19 22 to to ADP ajst-9436 19 23 its its PRON ajst-9436 19 24 serious serious ADJ ajst-9436 19 25 tendency tendency NOUN ajst-9436 19 26 to to PART ajst-9436 19 27 " " PUNCT ajst-9436 19 28 over over ADP ajst-9436 19 29 kill kill VERB ajst-9436 19 30 " " PUNCT ajst-9436 19 31 wavelet wavelet NOUN ajst-9436 19 32 coefficients coefficient NOUN ajst-9436 19 33 . . PUNCT ajst-9436 20 1 later later ADV ajst-9436 20 2 , , PUNCT ajst-9436 20 3 people people NOUN ajst-9436 20 4 also also ADV ajst-9436 20 5 studied study VERB ajst-9436 20 6 how how SCONJ ajst-9436 20 7 to to PART ajst-9436 20 8 select select VERB ajst-9436 20 9 threshold threshold NOUN ajst-9436 20 10 functions function NOUN ajst-9436 20 11 and and CCONJ ajst-9436 20 12 proposed propose VERB ajst-9436 20 13 different different ADJ ajst-9436 20 14 threshold threshold NOUN ajst-9436 20 15 functions function NOUN ajst-9436 20 16 . . PUNCT ajst-9436 21 1 however however ADV ajst-9436 21 2 , , PUNCT ajst-9436 21 3 when when SCONJ ajst-9436 21 4 these these DET ajst-9436 21 5 methods method NOUN ajst-9436 21 6 are be AUX ajst-9436 21 7 used use VERB ajst-9436 21 8 in in ADP ajst-9436 21 9 non non ADJ ajst-9436 21 10 gaussian gaussian NOUN ajst-9436 21 11 and and CCONJ ajst-9436 21 12 colored colored ADJ ajst-9436 21 13 noise noise NOUN ajst-9436 21 14 situations situation NOUN ajst-9436 21 15 , , PUNCT ajst-9436 21 16 the the DET ajst-9436 21 17 results result NOUN ajst-9436 21 18 are be AUX ajst-9436 21 19 not not PART ajst-9436 21 20 very very ADV ajst-9436 21 21 ideal ideal ADJ ajst-9436 21 22 , , PUNCT ajst-9436 21 23 this this PRON ajst-9436 21 24 is be AUX ajst-9436 21 25 mainly mainly ADV ajst-9436 21 26 because because SCONJ ajst-9436 21 27 these these DET ajst-9436 21 28 methods method NOUN ajst-9436 21 29 are be AUX ajst-9436 21 30 based base VERB ajst-9436 21 31 on on ADP ajst-9436 21 32 the the DET ajst-9436 21 33 assumption assumption NOUN ajst-9436 21 34 of of ADP ajst-9436 21 35 independent independent ADJ ajst-9436 21 36 and and CCONJ ajst-9436 21 37 identically identically ADV ajst-9436 21 38 distributed distribute VERB ajst-9436 21 39 noise noise NOUN ajst-9436 21 40 ( ( PUNCT ajst-9436 21 41 i.i.d i.i.d ADJ ajst-9436 21 42 ) ) PUNCT ajst-9436 21 43 , , PUNCT ajst-9436 21 44 and and CCONJ ajst-9436 21 45 most most ADJ ajst-9436 21 46 of of ADP ajst-9436 21 47 these these DET ajst-9436 21 48 methods method NOUN ajst-9436 21 49 are be AUX ajst-9436 21 50 developed develop VERB ajst-9436 21 51 from from ADP ajst-9436 21 52 the the DET ajst-9436 21 53 methods method NOUN ajst-9436 21 54 given give VERB ajst-9436 21 55 by by ADP ajst-9436 21 56 donoho donoho NOUN ajst-9436 21 57 and and CCONJ ajst-9436 21 58 johnstone johnstone PROPN ajst-9436 21 59 , , PUNCT ajst-9436 21 60 so so ADV ajst-9436 21 61 their their PRON ajst-9436 21 62 final final ADJ ajst-9436 21 63 denoising denoising NOUN ajst-9436 21 64 performance performance NOUN ajst-9436 21 65 also also ADV ajst-9436 21 66 depends depend VERB ajst-9436 21 67 on on ADP ajst-9436 21 68 the the DET ajst-9436 21 69 assumption assumption NOUN ajst-9436 21 70 that that SCONJ ajst-9436 21 71 the the DET ajst-9436 21 72 noise noise NOUN ajst-9436 21 73 obeys obey VERB ajst-9436 21 74 independent independent ADJ ajst-9436 21 75 normal normal ADJ ajst-9436 21 76 distribution distribution NOUN ajst-9436 21 77 when when SCONJ ajst-9436 21 78 using use VERB ajst-9436 21 79 waveshrink waveshrink NOUN ajst-9436 21 80 to to PART ajst-9436 21 81 determine determine VERB ajst-9436 21 82 the the DET ajst-9436 21 83 threshold threshold NOUN ajst-9436 21 84 . . PUNCT ajst-9436 22 1 in in ADP ajst-9436 22 2 china china PROPN ajst-9436 22 3 , , PUNCT ajst-9436 22 4 professors professor NOUN ajst-9436 22 5 from from ADP ajst-9436 22 6 northwestern northwestern PROPN ajst-9436 22 7 polytechnical polytechnical PROPN ajst-9436 22 8 university university PROPN ajst-9436 22 9 have have AUX ajst-9436 22 10 proposed propose VERB ajst-9436 22 11 a a DET ajst-9436 22 12 related related ADJ ajst-9436 22 13 filtering filtering NOUN ajst-9436 22 14 algorithm algorithm NOUN ajst-9436 22 15 through through ADP ajst-9436 22 16 research research NOUN ajst-9436 22 17 , , PUNCT ajst-9436 22 18 and and CCONJ ajst-9436 22 19 have have AUX ajst-9436 22 20 made make VERB ajst-9436 22 21 significant significant ADJ ajst-9436 22 22 breakthroughs breakthrough NOUN ajst-9436 22 23 in in ADP ajst-9436 22 24 wavelet wavelet NOUN ajst-9436 22 25 threshold threshold NOUN ajst-9436 22 26 filtering filter VERB ajst-9436 22 27 algorithms algorithm NOUN ajst-9436 22 28 . . PUNCT ajst-9436 23 1 professors professor NOUN ajst-9436 23 2 from from ADP ajst-9436 23 3 beijing beijing PROPN ajst-9436 23 4 university university PROPN ajst-9436 23 5 of of ADP ajst-9436 23 6 technology technology NOUN ajst-9436 23 7 have have AUX ajst-9436 23 8 developed develop VERB ajst-9436 23 9 a a DET ajst-9436 23 10 battlefield battlefield NOUN ajst-9436 23 11 ground ground NOUN ajst-9436 23 12 target target NOUN ajst-9436 23 13 localization localization NOUN ajst-9436 23 14 technology technology NOUN ajst-9436 23 15 based base VERB ajst-9436 23 16 on on ADP ajst-9436 23 17 wavelet wavelet NOUN ajst-9436 23 18 analysis analysis NOUN ajst-9436 23 19 . . PUNCT ajst-9436 24 1 among among ADP ajst-9436 24 2 them they PRON ajst-9436 24 3 , , PUNCT ajst-9436 24 4 wavelet wavelet NOUN ajst-9436 24 5 denoising denoising NOUN ajst-9436 24 6 has have AUX ajst-9436 24 7 published publish VERB ajst-9436 24 8 the the DET ajst-9436 24 9 most most ADJ ajst-9436 24 10 articles article NOUN ajst-9436 24 11 on on ADP ajst-9436 24 12 telecommunications telecommunication NOUN ajst-9436 24 13 technology technology NOUN ajst-9436 24 14 in in ADP ajst-9436 24 15 the the DET ajst-9436 24 16 past past ADJ ajst-9436 24 17 five five NUM ajst-9436 24 18 years year NOUN ajst-9436 24 19 , , PUNCT ajst-9436 24 20 with with ADP ajst-9436 24 21 884 884 NUM ajst-9436 24 22 articles article NOUN ajst-9436 24 23 available available ADJ ajst-9436 24 24 on on ADP ajst-9436 24 25 zhiwang zhiwang PROPN ajst-9436 24 26 , , PUNCT ajst-9436 24 27 accounting account VERB ajst-9436 24 28 for for ADP ajst-9436 24 29 21.91 21.91 NUM ajst-9436 24 30 % % NOUN ajst-9436 24 31 of of ADP ajst-9436 24 32 the the DET ajst-9436 24 33 published publish VERB ajst-9436 24 34 articles article NOUN ajst-9436 24 35 in in ADP ajst-9436 24 36 the the DET ajst-9436 24 37 past past ADJ ajst-9436 24 38 five five NUM ajst-9436 24 39 years year NOUN ajst-9436 24 40 . . PUNCT ajst-9436 25 1 there there PRON ajst-9436 25 2 are be VERB ajst-9436 25 3 732 732 NUM ajst-9436 25 4 articles article NOUN ajst-9436 25 5 on on ADP ajst-9436 25 6 computer computer NOUN ajst-9436 25 7 software software NOUN ajst-9436 25 8 and and CCONJ ajst-9436 25 9 computer computer NOUN ajst-9436 25 10 applications application NOUN ajst-9436 25 11 , , PUNCT ajst-9436 25 12 accounting account VERB ajst-9436 25 13 for for ADP ajst-9436 25 14 18.17 18.17 NUM ajst-9436 25 15 % % NOUN ajst-9436 25 16 . . PUNCT ajst-9436 26 1 there there PRON ajst-9436 26 2 are be VERB ajst-9436 26 3 347 347 NUM ajst-9436 26 4 and and CCONJ ajst-9436 26 5 248 248 NUM ajst-9436 26 6 articles article NOUN ajst-9436 26 7 on on ADP ajst-9436 26 8 automation automation NOUN ajst-9436 26 9 technology technology NOUN ajst-9436 26 10 and and CCONJ ajst-9436 26 11 electrical electrical ADJ ajst-9436 26 12 industry industry NOUN ajst-9436 26 13 , , PUNCT ajst-9436 26 14 8.60 8.60 NUM ajst-9436 26 15 % % NOUN ajst-9436 26 16 and and CCONJ ajst-9436 26 17 6.15 6.15 NUM ajst-9436 26 18 % % NOUN ajst-9436 26 19 , , PUNCT ajst-9436 26 20 respectively respectively ADV ajst-9436 26 21 . . PUNCT ajst-9436 27 1 from from ADP ajst-9436 27 2 these these DET ajst-9436 27 3 numbers number NOUN ajst-9436 27 4 , , PUNCT ajst-9436 27 5 it it PRON ajst-9436 27 6 can can AUX ajst-9436 27 7 be be AUX ajst-9436 27 8 found find VERB ajst-9436 27 9 that that SCONJ ajst-9436 27 10 the the DET ajst-9436 27 11 application application NOUN ajst-9436 27 12 of of ADP ajst-9436 27 13 wavelet wavelet NOUN ajst-9436 27 14 denoising denoising NOUN ajst-9436 27 15 is be AUX ajst-9436 27 16 the the DET ajst-9436 27 17 most most ADV ajst-9436 27 18 widely widely ADV ajst-9436 27 19 used use VERB ajst-9436 27 20 in in ADP ajst-9436 27 21 technical technical ADJ ajst-9436 27 22 research research NOUN ajst-9436 27 23 . . PUNCT ajst-9436 28 1 at at ADP ajst-9436 28 2 the the DET ajst-9436 28 3 same same ADJ ajst-9436 28 4 time time NOUN ajst-9436 28 5 , , PUNCT ajst-9436 28 6 the the DET ajst-9436 28 7 number number NOUN ajst-9436 28 8 of of ADP ajst-9436 28 9 publications publication NOUN ajst-9436 28 10 in in ADP ajst-9436 28 11 these these DET ajst-9436 28 12 articles article NOUN ajst-9436 28 13 shows show VERB ajst-9436 28 14 that that SCONJ ajst-9436 28 15 the the DET ajst-9436 28 16 development development NOUN ajst-9436 28 17 of of ADP ajst-9436 28 18 wavelet wavelet NOUN ajst-9436 28 19 denoising denoising NOUN ajst-9436 28 20 is be AUX ajst-9436 28 21 very very ADV ajst-9436 28 22 promising promising ADJ ajst-9436 28 23 . . PUNCT ajst-9436 29 1 2 2 X ajst-9436 29 2 . . X ajst-9436 29 3 principle principle NOUN ajst-9436 29 4 of of ADP ajst-9436 29 5 wavelet wavelet NOUN ajst-9436 29 6 denoising denoise VERB ajst-9436 29 7 2.1 2.1 NUM ajst-9436 29 8 . . PUNCT ajst-9436 30 1 wavelet wavelet NOUN ajst-9436 30 2 transform transform NOUN ajst-9436 30 3 and and CCONJ ajst-9436 30 4 discrete discrete ADJ ajst-9436 30 5 wavelet wavelet NOUN ajst-9436 30 6 transform transform NOUN ajst-9436 30 7 wavelet wavelet NOUN ajst-9436 30 8 transform transform NOUN ajst-9436 30 9 , , PUNCT ajst-9436 30 10 discrete discrete ADJ ajst-9436 30 11 wavelet wavelet NOUN ajst-9436 30 12 transform transform NOUN ajst-9436 30 13 , , PUNCT ajst-9436 30 14 and and CCONJ ajst-9436 30 15 inverse inverse NOUN ajst-9436 30 16 wavelet wavelet NOUN ajst-9436 30 17 transform transform NOUN ajst-9436 30 18 are be AUX ajst-9436 30 19 the the DET ajst-9436 30 20 theoretical theoretical ADJ ajst-9436 30 21 foundations foundation NOUN ajst-9436 30 22 of of ADP ajst-9436 30 23 wavelet wavelet NOUN ajst-9436 30 24 decomposition decomposition NOUN ajst-9436 30 25 and and CCONJ ajst-9436 30 26 wavelet wavelet NOUN ajst-9436 30 27 reconstruction reconstruction NOUN ajst-9436 30 28 , , PUNCT ajst-9436 30 29 so so CCONJ ajst-9436 30 30 their their PRON ajst-9436 30 31 definitions definition NOUN ajst-9436 30 32 will will AUX ajst-9436 30 33 be be AUX ajst-9436 30 34 explained explain VERB ajst-9436 30 35 next next ADV ajst-9436 30 36 . . PUNCT ajst-9436 31 1 let let VERB ajst-9436 31 2 the the DET ajst-9436 31 3 fourier fourier NOUN ajst-9436 31 4 transform transform NOUN ajst-9436 31 5 of of ADP ajst-9436 31 6 function function NOUN ajst-9436 31 7 πœ™ πœ™ PROPN ajst-9436 31 8 𝑑 𝑑 VERB ajst-9436 31 9 be be VERB ajst-9436 31 10 πœ™ πœ™ NOUN ajst-9436 31 11 𝑗𝛺 𝑗𝛺 ADJ ajst-9436 31 12 , , PUNCT ajst-9436 31 13 if if SCONJ ajst-9436 31 14 it it PRON ajst-9436 31 15 satisfies satisfy VERB ajst-9436 31 16 cΟ† cΟ† NOUN ajst-9436 31 17 r r NOUN ajst-9436 31 18 βˆ— βˆ— NOUN ajst-9436 31 19 |Ο† |Ο† PROPN ajst-9436 32 1 jΟ‰ jΟ‰ INTJ ajst-9436 33 1 | | ADV ajst-9436 33 2 2 2 NUM ajst-9436 33 3 |Ο‰| |Ο‰| VERB ajst-9436 33 4 dΟ‰ dΟ‰ ADP ajst-9436 33 5 ∞ ∞ PROPN ajst-9436 33 6 1 1 NUM ajst-9436 33 7 in in ADP ajst-9436 33 8 the the DET ajst-9436 33 9 formula formula NOUN ajst-9436 33 10 , , PUNCT ajst-9436 33 11 r r X ajst-9436 33 12 * * PUNCT ajst-9436 33 13 represents represent VERB ajst-9436 33 14 ( ( PUNCT ajst-9436 33 15 -∞ -∞ X ajst-9436 33 16 , , PUNCT ajst-9436 33 17 0 0 NUM ajst-9436 33 18 ) ) PUNCT ajst-9436 33 19 u u NOUN ajst-9436 33 20 ( ( PUNCT ajst-9436 33 21 0,+∞ 0,+∞ NUM ajst-9436 33 22 ) ) PUNCT ajst-9436 33 23 , , PUNCT ajst-9436 33 24 then then ADV ajst-9436 33 25 it it PRON ajst-9436 33 26 is be AUX ajst-9436 33 27 said say VERB ajst-9436 33 28 to to PART ajst-9436 33 29 be be AUX ajst-9436 33 30 the the DET ajst-9436 33 31 basic basic ADJ ajst-9436 33 32 wavelet wavelet NOUN ajst-9436 33 33 function function NOUN ajst-9436 33 34 . . PUNCT ajst-9436 34 1 equation equation NOUN ajst-9436 34 2 ( ( PUNCT ajst-9436 34 3 1 1 X ajst-9436 34 4 ) ) PUNCT ajst-9436 34 5 is be AUX ajst-9436 34 6 often often ADV ajst-9436 34 7 called call VERB ajst-9436 34 8 the the DET ajst-9436 34 9 admissibility admissibility NOUN ajst-9436 34 10 condition condition NOUN ajst-9436 34 11 of of ADP ajst-9436 34 12 wavelet wavelet NOUN ajst-9436 34 13 function function NOUN ajst-9436 34 14 . . PUNCT ajst-9436 35 1 equation equation NOUN ajst-9436 35 2 ( ( PUNCT ajst-9436 35 3 1 1 X ajst-9436 35 4 ) ) PUNCT ajst-9436 35 5 is be AUX ajst-9436 35 6 equivalent equivalent ADJ ajst-9436 35 7 to to ADP ajst-9436 35 8 𝑅 𝑅 PROPN ajst-9436 35 9 πœ™ πœ™ NOUN ajst-9436 35 10 𝑑 𝑑 NOUN ajst-9436 35 11 𝑑𝑑 𝑑𝑑 ADP ajst-9436 35 12 0 0 NUM ajst-9436 35 13 2 2 NUM ajst-9436 35 14 13 13 NUM ajst-9436 35 15 that that PRON ajst-9436 35 16 is be AUX ajst-9436 35 17 to to PART ajst-9436 35 18 say say VERB ajst-9436 35 19 , , PUNCT ajst-9436 35 20 the the DET ajst-9436 35 21 area area NOUN ajst-9436 35 22 enclosed enclose VERB ajst-9436 35 23 by by ADP ajst-9436 35 24 the the DET ajst-9436 35 25 function function NOUN ajst-9436 35 26 πœ™ πœ™ PROPN ajst-9436 35 27 𝑑 𝑑 PROPN ajst-9436 35 28 and and CCONJ ajst-9436 35 29 the the DET ajst-9436 35 30 horizontal horizontal ADJ ajst-9436 35 31 axis axis NOUN ajst-9436 35 32 is be AUX ajst-9436 35 33 0 0 NUM ajst-9436 35 34 , , PUNCT ajst-9436 35 35 which which PRON ajst-9436 35 36 means mean VERB ajst-9436 35 37 that that SCONJ ajst-9436 35 38 the the DET ajst-9436 35 39 graph graph NOUN ajst-9436 35 40 of of ADP ajst-9436 35 41 the the DET ajst-9436 35 42 function function NOUN ajst-9436 35 43 oscillates oscillate VERB ajst-9436 35 44 up up ADP ajst-9436 35 45 and and CCONJ ajst-9436 35 46 down down ADV ajst-9436 35 47 on on ADP ajst-9436 35 48 the the DET ajst-9436 35 49 horizontal horizontal ADJ ajst-9436 35 50 axis axis NOUN ajst-9436 35 51 , , PUNCT ajst-9436 35 52 and and CCONJ ajst-9436 35 53 its its PRON ajst-9436 35 54 definition definition NOUN ajst-9436 35 55 domain domain NOUN ajst-9436 35 56 is be AUX ajst-9436 35 57 not not PART ajst-9436 35 58 infinite infinite ADJ ajst-9436 35 59 . . PUNCT ajst-9436 36 1 there there PRON ajst-9436 36 2 is be VERB ajst-9436 36 3 also also ADV ajst-9436 36 4 information information NOUN ajst-9436 36 5 that that PRON ajst-9436 36 6 can can AUX ajst-9436 36 7 be be AUX ajst-9436 36 8 clearly clearly ADV ajst-9436 36 9 known know VERB ajst-9436 36 10 , , PUNCT ajst-9436 36 11 that that PRON ajst-9436 36 12 is be AUX ajst-9436 36 13 πœ‘ πœ‘ PROPN ajst-9436 36 14 𝑗𝛺 𝑗𝛺 NOUN ajst-9436 36 15 |𝛺 |𝛺 PUNCT ajst-9436 36 16 0 0 NUM ajst-9436 36 17 0 0 NUM ajst-9436 36 18 . . PUNCT ajst-9436 37 1 introducing introduce VERB ajst-9436 37 2 scale scale NOUN ajst-9436 37 3 factor factor NOUN ajst-9436 37 4 a a PRON ajst-9436 37 5 and and CCONJ ajst-9436 37 6 translation translation NOUN ajst-9436 37 7 factor factor NOUN ajst-9436 37 8 b b PROPN ajst-9436 37 9 , , PUNCT ajst-9436 37 10 let let VERB ajst-9436 37 11 π‘ŽοΌŒπ‘ π‘ŽοΌŒπ‘ PROPN ajst-9436 37 12 ∈ ∈ PROPN ajst-9436 37 13 𝑅 𝑅 PROPN ajst-9436 37 14 ， ， PROPN ajst-9436 37 15 π‘Ž π‘Ž PROPN ajst-9436 37 16 0 0 NUM ajst-9436 37 17 ， ， PUNCT ajst-9436 37 18 πœ™ πœ™ PUNCT ajst-9436 37 19 𝑑 𝑑 PROPN ajst-9436 37 20 get get VERB ajst-9436 37 21 continuous continuous ADJ ajst-9436 37 22 wavelet wavelet NOUN ajst-9436 37 23 function function NOUN ajst-9436 37 24 under under ADP ajst-9436 37 25 the the DET ajst-9436 37 26 action action NOUN ajst-9436 37 27 of of ADP ajst-9436 37 28 a a DET ajst-9436 37 29 , , PUNCT ajst-9436 37 30 b b PROPN ajst-9436 37 31 πœ™π‘Ž πœ™π‘Ž PROPN ajst-9436 37 32 , , PUNCT ajst-9436 37 33 𝑏 𝑏 PROPN ajst-9436 37 34 𝑑 𝑑 PROPN ajst-9436 37 35 1 1 NUM ajst-9436 37 36 |π‘Ž| |π‘Ž| ADP ajst-9436 37 37 πœ™ πœ™ PROPN ajst-9436 37 38 𝑑 𝑑 VERB ajst-9436 37 39 𝑏 𝑏 PROPN ajst-9436 37 40 π‘Ž π‘Ž PROPN ajst-9436 37 41 3 3 NUM ajst-9436 37 42 in in ADP ajst-9436 37 43 this this DET ajst-9436 37 44 way way NOUN ajst-9436 37 45 , , PUNCT ajst-9436 37 46 the the DET ajst-9436 37 47 continuous continuous ADJ ajst-9436 37 48 wavelet wavelet NOUN ajst-9436 37 49 transform transform NOUN ajst-9436 37 50 ( ( PUNCT ajst-9436 37 51 cwt cwt NOUN ajst-9436 37 52 ) ) PUNCT ajst-9436 37 53 of of ADP ajst-9436 37 54 the the DET ajst-9436 37 55 signal𝑓 signal𝑓 NOUN ajst-9436 37 56 𝑑 𝑑 PROPN ajst-9436 37 57 ∈ ∈ PROPN ajst-9436 37 58 𝐿 𝐿 PROPN ajst-9436 37 59 2 2 NUM ajst-9436 37 60 𝑅 𝑅 PROPN ajst-9436 37 61 can can AUX ajst-9436 37 62 be be AUX ajst-9436 37 63 transformed transform VERB ajst-9436 37 64 into into ADP ajst-9436 37 65 π‘Šπœ™π‘“ π‘Šπœ™π‘“ PROPN ajst-9436 37 66 π‘Ž π‘Ž NOUN ajst-9436 37 67 , , PUNCT ajst-9436 37 68 𝑏 𝑏 PROPN ajst-9436 37 69 𝑓 𝑓 PROPN ajst-9436 37 70 𝑑 𝑑 PROPN ajst-9436 37 71 , , PUNCT ajst-9436 37 72 πœ™π‘Ž πœ™π‘Ž NOUN ajst-9436 37 73 , , PUNCT ajst-9436 37 74 𝑏 𝑏 PROPN ajst-9436 37 75 𝑑 𝑑 PROPN ajst-9436 37 76 𝑅 𝑅 PROPN ajst-9436 37 77 𝑓 𝑓 PROPN ajst-9436 37 78 𝑑 𝑑 PROPN ajst-9436 37 79 πœ™π‘Ž πœ™π‘Ž PROPN ajst-9436 37 80 , , PUNCT ajst-9436 37 81 𝑏 𝑏 PROPN ajst-9436 37 82 𝑑 𝑑 PROPN ajst-9436 37 83 𝑑𝑑 𝑑𝑑 ADP ajst-9436 37 84 1 1 NUM ajst-9436 37 85 |π‘Ž| |π‘Ž| ADP ajst-9436 37 86 ∞ ∞ NUM ajst-9436 37 87 ∞ ∞ NUM ajst-9436 38 1 𝑓 𝑓 PRON ajst-9436 38 2 𝑑 𝑑 X ajst-9436 38 3 πœ™ πœ™ NOUN ajst-9436 38 4 𝑑 𝑑 NOUN ajst-9436 38 5 𝑏 𝑏 PROPN ajst-9436 38 6 π‘Ž π‘Ž NOUN ajst-9436 38 7 𝑑𝑑 𝑑𝑑 ADP ajst-9436 38 8 4 4 NUM ajst-9436 38 9 by by ADP ajst-9436 38 10 using use VERB ajst-9436 38 11 the the DET ajst-9436 38 12 parseval parseval NOUN ajst-9436 38 13 identity identity NOUN ajst-9436 38 14 of of ADP ajst-9436 38 15 fourier fourier NOUN ajst-9436 38 16 transform transform NOUN ajst-9436 39 1 , , PUNCT ajst-9436 39 2 it it PRON ajst-9436 39 3 is be AUX ajst-9436 39 4 easy easy ADJ ajst-9436 39 5 to to PART ajst-9436 39 6 prove prove VERB ajst-9436 39 7 that that SCONJ ajst-9436 39 8 the the DET ajst-9436 39 9 inverse inverse NOUN ajst-9436 39 10 transform transform NOUN ajst-9436 39 11 ( ( PUNCT ajst-9436 39 12 icwt icwt NOUN ajst-9436 39 13 ) ) PUNCT ajst-9436 39 14 of of ADP ajst-9436 39 15 continuous continuous ADJ ajst-9436 39 16 wavelet wavelet NOUN ajst-9436 39 17 transform transform NOUN ajst-9436 39 18 is be AUX ajst-9436 39 19 𝑓 𝑓 PRON ajst-9436 39 20 𝑑 𝑑 NOUN ajst-9436 39 21 ∬ ∬ NOUN ajst-9436 39 22 π‘Šπœ™π‘“ π‘Šπœ™π‘“ PROPN ajst-9436 39 23 π‘Ž π‘Ž PROPN ajst-9436 39 24 , , PUNCT ajst-9436 39 25 𝑏 𝑏 PRON ajst-9436 39 26 πœ™π‘Ž πœ™π‘Ž PROPN ajst-9436 39 27 , , PUNCT ajst-9436 39 28 𝑏 𝑏 PROPN ajst-9436 39 29 𝑑 𝑑 PROPN ajst-9436 40 1 | | ADV ajst-9436 40 2 | | ADV ajst-9436 40 3 ∞ ∞ NUM ajst-9436 40 4 ∞ ∞ NUM ajst-9436 40 5 ∞ ∞ NUM ajst-9436 40 6 ∞ ∞ NUM ajst-9436 41 1 π‘Šπœ‘π‘“ π‘Šπœ‘π‘“ PROPN ajst-9436 41 2 π‘Ž π‘Ž NOUN ajst-9436 41 3 , , PUNCT ajst-9436 41 4 𝑏 𝑏 PROPN ajst-9436 41 5 πœ™ πœ™ PROPN ajst-9436 41 6 5 5 NUM ajst-9436 41 7 you you PRON ajst-9436 41 8 can can AUX ajst-9436 41 9 think think VERB ajst-9436 41 10 of of ADP ajst-9436 41 11 wavelet wavelet NOUN ajst-9436 41 12 transform transform NOUN ajst-9436 41 13 as as ADP ajst-9436 41 14 a a DET ajst-9436 41 15 transformation transformation NOUN ajst-9436 41 16 that that PRON ajst-9436 41 17 maps map VERB ajst-9436 41 18 one one NUM ajst-9436 41 19 - - PUNCT ajst-9436 41 20 dimensional dimensional ADJ ajst-9436 41 21 time time NOUN ajst-9436 41 22 signals signal NOUN ajst-9436 41 23 to to ADP ajst-9436 41 24 two two NUM ajst-9436 41 25 - - PUNCT ajst-9436 41 26 dimensional dimensional ADJ ajst-9436 41 27 space space NOUN ajst-9436 41 28 , , PUNCT ajst-9436 41 29 so so CCONJ ajst-9436 41 30 there there PRON ajst-9436 41 31 is be VERB ajst-9436 41 32 a a DET ajst-9436 41 33 lot lot NOUN ajst-9436 41 34 of of ADP ajst-9436 41 35 redundant redundant ADJ ajst-9436 41 36 information information NOUN ajst-9436 41 37 . . PUNCT ajst-9436 42 1 in in ADP ajst-9436 42 2 this this DET ajst-9436 42 3 case case NOUN ajst-9436 42 4 , , PUNCT ajst-9436 42 5 select select VERB ajst-9436 42 6 some some DET ajst-9436 42 7 discrete discrete ADJ ajst-9436 42 8 points point NOUN ajst-9436 42 9 and and CCONJ ajst-9436 42 10 use use VERB ajst-9436 42 11 the the DET ajst-9436 42 12 results result NOUN ajst-9436 42 13 of of ADP ajst-9436 42 14 wavelet wavelet NOUN ajst-9436 42 15 transform transform NOUN ajst-9436 42 16 to to PART ajst-9436 42 17 depict depict VERB ajst-9436 42 18 the the DET ajst-9436 42 19 signal signal NOUN ajst-9436 42 20 . . PUNCT ajst-9436 43 1 usually usually ADV ajst-9436 43 2 , , PUNCT ajst-9436 43 3 sampling sample VERB ajst-9436 43 4 is be AUX ajst-9436 43 5 carried carry VERB ajst-9436 43 6 out out ADP ajst-9436 43 7 based base VERB ajst-9436 43 8 on on ADP ajst-9436 43 9 the the DET ajst-9436 43 10 integer integer NOUN ajst-9436 43 11 power power NOUN ajst-9436 43 12 of of ADP ajst-9436 43 13 a a DET ajst-9436 43 14 certain certain ADJ ajst-9436 43 15 constant constant ADJ ajst-9436 43 16 a0 a0 NOUN ajst-9436 43 17 , , PUNCT ajst-9436 43 18 which which PRON ajst-9436 43 19 is be AUX ajst-9436 43 20 taken take VERB ajst-9436 43 21 as as ADP ajst-9436 43 22 a a DET ajst-9436 43 23 aj0 aj0 NOUN ajst-9436 43 24 π‘Ž0>0οΌŒπ‘— π‘Ž0>0οΌŒπ‘— NOUN ajst-9436 43 25 ∈ ∈ PROPN ajst-9436 43 26 𝑍 𝑍 PROPN ajst-9436 43 27 . . PUNCT ajst-9436 44 1 in in ADP ajst-9436 44 2 order order NOUN ajst-9436 44 3 to to PART ajst-9436 44 4 arrange arrange VERB ajst-9436 44 5 the the DET ajst-9436 44 6 frequency frequency NOUN ajst-9436 44 7 bands band NOUN ajst-9436 44 8 of of ADP ajst-9436 44 9 wavelets wavelet NOUN ajst-9436 44 10 of of ADP ajst-9436 44 11 different different ADJ ajst-9436 44 12 scales scale NOUN ajst-9436 44 13 adjacent adjacent ADJ ajst-9436 44 14 to to ADP ajst-9436 44 15 each each DET ajst-9436 44 16 other other ADJ ajst-9436 44 17 after after ADP ajst-9436 44 18 sampling sample VERB ajst-9436 44 19 , , PUNCT ajst-9436 44 20 covering cover VERB ajst-9436 44 21 the the DET ajst-9436 44 22 entire entire ADJ ajst-9436 44 23 positive positive ADJ ajst-9436 44 24 frequency frequency NOUN ajst-9436 44 25 axis axis NOUN ajst-9436 44 26 , , PUNCT ajst-9436 44 27 we we PRON ajst-9436 44 28 take take VERB ajst-9436 44 29 b b NOUN ajst-9436 44 30 kb0π‘Žj0 kb0π‘Žj0 NOUN ajst-9436 44 31 𝑏0 𝑏0 PROPN ajst-9436 44 32 ∈ ∈ PROPN ajst-9436 44 33 π‘…οΌŒπ‘— π‘…οΌŒπ‘— NOUN ajst-9436 44 34 ∈ ∈ PROPN ajst-9436 44 35 𝑍 𝑍 NOUN ajst-9436 44 36 .then .then VERB ajst-9436 44 37 the the DET ajst-9436 44 38 wavelet wavelet PROPN ajst-9436 44 39 πœ™a πœ™a PROPN ajst-9436 44 40 , , PUNCT ajst-9436 44 41 b b PROPN ajst-9436 44 42 𝑑 𝑑 PROPN ajst-9436 44 43 becomes become VERB ajst-9436 44 44 πœ™π‘Ž πœ™π‘Ž NOUN ajst-9436 44 45 , , PUNCT ajst-9436 44 46 𝑏 𝑏 PROPN ajst-9436 44 47 𝑑 𝑑 PROPN ajst-9436 44 48 π‘Ž π‘Ž PROPN ajst-9436 44 49 1 1 NUM ajst-9436 44 50 2πœ™ 2πœ™ NUM ajst-9436 44 51 𝑑 𝑑 VERB ajst-9436 44 52 𝑏 𝑏 PROPN ajst-9436 44 53 π‘Ž π‘Ž PROPN ajst-9436 44 54 π‘Ž0 π‘Ž0 PROPN ajst-9436 44 55 1 1 NUM ajst-9436 44 56 2πœ™ 2πœ™ NOUN ajst-9436 44 57 π‘Ž π‘Ž PRON ajst-9436 44 58 𝑗 𝑗 NOUN ajst-9436 44 59 0 0 NUM ajst-9436 44 60 𝑑 𝑑 NOUN ajst-9436 44 61 π‘˜π‘0 π‘˜π‘0 NOUN ajst-9436 44 62 6 6 NUM ajst-9436 44 63 let let VERB ajst-9436 44 64 π‘Ž0 π‘Ž0 PROPN ajst-9436 44 65 2 2 NUM ajst-9436 44 66 , , PUNCT ajst-9436 44 67 this this DET ajst-9436 44 68 formula formula NOUN ajst-9436 44 69 obtains obtain VERB ajst-9436 44 70 the the DET ajst-9436 44 71 dyadic dyadic ADJ ajst-9436 44 72 wavelet wavelet NOUN ajst-9436 44 73 , , PUNCT ajst-9436 44 74 and and CCONJ ajst-9436 44 75 using use VERB ajst-9436 44 76 this this DET ajst-9436 44 77 formula formula NOUN ajst-9436 44 78 for for ADP ajst-9436 44 79 transformation transformation NOUN ajst-9436 44 80 is be AUX ajst-9436 44 81 the the DET ajst-9436 44 82 dyadic dyadic ADJ ajst-9436 44 83 wavelet wavelet NOUN ajst-9436 44 84 transform transform NOUN ajst-9436 44 85 . . PUNCT ajst-9436 45 1 if if SCONJ ajst-9436 45 2 we we PRON ajst-9436 45 3 let let VERB ajst-9436 45 4 𝑏0 𝑏0 NOUN ajst-9436 45 5 1 1 NUM ajst-9436 45 6 , , PUNCT ajst-9436 45 7 we we PRON ajst-9436 45 8 can can AUX ajst-9436 45 9 obtain obtain VERB ajst-9436 45 10 a a DET ajst-9436 45 11 dyadic dyadic ADJ ajst-9436 45 12 orthogonal orthogonal ADJ ajst-9436 45 13 wavelet wavelet NOUN ajst-9436 45 14 using use VERB ajst-9436 45 15 this this DET ajst-9436 45 16 formula formula NOUN ajst-9436 45 17 . . PUNCT ajst-9436 46 1 as as SCONJ ajst-9436 46 2 shown show VERB ajst-9436 46 3 in in ADP ajst-9436 46 4 equations equation NOUN ajst-9436 46 5 7 7 NUM ajst-9436 46 6 πœ™π‘Ž πœ™π‘Ž NOUN ajst-9436 46 7 , , PUNCT ajst-9436 46 8 𝑏 𝑏 PROPN ajst-9436 46 9 𝑑 𝑑 PROPN ajst-9436 46 10 2 2 NUM ajst-9436 46 11 𝑗 𝑗 PROPN ajst-9436 46 12 2πœ™ 2πœ™ NOUN ajst-9436 46 13 2 2 NUM ajst-9436 46 14 𝑗 𝑗 NOUN ajst-9436 46 15 𝑑 𝑑 NOUN ajst-9436 46 16 π‘˜ π‘˜ PROPN ajst-9436 46 17 7 7 NUM ajst-9436 46 18 the the DET ajst-9436 46 19 dyadic dyadic ADJ ajst-9436 46 20 orthogonal orthogonal ADJ ajst-9436 46 21 wavelet wavelet NOUN ajst-9436 46 22 has have AUX ajst-9436 46 23 been be AUX ajst-9436 46 24 proven prove VERB ajst-9436 46 25 to to PART ajst-9436 46 26 be be AUX ajst-9436 46 27 a a DET ajst-9436 46 28 set set NOUN ajst-9436 46 29 of of ADP ajst-9436 46 30 standard standard ADJ ajst-9436 46 31 orthogonal orthogonal ADJ ajst-9436 46 32 bases basis NOUN ajst-9436 46 33 in in ADP ajst-9436 46 34 the the DET ajst-9436 46 35 function function NOUN ajst-9436 46 36 space space NOUN ajst-9436 46 37 𝐿 𝐿 PROPN ajst-9436 46 38 2 2 NUM ajst-9436 46 39 𝑅 𝑅 PROPN ajst-9436 46 40 , , PUNCT ajst-9436 46 41 and and CCONJ ajst-9436 46 42 the the DET ajst-9436 46 43 corresponding corresponding ADJ ajst-9436 46 44 wavelet wavelet NOUN ajst-9436 46 45 transform transform NOUN ajst-9436 46 46 is be AUX ajst-9436 46 47 called call VERB ajst-9436 46 48 the the DET ajst-9436 46 49 dyadic dyadic ADJ ajst-9436 46 50 orthogonal orthogonal ADJ ajst-9436 46 51 wavelet wavelet NOUN ajst-9436 46 52 transform transform NOUN ajst-9436 46 53 . . PUNCT ajst-9436 47 1 binary binary ADJ ajst-9436 47 2 discrete discrete ADJ ajst-9436 47 3 wavelet wavelet NOUN ajst-9436 47 4 transform transform NOUN ajst-9436 47 5 ( ( PUNCT ajst-9436 47 6 dwt dwt NOUN ajst-9436 47 7 ) ) PUNCT ajst-9436 47 8 is be AUX ajst-9436 47 9 shown show VERB ajst-9436 47 10 inequations inequation NOUN ajst-9436 47 11 8 8 NUM ajst-9436 47 12 π·πœ™π‘“ π·πœ™π‘“ PROPN ajst-9436 47 13 π‘Ž π‘Ž PROPN ajst-9436 47 14 , , PUNCT ajst-9436 47 15 𝑏 𝑏 PROPN ajst-9436 47 16 𝑓 𝑓 PROPN ajst-9436 47 17 𝑑 𝑑 PROPN ajst-9436 47 18 , , PUNCT ajst-9436 47 19 πœ™π‘Ž πœ™π‘Ž NOUN ajst-9436 47 20 , , PUNCT ajst-9436 47 21 𝑏 𝑏 PROPN ajst-9436 47 22 𝑑 𝑑 PROPN ajst-9436 47 23 2 2 NUM ajst-9436 47 24 𝑗 𝑗 PROPN ajst-9436 47 25 2 2 NUM ajst-9436 47 26 ∞ ∞ NUM ajst-9436 47 27 ∞ ∞ NUM ajst-9436 48 1 𝑓 𝑓 PROPN ajst-9436 48 2 𝑑 𝑑 NOUN ajst-9436 48 3 πœ™ πœ™ PROPN ajst-9436 48 4 2 2 NUM ajst-9436 48 5 𝑗 𝑗 VERB ajst-9436 48 6 𝑑 𝑑 X ajst-9436 48 7 π‘˜ π‘˜ PRON ajst-9436 48 8 𝑑𝑑 𝑑𝑑 ADP ajst-9436 48 9 8 8 NUM ajst-9436 48 10 for for ADP ajst-9436 48 11 digital digital ADJ ajst-9436 48 12 signal signal NOUN ajst-9436 48 13 processing processing NOUN ajst-9436 48 14 , , PUNCT ajst-9436 48 15 we we PRON ajst-9436 48 16 are be AUX ajst-9436 48 17 concerned concerned ADJ ajst-9436 48 18 with with ADP ajst-9436 48 19 the the DET ajst-9436 48 20 time time NOUN ajst-9436 48 21 - - PUNCT ajst-9436 48 22 domain domain NOUN ajst-9436 48 23 discrete discrete ADJ ajst-9436 48 24 signal signal NOUN ajst-9436 48 25 x(n x(n NOUN ajst-9436 48 26 ) ) PUNCT ajst-9436 48 27 . . PUNCT ajst-9436 49 1 define define VERB ajst-9436 49 2 the the DET ajst-9436 49 3 discrete discrete ADJ ajst-9436 49 4 wavelet wavelet NOUN ajst-9436 49 5 transform transform NOUN ajst-9436 49 6 of of ADP ajst-9436 49 7 sequence sequence NOUN ajst-9436 49 8 x x SYM ajst-9436 49 9 ( ( PUNCT ajst-9436 49 10 n n CCONJ ajst-9436 49 11 ) ) PUNCT ajst-9436 49 12 as as ADP ajst-9436 49 13 π·πœ™π‘‹ π·πœ™π‘‹ PROPN ajst-9436 49 14 𝑗 𝑗 PROPN ajst-9436 49 15 , , PUNCT ajst-9436 49 16 π‘˜ π‘˜ DET ajst-9436 49 17 π›₯ π›₯ NOUN ajst-9436 49 18 π·π‘Šπ‘‡πœ™π‘₯ π·π‘Šπ‘‡πœ™π‘₯ ADJ ajst-9436 49 19 2 2 NUM ajst-9436 49 20 𝑗 𝑗 NOUN ajst-9436 49 21 , , PUNCT ajst-9436 49 22 π‘˜2 π‘˜2 PROPN ajst-9436 49 23 𝑗 𝑗 INTJ ajst-9436 49 24 π‘₯ π‘₯ X ajst-9436 49 25 𝑛 𝑛 PRON ajst-9436 49 26 πœ™π‘— πœ™π‘— PROPN ajst-9436 49 27 , , PUNCT ajst-9436 49 28 π‘˜ π‘˜ PRON ajst-9436 49 29 𝑛 𝑛 PRON ajst-9436 49 30 2 2 NUM ajst-9436 49 31 π‘₯ π‘₯ NOUN ajst-9436 49 32 𝑛 𝑛 VERB ajst-9436 49 33 πœ‘ πœ‘ NOUN ajst-9436 49 34 2 2 NUM ajst-9436 49 35 𝑛 𝑛 DET ajst-9436 49 36 π‘˜ π‘˜ DET ajst-9436 49 37 9 9 NUM ajst-9436 49 38 2.2 2.2 NUM ajst-9436 49 39 . . PUNCT ajst-9436 50 1 wavelet wavelet NOUN ajst-9436 50 2 basis basis NOUN ajst-9436 50 3 function function VERB ajst-9436 50 4 different different ADJ ajst-9436 50 5 wavelet wavelet NOUN ajst-9436 50 6 bases basis NOUN ajst-9436 50 7 have have VERB ajst-9436 50 8 different different ADJ ajst-9436 50 9 properties property NOUN ajst-9436 50 10 , , PUNCT ajst-9436 50 11 and and CCONJ ajst-9436 50 12 their their PRON ajst-9436 50 13 denoising denoising NOUN ajst-9436 50 14 effects effect NOUN ajst-9436 50 15 are be AUX ajst-9436 50 16 inevitably inevitably ADV ajst-9436 50 17 different different ADJ ajst-9436 50 18 when when SCONJ ajst-9436 50 19 performing perform VERB ajst-9436 50 20 denoising denoising NOUN ajst-9436 50 21 processing processing NOUN ajst-9436 50 22 . . PUNCT ajst-9436 51 1 using use VERB ajst-9436 51 2 different different ADJ ajst-9436 51 3 wavelet wavelet NOUN ajst-9436 51 4 bases basis NOUN ajst-9436 51 5 to to PART ajst-9436 51 6 obtain obtain VERB ajst-9436 51 7 different different ADJ ajst-9436 51 8 denoised denoised ADJ ajst-9436 51 9 images image NOUN ajst-9436 51 10 will will AUX ajst-9436 51 11 introduce introduce VERB ajst-9436 51 12 the the DET ajst-9436 51 13 wavelet wavelet NOUN ajst-9436 51 14 bases basis NOUN ajst-9436 51 15 used use VERB ajst-9436 51 16 later later ADV ajst-9436 51 17 and and CCONJ ajst-9436 51 18 some some PRON ajst-9436 51 19 of of ADP ajst-9436 51 20 their their PRON ajst-9436 51 21 properties property NOUN ajst-9436 51 22 . . PUNCT ajst-9436 52 1 1 1 X ajst-9436 52 2 ) ) PUNCT ajst-9436 52 3 haar haar PROPN ajst-9436 52 4 wavelet wavelet PROPN ajst-9436 52 5 haar haar PROPN ajst-9436 52 6 is be AUX ajst-9436 52 7 an an DET ajst-9436 52 8 orthogonal orthogonal ADJ ajst-9436 52 9 wavelet wavelet NOUN ajst-9436 52 10 basis basis NOUN ajst-9436 52 11 with with ADP ajst-9436 52 12 tight tight ADJ ajst-9436 52 13 support support NOUN ajst-9436 52 14 , , PUNCT ajst-9436 52 15 which which PRON ajst-9436 52 16 is be AUX ajst-9436 52 17 the the DET ajst-9436 52 18 most most ADV ajst-9436 52 19 classic classic ADJ ajst-9436 52 20 and and CCONJ ajst-9436 52 21 simplest simple ADJ ajst-9436 52 22 wavelet wavelet NOUN ajst-9436 52 23 basis basis NOUN ajst-9436 52 24 . . PUNCT ajst-9436 53 1 its its PRON ajst-9436 53 2 function function NOUN ajst-9436 53 3 graph graph NOUN ajst-9436 53 4 is be AUX ajst-9436 53 5 a a DET ajst-9436 53 6 rectangular rectangular ADJ ajst-9436 53 7 wave wave NOUN ajst-9436 53 8 with with ADP ajst-9436 53 9 a a DET ajst-9436 53 10 support support NOUN ajst-9436 53 11 domain domain NOUN ajst-9436 53 12 of of ADP ajst-9436 53 13 𝑑 𝑑 PROPN ajst-9436 53 14 ∈ ∈ PROPN ajst-9436 53 15 0，1 0，1 NUM ajst-9436 53 16 . . PUNCT ajst-9436 54 1 2 2 X ajst-9436 54 2 ) ) PUNCT ajst-9436 54 3 daubechies daubechie NOUN ajst-9436 54 4 ( ( PUNCT ajst-9436 54 5 dbn dbn PROPN ajst-9436 54 6 ) ) PUNCT ajst-9436 54 7 wavelet wavelet NOUN ajst-9436 54 8 daubechies daubechie NOUN ajst-9436 54 9 wavelet wavelet NOUN ajst-9436 54 10 is be AUX ajst-9436 54 11 written write VERB ajst-9436 54 12 as as ADP ajst-9436 54 13 dbn dbn PROPN ajst-9436 54 14 in in ADP ajst-9436 54 15 daily daily ADJ ajst-9436 54 16 use use NOUN ajst-9436 54 17 , , PUNCT ajst-9436 54 18 with with ADP ajst-9436 54 19 n n PRON ajst-9436 54 20 being be AUX ajst-9436 54 21 the the DET ajst-9436 54 22 order order NOUN ajst-9436 54 23 . . PUNCT ajst-9436 55 1 the the DET ajst-9436 55 2 dbn dbn PROPN ajst-9436 55 3 wavelet wavelet PROPN ajst-9436 55 4 basis basis NOUN ajst-9436 55 5 has have VERB ajst-9436 55 6 good good ADJ ajst-9436 55 7 regularity regularity NOUN ajst-9436 55 8 and and CCONJ ajst-9436 55 9 is be AUX ajst-9436 55 10 relatively relatively ADV ajst-9436 55 11 smooth smooth ADJ ajst-9436 55 12 . . PUNCT ajst-9436 56 1 only only ADV ajst-9436 56 2 when when SCONJ ajst-9436 56 3 n=1 n=1 PROPN ajst-9436 56 4 , , PUNCT ajst-9436 56 5 this this DET ajst-9436 56 6 wavelet wavelet NOUN ajst-9436 56 7 basis basis NOUN ajst-9436 56 8 has have VERB ajst-9436 56 9 symmetry symmetry NOUN ajst-9436 56 10 , , PUNCT ajst-9436 56 11 while while SCONJ ajst-9436 56 12 other other ADJ ajst-9436 56 13 dbn dbn PROPN ajst-9436 56 14 wavelet wavelet NOUN ajst-9436 56 15 bases basis NOUN ajst-9436 56 16 do do VERB ajst-9436 56 17 not not PART ajst-9436 56 18 . . PUNCT ajst-9436 57 1 the the DET ajst-9436 57 2 lack lack NOUN ajst-9436 57 3 of of ADP ajst-9436 57 4 symmetry symmetry NOUN ajst-9436 57 5 can can AUX ajst-9436 57 6 result result VERB ajst-9436 57 7 in in ADP ajst-9436 57 8 certain certain ADJ ajst-9436 57 9 phase phase NOUN ajst-9436 57 10 distortion distortion NOUN ajst-9436 57 11 when when SCONJ ajst-9436 57 12 decomposing decompose VERB ajst-9436 57 13 and and CCONJ ajst-9436 57 14 reconstructing reconstruct VERB ajst-9436 57 15 signals signal NOUN ajst-9436 57 16 . . PUNCT ajst-9436 58 1 the the DET ajst-9436 58 2 dbn dbn PROPN ajst-9436 58 3 wavelet wavelet PROPN ajst-9436 58 4 basis basis NOUN ajst-9436 58 5 only only ADV ajst-9436 58 6 has have VERB ajst-9436 58 7 a a DET ajst-9436 58 8 fixed fix VERB ajst-9436 58 9 formula formula NOUN ajst-9436 58 10 when when SCONJ ajst-9436 58 11 n=1 n=1 PROPN ajst-9436 58 12 , , PUNCT ajst-9436 58 13 and and CCONJ ajst-9436 58 14 when when SCONJ ajst-9436 58 15 n=1 n=1 PROPN ajst-9436 58 16 , , PUNCT ajst-9436 58 17 db1 db1 NOUN ajst-9436 58 18 is be AUX ajst-9436 58 19 the the DET ajst-9436 58 20 haar haar PROPN ajst-9436 58 21 wavelet wavelet NOUN ajst-9436 58 22 . . PUNCT ajst-9436 59 1 3 3 X ajst-9436 59 2 ) ) PUNCT ajst-9436 59 3 symlet symlet NOUN ajst-9436 59 4 ( ( PUNCT ajst-9436 59 5 symn symn NOUN ajst-9436 59 6 ) ) PUNCT ajst-9436 59 7 wavelet wavelet NOUN ajst-9436 59 8 symlet symlet PROPN ajst-9436 59 9 wavelet wavelet NOUN ajst-9436 59 10 bases basis NOUN ajst-9436 59 11 are be AUX ajst-9436 59 12 written write VERB ajst-9436 59 13 as as ADP ajst-9436 59 14 symn symn ADJ ajst-9436 59 15 in in ADP ajst-9436 59 16 daily daily ADJ ajst-9436 59 17 use use NOUN ajst-9436 59 18 , , PUNCT ajst-9436 59 19 with with ADP ajst-9436 59 20 n n PRON ajst-9436 59 21 being be AUX ajst-9436 59 22 the the DET ajst-9436 59 23 order order NOUN ajst-9436 59 24 , , PUNCT ajst-9436 59 25 starting start VERB ajst-9436 59 26 from from ADP ajst-9436 59 27 2 2 NUM ajst-9436 59 28 to to ADP ajst-9436 59 29 8 8 NUM ajst-9436 59 30 . . PUNCT ajst-9436 60 1 this this DET ajst-9436 60 2 type type NOUN ajst-9436 60 3 of of ADP ajst-9436 60 4 wavelet wavelet NOUN ajst-9436 60 5 is be AUX ajst-9436 60 6 essentially essentially ADV ajst-9436 60 7 derived derive VERB ajst-9436 60 8 from from ADP ajst-9436 60 9 dbn dbn PROPN ajst-9436 60 10 . . PUNCT ajst-9436 61 1 the the DET ajst-9436 61 2 symmetry symmetry NOUN ajst-9436 61 3 of of ADP ajst-9436 61 4 symn symn PROPN ajst-9436 61 5 is be AUX ajst-9436 61 6 very very ADV ajst-9436 61 7 good good ADJ ajst-9436 61 8 , , PUNCT ajst-9436 61 9 which which PRON ajst-9436 61 10 can can AUX ajst-9436 61 11 reduce reduce VERB ajst-9436 61 12 some some DET ajst-9436 61 13 distortion distortion NOUN ajst-9436 61 14 problems problem NOUN ajst-9436 61 15 during during ADP ajst-9436 61 16 image image NOUN ajst-9436 61 17 decomposition decomposition NOUN ajst-9436 61 18 and and CCONJ ajst-9436 61 19 reconstruction reconstruction NOUN ajst-9436 61 20 . . PUNCT ajst-9436 62 1 4 4 X ajst-9436 62 2 ) ) PUNCT ajst-9436 62 3 coiflet coiflet NOUN ajst-9436 62 4 ( ( PUNCT ajst-9436 62 5 coifn coifn NOUN ajst-9436 62 6 ) ) PUNCT ajst-9436 62 7 wavelet wavelet NOUN ajst-9436 62 8 coiflet coiflet NOUN ajst-9436 62 9 is be AUX ajst-9436 62 10 generally generally ADV ajst-9436 62 11 abbreviated abbreviate VERB ajst-9436 62 12 as as ADP ajst-9436 62 13 coifn coifn NOUN ajst-9436 62 14 , , PUNCT ajst-9436 62 15 where where SCONJ ajst-9436 62 16 n n X ajst-9436 62 17 is be AUX ajst-9436 62 18 the the DET ajst-9436 62 19 order order NOUN ajst-9436 62 20 , , PUNCT ajst-9436 62 21 ranging range VERB ajst-9436 62 22 from from ADP ajst-9436 62 23 1 1 NUM ajst-9436 62 24 to to ADP ajst-9436 62 25 5 5 NUM ajst-9436 62 26 . . PUNCT ajst-9436 63 1 the the DET ajst-9436 63 2 2n 2n NUM ajst-9436 63 3 order order NOUN ajst-9436 63 4 moment moment NOUN ajst-9436 63 5 of of ADP ajst-9436 63 6 coiflet coiflet PROPN ajst-9436 63 7 's 's PART ajst-9436 63 8 wavelet wavelet NOUN ajst-9436 63 9 functionπœ‘ functionπœ‘ ADJ ajst-9436 63 10 𝑑 𝑑 PROPN ajst-9436 63 11 is be AUX ajst-9436 63 12 zero zero NUM ajst-9436 63 13 , , PUNCT ajst-9436 63 14 and and CCONJ ajst-9436 63 15 the the DET ajst-9436 63 16 1 1 NUM ajst-9436 63 17 - - PUNCT ajst-9436 63 18 2n 2n NUM ajst-9436 63 19 order order NOUN ajst-9436 63 20 moment moment NOUN ajst-9436 63 21 of of ADP ajst-9436 63 22 the the DET ajst-9436 63 23 scale scale NOUN ajst-9436 63 24 function function NOUN ajst-9436 63 25 πœ™ πœ™ PROPN ajst-9436 63 26 𝑑 𝑑 PROPN ajst-9436 63 27 is be AUX ajst-9436 63 28 zero zero NUM ajst-9436 63 29 . . PUNCT ajst-9436 64 1 the the DET ajst-9436 64 2 symmetry symmetry NOUN ajst-9436 64 3 of of ADP ajst-9436 64 4 the the DET ajst-9436 64 5 wavelet wavelet NOUN ajst-9436 64 6 function function NOUN ajst-9436 64 7 and and CCONJ ajst-9436 64 8 scale scale NOUN ajst-9436 64 9 function function NOUN ajst-9436 64 10 of of ADP ajst-9436 64 11 the the DET ajst-9436 64 12 dbn dbn PROPN ajst-9436 64 13 wavelet wavelet NOUN ajst-9436 64 14 base base NOUN ajst-9436 64 15 is be AUX ajst-9436 64 16 not not PART ajst-9436 64 17 as as ADV ajst-9436 64 18 good good ADJ ajst-9436 64 19 as as ADP ajst-9436 64 20 coifn coifn NOUN ajst-9436 64 21 wavelet wavelet NOUN ajst-9436 64 22 base base NOUN ajst-9436 64 23 , , PUNCT ajst-9436 64 24 that that ADV ajst-9436 64 25 is is ADV ajst-9436 64 26 , , PUNCT ajst-9436 64 27 the the DET ajst-9436 64 28 smoothness smoothness NOUN ajst-9436 64 29 is be AUX ajst-9436 64 30 not not PART ajst-9436 64 31 as as ADP ajst-9436 64 32 14 14 NUM ajst-9436 64 33 good good ADJ ajst-9436 64 34 as as ADP ajst-9436 64 35 coifn coifn NOUN ajst-9436 64 36 3 3 NUM ajst-9436 64 37 . . PUNCT ajst-9436 64 38 comparison comparison NOUN ajst-9436 64 39 of of ADP ajst-9436 64 40 simulation simulation NOUN ajst-9436 64 41 results result VERB ajst-9436 64 42 3.1 3.1 NUM ajst-9436 64 43 . . PUNCT ajst-9436 64 44 comparison comparison NOUN ajst-9436 64 45 of of ADP ajst-9436 64 46 denoising denoising NOUN ajst-9436 64 47 effects effect NOUN ajst-9436 64 48 using use VERB ajst-9436 64 49 different different ADJ ajst-9436 64 50 threshold threshold NOUN ajst-9436 64 51 determination determination NOUN ajst-9436 64 52 methods method NOUN ajst-9436 64 53 1 1 NUM ajst-9436 64 54 ) ) PUNCT ajst-9436 64 55 functional functional ADJ ajst-9436 64 56 method method NOUN ajst-9436 64 57 the the DET ajst-9436 64 58 function function NOUN ajst-9436 64 59 method method NOUN ajst-9436 64 60 ddencmp ddencmp NOUN ajst-9436 64 61 is be AUX ajst-9436 64 62 used use VERB ajst-9436 64 63 to to PART ajst-9436 64 64 achieve achieve VERB ajst-9436 64 65 automatic automatic ADJ ajst-9436 64 66 threshold threshold NOUN ajst-9436 64 67 acquisition acquisition NOUN ajst-9436 64 68 , , PUNCT ajst-9436 64 69 while while SCONJ ajst-9436 64 70 wdncmp wdncmp ADJ ajst-9436 64 71 is be AUX ajst-9436 64 72 used use VERB ajst-9436 64 73 to to PART ajst-9436 64 74 achieve achieve VERB ajst-9436 64 75 automatic automatic ADJ ajst-9436 64 76 noise noise NOUN ajst-9436 64 77 reduction reduction NOUN ajst-9436 64 78 function function NOUN ajst-9436 64 79 , , PUNCT ajst-9436 64 80 which which PRON ajst-9436 64 81 can can AUX ajst-9436 64 82 change change VERB ajst-9436 64 83 parameters parameter NOUN ajst-9436 64 84 to to PART ajst-9436 64 85 achieve achieve VERB ajst-9436 64 86 soft soft ADJ ajst-9436 64 87 and and CCONJ ajst-9436 64 88 hard hard ADJ ajst-9436 64 89 threshold threshold NOUN ajst-9436 64 90 denoising denoising NOUN ajst-9436 64 91 . . PUNCT ajst-9436 65 1 the the DET ajst-9436 65 2 function function NOUN ajst-9436 65 3 method method NOUN ajst-9436 65 4 mainly mainly ADV ajst-9436 65 5 uses use VERB ajst-9436 65 6 the the DET ajst-9436 65 7 two two NUM ajst-9436 65 8 unique unique ADJ ajst-9436 65 9 functions function NOUN ajst-9436 65 10 in in ADP ajst-9436 65 11 matlab matlab PROPN ajst-9436 65 12 to to PART ajst-9436 65 13 achieve achieve VERB ajst-9436 65 14 threshold threshold NOUN ajst-9436 65 15 acquisition acquisition NOUN ajst-9436 65 16 and and CCONJ ajst-9436 65 17 image image NOUN ajst-9436 65 18 soft soft ADJ ajst-9436 65 19 and and CCONJ ajst-9436 65 20 hard hard ADJ ajst-9436 65 21 threshold threshold NOUN ajst-9436 65 22 denoising denoise VERB ajst-9436 65 23 . . PUNCT ajst-9436 66 1 figure figure NOUN ajst-9436 66 2 1 1 NUM ajst-9436 66 3 . . PUNCT ajst-9436 67 1 function function NOUN ajst-9436 67 2 method method NOUN ajst-9436 67 3 threshold threshold NOUN ajst-9436 67 4 denoising denoise VERB ajst-9436 67 5 image image NOUN ajst-9436 67 6 figure figure NOUN ajst-9436 67 7 2 2 NUM ajst-9436 67 8 . . PUNCT ajst-9436 67 9 histogram histogram NOUN ajst-9436 67 10 before before ADV ajst-9436 67 11 and and CCONJ ajst-9436 67 12 after after ADP ajst-9436 67 13 threshold threshold NOUN ajst-9436 67 14 denoising denoise VERB ajst-9436 67 15 using use VERB ajst-9436 67 16 the the DET ajst-9436 67 17 function function NOUN ajst-9436 67 18 method method NOUN ajst-9436 67 19 2 2 NUM ajst-9436 67 20 ) ) PUNCT ajst-9436 67 21 triple triple ADJ ajst-9436 67 22 standard standard ADJ ajst-9436 67 23 deviation deviation NOUN ajst-9436 67 24 method method NOUN ajst-9436 67 25 step step NOUN ajst-9436 67 26 1 1 NUM ajst-9436 67 27 : : PUNCT ajst-9436 67 28 calculate calculate VERB ajst-9436 67 29 the the DET ajst-9436 67 30 standard standard ADJ ajst-9436 67 31 deviation deviation NOUN ajst-9436 67 32 of of ADP ajst-9436 67 33 wavelet wavelet NOUN ajst-9436 67 34 coefficients coefficient NOUN ajst-9436 67 35 . . PUNCT ajst-9436 68 1 step step NOUN ajst-9436 68 2 2 2 NUM ajst-9436 68 3 : : PUNCT ajst-9436 68 4 set set VERB ajst-9436 68 5 the the DET ajst-9436 68 6 wavelet wavelet NOUN ajst-9436 68 7 threshold threshold NOUN ajst-9436 68 8 to to ADP ajst-9436 68 9 three three NUM ajst-9436 68 10 times time NOUN ajst-9436 68 11 the the DET ajst-9436 68 12 noise noise NOUN ajst-9436 68 13 standard standard ADJ ajst-9436 68 14 deviation deviation NOUN ajst-9436 68 15 . . PUNCT ajst-9436 69 1 if if SCONJ ajst-9436 69 2 the the DET ajst-9436 69 3 monitoring monitoring NOUN ajst-9436 69 4 data datum NOUN ajst-9436 69 5 obtained obtain VERB ajst-9436 69 6 from from ADP ajst-9436 69 7 a a DET ajst-9436 69 8 certain certain ADJ ajst-9436 69 9 detection detection NOUN ajst-9436 69 10 is be AUX ajst-9436 69 11 x1 x1 PROPN ajst-9436 69 12 , , PUNCT ajst-9436 69 13 x2 x2 PROPN ajst-9436 69 14 , , PUNCT ajst-9436 69 15 x3 x3 PROPN ajst-9436 69 16 ... ... PUNCT ajst-9436 69 17 xn xn X ajst-9436 69 18 , , PUNCT ajst-9436 69 19 the the DET ajst-9436 69 20 average average ADJ ajst-9436 69 21 value value NOUN ajst-9436 69 22 is be AUX ajst-9436 69 23 : : PUNCT ajst-9436 69 24 π‘₯ π‘₯ PROPN ajst-9436 69 25 π‘₯1 π‘₯1 NOUN ajst-9436 69 26 π‘₯2 π‘₯2 PROPN ajst-9436 69 27 π‘₯3 π‘₯3 NOUN ajst-9436 69 28 β‹― β‹― PROPN ajst-9436 69 29 π‘₯𝑛 π‘₯𝑛 PROPN ajst-9436 69 30 𝑛 𝑛 PROPN ajst-9436 69 31 βˆ‘ βˆ‘ PROPN ajst-9436 69 32 π‘₯𝑖 π‘₯𝑖 PROPN ajst-9436 69 33 𝑛 𝑛 PROPN ajst-9436 69 34 10 10 NUM ajst-9436 69 35 the the DET ajst-9436 69 36 standard standard ADJ ajst-9436 69 37 deviation deviation NOUN ajst-9436 69 38 is be AUX ajst-9436 69 39 : : PUNCT ajst-9436 69 40 𝜎 𝜎 PROPN ajst-9436 69 41 π‘₯1 π‘₯1 NOUN ajst-9436 69 42 π‘₯ π‘₯ NOUN ajst-9436 69 43 2 2 NUM ajst-9436 69 44 π‘₯2 π‘₯2 NOUN ajst-9436 69 45 π‘₯ π‘₯ NOUN ajst-9436 69 46 2 2 NUM ajst-9436 69 47 β‹― β‹― ADP ajst-9436 69 48 π‘₯𝑛 π‘₯𝑛 NOUN ajst-9436 69 49 π‘₯ π‘₯ PROPN ajst-9436 69 50 2 2 NUM ajst-9436 69 51 𝑛 𝑛 PROPN ajst-9436 69 52 βˆ‘ βˆ‘ ADP ajst-9436 69 53 π‘₯𝑖 π‘₯𝑖 ADP ajst-9436 69 54 π‘₯ π‘₯ DET ajst-9436 69 55 2 2 NUM ajst-9436 69 56 𝑛 𝑛 DET ajst-9436 69 57 11 11 NUM ajst-9436 69 58 value value NOUN ajst-9436 69 59 within within ADP ajst-9436 69 60 x x PROPN ajst-9436 69 61 Β± Β± NUM ajst-9436 69 62 3 3 NUM ajst-9436 69 63 Οƒ Οƒ NOUN ajst-9436 69 64 the the DET ajst-9436 69 65 values value NOUN ajst-9436 69 66 within within ADP ajst-9436 69 67 this this DET ajst-9436 69 68 range range NOUN ajst-9436 69 69 are be AUX ajst-9436 69 70 normal normal ADJ ajst-9436 69 71 values value NOUN ajst-9436 69 72 , , PUNCT ajst-9436 69 73 while while SCONJ ajst-9436 69 74 those those PRON ajst-9436 69 75 outside outside ADP ajst-9436 69 76 this this DET ajst-9436 69 77 range range NOUN ajst-9436 69 78 are be AUX ajst-9436 69 79 outliers outlier NOUN ajst-9436 69 80 . . PUNCT ajst-9436 70 1 figure figure VERB ajst-9436 70 2 3 3 NUM ajst-9436 70 3 . . NOUN ajst-9436 70 4 thresholding thresholde VERB ajst-9436 70 5 denoising denoise VERB ajst-9436 70 6 image image NOUN ajst-9436 70 7 using use VERB ajst-9436 70 8 triple triple ADJ ajst-9436 70 9 standard standard ADJ ajst-9436 70 10 deviation deviation NOUN ajst-9436 70 11 method method NOUN ajst-9436 70 12 figure figure NOUN ajst-9436 70 13 4 4 NUM ajst-9436 70 14 . . NOUN ajst-9436 70 15 histogram histogram NOUN ajst-9436 70 16 before before ADV ajst-9436 70 17 and and CCONJ ajst-9436 70 18 after after ADP ajst-9436 70 19 threshold threshold NOUN ajst-9436 70 20 denoising denoise VERB ajst-9436 70 21 using use VERB ajst-9436 70 22 triple triple ADJ ajst-9436 70 23 standard standard ADJ ajst-9436 70 24 deviation deviation NOUN ajst-9436 70 25 method method NOUN ajst-9436 70 26 fixed fix VERB ajst-9436 70 27 threshold threshold NOUN ajst-9436 70 28 estimation estimation NOUN ajst-9436 70 29 method method NOUN ajst-9436 70 30 step step NOUN ajst-9436 70 31 1 1 NUM ajst-9436 70 32 : : PUNCT ajst-9436 70 33 calculate calculate VERB ajst-9436 70 34 the the DET ajst-9436 70 35 variance variance NOUN ajst-9436 70 36 of of ADP ajst-9436 70 37 the the DET ajst-9436 70 38 noise noise NOUN ajst-9436 70 39 . . PUNCT ajst-9436 71 1 step step NOUN ajst-9436 71 2 2 2 NUM ajst-9436 71 3 : : PUNCT ajst-9436 71 4 use use VERB ajst-9436 71 5 the the DET ajst-9436 71 6 fixed fix VERB ajst-9436 71 7 threshold threshold NOUN ajst-9436 71 8 formula formula NOUN ajst-9436 71 9 to to PART ajst-9436 71 10 calculate calculate VERB ajst-9436 71 11 the the DET ajst-9436 71 12 wavelet wavelet NOUN ajst-9436 71 13 threshold threshold NOUN ajst-9436 71 14 . . PUNCT ajst-9436 72 1 πœ† πœ† DET ajst-9436 72 2 πœŽπ‘’οΌŒπ‘—βˆš2lnn πœŽπ‘’οΌŒπ‘—βˆš2lnn NOUN ajst-9436 72 3 , , PUNCT ajst-9436 72 4 Οƒ Οƒ PROPN ajst-9436 72 5 represents represent VERB ajst-9436 72 6 the the DET ajst-9436 72 7 standard standard ADJ ajst-9436 72 8 deviation deviation NOUN ajst-9436 72 9 of of ADP ajst-9436 72 10 the the DET ajst-9436 72 11 noise noise NOUN ajst-9436 72 12 calculated calculate VERB ajst-9436 72 13 above above ADV ajst-9436 72 14 , , PUNCT ajst-9436 72 15 and and CCONJ ajst-9436 72 16 n n CCONJ ajst-9436 72 17 represents represent VERB ajst-9436 72 18 the the DET ajst-9436 72 19 size size NOUN ajst-9436 72 20 of of ADP ajst-9436 72 21 the the DET ajst-9436 72 22 image image NOUN ajst-9436 72 23 . . PUNCT ajst-9436 73 1 15 15 NUM ajst-9436 73 2 figure figure NOUN ajst-9436 73 3 5 5 NUM ajst-9436 73 4 . . PUNCT ajst-9436 73 5 fixed fix VERB ajst-9436 73 6 threshold threshold NOUN ajst-9436 73 7 method method NOUN ajst-9436 73 8 threshold threshold NOUN ajst-9436 73 9 denoising denoise VERB ajst-9436 73 10 image image NOUN ajst-9436 73 11 figure figure NOUN ajst-9436 73 12 figure figure NOUN ajst-9436 73 13 6 6 NUM ajst-9436 73 14 . . PUNCT ajst-9436 73 15 fixed fix VERB ajst-9436 73 16 threshold threshold NOUN ajst-9436 73 17 method method NOUN ajst-9436 73 18 threshold threshold NOUN ajst-9436 73 19 denoising denoise VERB ajst-9436 73 20 before before ADV ajst-9436 73 21 and and CCONJ ajst-9436 73 22 after after ADP ajst-9436 73 23 histogram histogram NOUN ajst-9436 73 24 the the DET ajst-9436 73 25 above above ADJ ajst-9436 73 26 introduces introduce NOUN ajst-9436 73 27 various various ADJ ajst-9436 73 28 threshold threshold NOUN ajst-9436 73 29 methods method NOUN ajst-9436 73 30 and and CCONJ ajst-9436 73 31 obtains obtain VERB ajst-9436 73 32 simulation simulation NOUN ajst-9436 73 33 images image NOUN ajst-9436 73 34 of of ADP ajst-9436 73 35 each each DET ajst-9436 73 36 threshold threshold NOUN ajst-9436 73 37 method method NOUN ajst-9436 73 38 . . PUNCT ajst-9436 74 1 from from ADP ajst-9436 74 2 figures figure NOUN ajst-9436 74 3 1 1 NUM ajst-9436 74 4 , , PUNCT ajst-9436 74 5 3 3 NUM ajst-9436 74 6 , , PUNCT ajst-9436 74 7 and and CCONJ ajst-9436 74 8 5 5 NUM ajst-9436 74 9 , , PUNCT ajst-9436 74 10 it it PRON ajst-9436 74 11 can can AUX ajst-9436 74 12 be be AUX ajst-9436 74 13 seen see VERB ajst-9436 74 14 that that SCONJ ajst-9436 74 15 regardless regardless ADV ajst-9436 74 16 of of ADP ajst-9436 74 17 which which DET ajst-9436 74 18 threshold threshold NOUN ajst-9436 74 19 method method NOUN ajst-9436 74 20 is be AUX ajst-9436 74 21 used use VERB ajst-9436 74 22 to to PART ajst-9436 74 23 obtain obtain VERB ajst-9436 74 24 the the DET ajst-9436 74 25 threshold threshold NOUN ajst-9436 74 26 , , PUNCT ajst-9436 74 27 the the DET ajst-9436 74 28 simulated simulate VERB ajst-9436 74 29 hard hard ADJ ajst-9436 74 30 threshold threshold NOUN ajst-9436 74 31 denoising denoise VERB ajst-9436 74 32 image image NOUN ajst-9436 74 33 is be AUX ajst-9436 74 34 brighter bright ADJ ajst-9436 74 35 . . PUNCT ajst-9436 75 1 however however ADV ajst-9436 75 2 , , PUNCT ajst-9436 75 3 the the DET ajst-9436 75 4 soft soft ADJ ajst-9436 75 5 threshold threshold NOUN ajst-9436 75 6 denoising denoising NOUN ajst-9436 75 7 has have VERB ajst-9436 75 8 fewer few ADJ ajst-9436 75 9 noise noise NOUN ajst-9436 75 10 points point NOUN ajst-9436 75 11 , , PUNCT ajst-9436 75 12 clearer clear ADJ ajst-9436 75 13 details detail NOUN ajst-9436 75 14 and and CCONJ ajst-9436 75 15 edges edge NOUN ajst-9436 75 16 , , PUNCT ajst-9436 75 17 and and CCONJ ajst-9436 75 18 is be AUX ajst-9436 75 19 closer close ADJ ajst-9436 75 20 to to ADP ajst-9436 75 21 the the DET ajst-9436 75 22 original original ADJ ajst-9436 75 23 image image NOUN ajst-9436 75 24 . . PUNCT ajst-9436 76 1 from from ADP ajst-9436 76 2 figure figure NOUN ajst-9436 76 3 1 1 NUM ajst-9436 76 4 , , PUNCT ajst-9436 76 5 it it PRON ajst-9436 76 6 is be AUX ajst-9436 76 7 found find VERB ajst-9436 76 8 that that SCONJ ajst-9436 76 9 the the DET ajst-9436 76 10 denoising denoise VERB ajst-9436 76 11 effect effect NOUN ajst-9436 76 12 of of ADP ajst-9436 76 13 using use VERB ajst-9436 76 14 function function NOUN ajst-9436 76 15 method method NOUN ajst-9436 76 16 soft soft ADJ ajst-9436 76 17 and and CCONJ ajst-9436 76 18 hard hard ADJ ajst-9436 76 19 threshold threshold NOUN ajst-9436 76 20 denoising denoise VERB ajst-9436 76 21 on on ADP ajst-9436 76 22 images image NOUN ajst-9436 76 23 is be AUX ajst-9436 76 24 not not PART ajst-9436 76 25 significantly significantly ADV ajst-9436 76 26 different different ADJ ajst-9436 76 27 , , PUNCT ajst-9436 76 28 and and CCONJ ajst-9436 76 29 both both CCONJ ajst-9436 76 30 soft soft ADJ ajst-9436 76 31 and and CCONJ ajst-9436 76 32 hard hard ADJ ajst-9436 76 33 threshold threshold NOUN ajst-9436 76 34 denoising denoising NOUN ajst-9436 76 35 effects effect NOUN ajst-9436 76 36 are be AUX ajst-9436 76 37 good good ADJ ajst-9436 76 38 . . PUNCT ajst-9436 77 1 from from ADP ajst-9436 77 2 figure figure NOUN ajst-9436 77 3 5 5 NUM ajst-9436 77 4 , , PUNCT ajst-9436 77 5 it it PRON ajst-9436 77 6 can can AUX ajst-9436 77 7 be be AUX ajst-9436 77 8 seen see VERB ajst-9436 77 9 that that SCONJ ajst-9436 77 10 the the DET ajst-9436 77 11 denoising denoise VERB ajst-9436 77 12 effect effect NOUN ajst-9436 77 13 using use VERB ajst-9436 77 14 the the DET ajst-9436 77 15 fixed fix VERB ajst-9436 77 16 threshold threshold NOUN ajst-9436 77 17 estimation estimation NOUN ajst-9436 77 18 method method NOUN ajst-9436 77 19 is be AUX ajst-9436 77 20 also also ADV ajst-9436 77 21 better well ADJ ajst-9436 77 22 , , PUNCT ajst-9436 77 23 and and CCONJ ajst-9436 77 24 the the DET ajst-9436 77 25 soft soft ADJ ajst-9436 77 26 threshold threshold NOUN ajst-9436 77 27 denoising denoising NOUN ajst-9436 77 28 is be AUX ajst-9436 77 29 closer close ADJ ajst-9436 77 30 to to ADP ajst-9436 77 31 the the DET ajst-9436 77 32 original original ADJ ajst-9436 77 33 image image NOUN ajst-9436 77 34 , , PUNCT ajst-9436 77 35 while while SCONJ ajst-9436 77 36 the the DET ajst-9436 77 37 hard hard ADJ ajst-9436 77 38 threshold threshold NOUN ajst-9436 77 39 denoising denoising NOUN ajst-9436 77 40 is be AUX ajst-9436 77 41 whiter white ADJ ajst-9436 77 42 than than ADP ajst-9436 77 43 the the DET ajst-9436 77 44 original original ADJ ajst-9436 77 45 image image NOUN ajst-9436 77 46 , , PUNCT ajst-9436 77 47 with with ADP ajst-9436 77 48 unclear unclear ADJ ajst-9436 77 49 dark dark ADJ ajst-9436 77 50 details detail NOUN ajst-9436 77 51 and and CCONJ ajst-9436 77 52 blurry blurry ADJ ajst-9436 77 53 edges edge NOUN ajst-9436 77 54 . . PUNCT ajst-9436 78 1 the the DET ajst-9436 78 2 triple triple ADJ ajst-9436 78 3 threshold threshold NOUN ajst-9436 78 4 standard standard ADJ ajst-9436 78 5 deviation deviation NOUN ajst-9436 78 6 rule rule NOUN ajst-9436 78 7 shown show VERB ajst-9436 78 8 in in ADP ajst-9436 78 9 figures figure NOUN ajst-9436 78 10 3 3 NUM ajst-9436 78 11 is be AUX ajst-9436 78 12 the the DET ajst-9436 78 13 worst bad ADJ ajst-9436 78 14 denoising denoising NOUN ajst-9436 78 15 method method NOUN ajst-9436 78 16 . . PUNCT ajst-9436 79 1 similarly similarly ADV ajst-9436 79 2 , , PUNCT ajst-9436 79 3 soft soft ADJ ajst-9436 79 4 threshold threshold NOUN ajst-9436 79 5 denoising denoise VERB ajst-9436 79 6 displays display NOUN ajst-9436 79 7 images image NOUN ajst-9436 79 8 that that PRON ajst-9436 79 9 are be AUX ajst-9436 79 10 relatively relatively ADV ajst-9436 79 11 black black ADJ ajst-9436 79 12 , , PUNCT ajst-9436 79 13 while while SCONJ ajst-9436 79 14 hard hard ADJ ajst-9436 79 15 threshold threshold NOUN ajst-9436 79 16 denoising denoise VERB ajst-9436 79 17 displays display NOUN ajst-9436 79 18 images image NOUN ajst-9436 79 19 that that PRON ajst-9436 79 20 are be AUX ajst-9436 79 21 relatively relatively ADV ajst-9436 79 22 white white ADJ ajst-9436 79 23 . . PUNCT ajst-9436 80 1 however however ADV ajst-9436 80 2 , , PUNCT ajst-9436 80 3 their their PRON ajst-9436 80 4 images image NOUN ajst-9436 80 5 contain contain VERB ajst-9436 80 6 more more ADJ ajst-9436 80 7 noise noise NOUN ajst-9436 80 8 points point NOUN ajst-9436 80 9 and and CCONJ ajst-9436 80 10 are be AUX ajst-9436 80 11 blurry blurry ADJ ajst-9436 80 12 . . PUNCT ajst-9436 81 1 due due ADP ajst-9436 81 2 to to ADP ajst-9436 81 3 the the DET ajst-9436 81 4 black black ADJ ajst-9436 81 5 nature nature NOUN ajst-9436 81 6 of of ADP ajst-9436 81 7 soft soft ADJ ajst-9436 81 8 threshold threshold NOUN ajst-9436 81 9 denoising denoising NOUN ajst-9436 81 10 , , PUNCT ajst-9436 81 11 the the DET ajst-9436 81 12 lower low ADJ ajst-9436 81 13 edges edge NOUN ajst-9436 81 14 are be AUX ajst-9436 81 15 not not PART ajst-9436 81 16 visible visible ADJ ajst-9436 81 17 and and CCONJ ajst-9436 81 18 details detail NOUN ajst-9436 81 19 are be AUX ajst-9436 81 20 lost lose VERB ajst-9436 81 21 more more ADJ ajst-9436 81 22 . . PUNCT ajst-9436 82 1 compared compare VERB ajst-9436 82 2 to to ADP ajst-9436 82 3 hard hard ADJ ajst-9436 82 4 threshold threshold NOUN ajst-9436 82 5 denoising denoising NOUN ajst-9436 82 6 , , PUNCT ajst-9436 82 7 they they PRON ajst-9436 82 8 are be AUX ajst-9436 82 9 brighter bright ADJ ajst-9436 82 10 , , PUNCT ajst-9436 82 11 so so CCONJ ajst-9436 82 12 there there PRON ajst-9436 82 13 is be VERB ajst-9436 82 14 less less ADJ ajst-9436 82 15 loss loss NOUN ajst-9436 82 16 of of ADP ajst-9436 82 17 details detail NOUN ajst-9436 82 18 and and CCONJ ajst-9436 82 19 clearer clear ADJ ajst-9436 82 20 edges edge NOUN ajst-9436 82 21 . . PUNCT ajst-9436 83 1 comparing compare VERB ajst-9436 83 2 images image NOUN ajst-9436 83 3 2 2 NUM ajst-9436 83 4 , , PUNCT ajst-9436 83 5 4 4 NUM ajst-9436 83 6 , , PUNCT ajst-9436 83 7 and and CCONJ ajst-9436 83 8 6 6 NUM ajst-9436 83 9 , , PUNCT ajst-9436 83 10 it it PRON ajst-9436 83 11 can can AUX ajst-9436 83 12 be be AUX ajst-9436 83 13 seen see VERB ajst-9436 83 14 that that SCONJ ajst-9436 83 15 the the DET ajst-9436 83 16 pixel pixel ADJ ajst-9436 83 17 distribution distribution NOUN ajst-9436 83 18 of of ADP ajst-9436 83 19 the the DET ajst-9436 83 20 triple triple ADJ ajst-9436 83 21 threshold threshold NOUN ajst-9436 83 22 method method NOUN ajst-9436 83 23 in in ADP ajst-9436 83 24 images image NOUN ajst-9436 83 25 4 4 NUM ajst-9436 83 26 differs differ VERB ajst-9436 83 27 significantly significantly ADV ajst-9436 83 28 from from ADP ajst-9436 83 29 the the DET ajst-9436 83 30 original original ADJ ajst-9436 83 31 image image NOUN ajst-9436 83 32 , , PUNCT ajst-9436 83 33 resulting result VERB ajst-9436 83 34 in in ADP ajst-9436 83 35 too too ADV ajst-9436 83 36 much much ADJ ajst-9436 83 37 image image NOUN ajst-9436 83 38 distortion distortion NOUN ajst-9436 83 39 . . PUNCT ajst-9436 84 1 however however ADV ajst-9436 84 2 , , PUNCT ajst-9436 84 3 the the DET ajst-9436 84 4 function function NOUN ajst-9436 84 5 method method NOUN ajst-9436 84 6 and and CCONJ ajst-9436 84 7 fixed fix VERB ajst-9436 84 8 threshold threshold NOUN ajst-9436 84 9 method method NOUN ajst-9436 84 10 in in ADP ajst-9436 84 11 images image NOUN ajst-9436 84 12 2 2 NUM ajst-9436 84 13 and and CCONJ ajst-9436 84 14 6 6 NUM ajst-9436 84 15 are be AUX ajst-9436 84 16 similar similar ADJ ajst-9436 84 17 , , PUNCT ajst-9436 84 18 but but CCONJ ajst-9436 84 19 the the DET ajst-9436 84 20 pixel pixel ADJ ajst-9436 84 21 distribution distribution NOUN ajst-9436 84 22 of of ADP ajst-9436 84 23 the the DET ajst-9436 84 24 fixed fix VERB ajst-9436 84 25 threshold threshold NOUN ajst-9436 84 26 method method NOUN ajst-9436 84 27 is be AUX ajst-9436 84 28 closer close ADJ ajst-9436 84 29 to to ADP ajst-9436 84 30 the the DET ajst-9436 84 31 original original ADJ ajst-9436 84 32 image image NOUN ajst-9436 84 33 than than ADP ajst-9436 84 34 the the DET ajst-9436 84 35 function function NOUN ajst-9436 84 36 method method NOUN ajst-9436 84 37 . . PUNCT ajst-9436 85 1 3.2 3.2 NUM ajst-9436 85 2 . . PUNCT ajst-9436 86 1 comparison comparison NOUN ajst-9436 86 2 of of ADP ajst-9436 86 3 denoising denoising NOUN ajst-9436 86 4 effects effect NOUN ajst-9436 86 5 using use VERB ajst-9436 86 6 different different ADJ ajst-9436 86 7 wavelet wavelet NOUN ajst-9436 86 8 bases basis NOUN ajst-9436 86 9 figure figure VERB ajst-9436 86 10 7 7 NUM ajst-9436 86 11 . . PROPN ajst-9436 86 12 haar haar PROPN ajst-9436 86 13 wavelet wavelet PROPN ajst-9436 86 14 based base VERB ajst-9436 86 15 threshold threshold NOUN ajst-9436 86 16 denoising denoise VERB ajst-9436 86 17 image image NOUN ajst-9436 86 18 figure figure NOUN ajst-9436 86 19 8 8 NUM ajst-9436 86 20 . . PUNCT ajst-9436 86 21 haar haar PROPN ajst-9436 86 22 wavelet wavelet PROPN ajst-9436 86 23 based base VERB ajst-9436 86 24 threshold threshold NOUN ajst-9436 86 25 denoising denoise VERB ajst-9436 86 26 before before ADV ajst-9436 86 27 and and CCONJ ajst-9436 86 28 after after ADP ajst-9436 86 29 histogram histogram NOUN ajst-9436 86 30 figure figure NOUN ajst-9436 86 31 9 9 NUM ajst-9436 86 32 . . PUNCT ajst-9436 86 33 sym5 sym5 PROPN ajst-9436 86 34 wavelet wavelet PROPN ajst-9436 86 35 based base VERB ajst-9436 86 36 threshold threshold NOUN ajst-9436 86 37 denoising denoise VERB ajst-9436 86 38 image image NOUN ajst-9436 86 39 16 16 NUM ajst-9436 86 40 figure figure NOUN ajst-9436 86 41 10 10 NUM ajst-9436 86 42 . . PUNCT ajst-9436 86 43 histogram histogram NOUN ajst-9436 86 44 of of ADP ajst-9436 86 45 sym5 sym5 PROPN ajst-9436 86 46 wavelet wavelet NOUN ajst-9436 86 47 based base VERB ajst-9436 86 48 threshold threshold NOUN ajst-9436 86 49 before before ADP ajst-9436 86 50 and and CCONJ ajst-9436 86 51 after after ADP ajst-9436 86 52 denoising denoise VERB ajst-9436 86 53 figure figure NOUN ajst-9436 86 54 11 11 NUM ajst-9436 86 55 . . PUNCT ajst-9436 87 1 coif3 coif3 NOUN ajst-9436 87 2 wavelet wavelet NOUN ajst-9436 87 3 based base VERB ajst-9436 87 4 threshold threshold NOUN ajst-9436 87 5 denoising denoise VERB ajst-9436 87 6 image image NOUN ajst-9436 87 7 figure figure NOUN ajst-9436 87 8 12 12 NUM ajst-9436 87 9 . . PUNCT ajst-9436 88 1 coif3 coif3 NOUN ajst-9436 88 2 wavelet wavelet NOUN ajst-9436 88 3 based base VERB ajst-9436 88 4 threshold threshold NOUN ajst-9436 88 5 denoising denoise VERB ajst-9436 88 6 before before ADV ajst-9436 88 7 and and CCONJ ajst-9436 88 8 after after ADP ajst-9436 88 9 histogram histogram NOUN ajst-9436 88 10 figure figure NOUN ajst-9436 88 11 13 13 NUM ajst-9436 88 12 . . PUNCT ajst-9436 89 1 denoising denoise VERB ajst-9436 89 2 image image NOUN ajst-9436 89 3 of of ADP ajst-9436 89 4 db3 db3 PROPN ajst-9436 89 5 wavelet wavelet NOUN ajst-9436 89 6 based base VERB ajst-9436 89 7 threshold threshold NOUN ajst-9436 89 8 figure figure NOUN ajst-9436 89 9 14 14 NUM ajst-9436 89 10 . . PUNCT ajst-9436 89 11 histogram histogram NOUN ajst-9436 89 12 of of ADP ajst-9436 89 13 db3 db3 PROPN ajst-9436 89 14 wavelet wavelet PROPN ajst-9436 89 15 based base VERB ajst-9436 89 16 threshold threshold NOUN ajst-9436 89 17 denoising denoise VERB ajst-9436 89 18 before before ADV ajst-9436 89 19 and and CCONJ ajst-9436 89 20 after after ADP ajst-9436 89 21 denoising denoise VERB ajst-9436 89 22 comparing compare VERB ajst-9436 89 23 images image NOUN ajst-9436 89 24 7 7 NUM ajst-9436 89 25 , , PUNCT ajst-9436 89 26 9 9 NUM ajst-9436 89 27 , , PUNCT ajst-9436 89 28 11 11 NUM ajst-9436 89 29 , , PUNCT ajst-9436 89 30 13 13 NUM ajst-9436 89 31 , , PUNCT ajst-9436 89 32 it it PRON ajst-9436 89 33 can can AUX ajst-9436 89 34 be be AUX ajst-9436 89 35 seen see VERB ajst-9436 89 36 that that SCONJ ajst-9436 89 37 the the DET ajst-9436 89 38 haar haar PROPN ajst-9436 89 39 wavelet wavelet PROPN ajst-9436 89 40 basis basis NOUN ajst-9436 89 41 has have VERB ajst-9436 89 42 the the DET ajst-9436 89 43 best good ADJ ajst-9436 89 44 denoising denoising NOUN ajst-9436 89 45 effect effect NOUN ajst-9436 89 46 , , PUNCT ajst-9436 89 47 with with ADP ajst-9436 89 48 good good ADJ ajst-9436 89 49 soft soft ADJ ajst-9436 89 50 and and CCONJ ajst-9436 89 51 hard hard ADJ ajst-9436 89 52 threshold threshold NOUN ajst-9436 89 53 denoising denoising NOUN ajst-9436 89 54 effects effect NOUN ajst-9436 89 55 , , PUNCT ajst-9436 89 56 clear clear ADJ ajst-9436 89 57 edges edge NOUN ajst-9436 89 58 , , PUNCT ajst-9436 89 59 and and CCONJ ajst-9436 89 60 slightly slightly ADV ajst-9436 89 61 inferior inferior ADJ ajst-9436 89 62 details detail NOUN ajst-9436 89 63 . . PUNCT ajst-9436 90 1 the the DET ajst-9436 90 2 sym5 sym5 PROPN ajst-9436 90 3 wavelet wavelet NOUN ajst-9436 90 4 basis basis NOUN ajst-9436 90 5 has have VERB ajst-9436 90 6 a a DET ajst-9436 90 7 slightly slightly ADV ajst-9436 90 8 worse bad ADJ ajst-9436 90 9 denoising denoising NOUN ajst-9436 90 10 effect effect NOUN ajst-9436 90 11 , , PUNCT ajst-9436 90 12 with with ADP ajst-9436 90 13 a a DET ajst-9436 90 14 slightly slightly ADV ajst-9436 90 15 worse bad ADJ ajst-9436 90 16 hard hard ADJ ajst-9436 90 17 threshold threshold NOUN ajst-9436 90 18 denoising denoising NOUN ajst-9436 90 19 and and CCONJ ajst-9436 90 20 more more ADJ ajst-9436 90 21 noise noise NOUN ajst-9436 90 22 , , PUNCT ajst-9436 90 23 while while SCONJ ajst-9436 90 24 a a DET ajst-9436 90 25 better well ADJ ajst-9436 90 26 soft soft ADJ ajst-9436 90 27 threshold threshold NOUN ajst-9436 90 28 denoising denoising NOUN ajst-9436 90 29 and and CCONJ ajst-9436 90 30 better well ADJ ajst-9436 90 31 details detail NOUN ajst-9436 90 32 . . PUNCT ajst-9436 91 1 the the DET ajst-9436 91 2 denoising denoise VERB ajst-9436 91 3 effect effect NOUN ajst-9436 91 4 is be AUX ajst-9436 91 5 further far ADV ajst-9436 91 6 improved improve VERB ajst-9436 91 7 by by ADP ajst-9436 91 8 using use VERB ajst-9436 91 9 the the DET ajst-9436 91 10 db3 db3 PROPN ajst-9436 91 11 wavelet wavelet NOUN ajst-9436 91 12 basis basis NOUN ajst-9436 91 13 . . PUNCT ajst-9436 92 1 the the DET ajst-9436 92 2 hard hard ADJ ajst-9436 92 3 threshold threshold NOUN ajst-9436 92 4 denoising denoising NOUN ajst-9436 92 5 is be AUX ajst-9436 92 6 more more ADV ajst-9436 92 7 blurry blurry ADJ ajst-9436 92 8 , , PUNCT ajst-9436 92 9 while while SCONJ ajst-9436 92 10 the the DET ajst-9436 92 11 soft soft ADJ ajst-9436 92 12 threshold threshold NOUN ajst-9436 92 13 denoising denoising NOUN ajst-9436 92 14 is be AUX ajst-9436 92 15 slightly slightly ADV ajst-9436 92 16 better well ADJ ajst-9436 92 17 , , PUNCT ajst-9436 92 18 with with ADP ajst-9436 92 19 clearer clear ADJ ajst-9436 92 20 edges edge NOUN ajst-9436 92 21 . . PUNCT ajst-9436 93 1 the the DET ajst-9436 93 2 worst bad ADJ ajst-9436 93 3 denoising denoising NOUN ajst-9436 93 4 effect effect NOUN ajst-9436 93 5 is be AUX ajst-9436 93 6 the the DET ajst-9436 93 7 coif3 coif3 PROPN ajst-9436 93 8 wavelet wavelet NOUN ajst-9436 93 9 basis basis NOUN ajst-9436 93 10 , , PUNCT ajst-9436 93 11 which which PRON ajst-9436 93 12 not not PART ajst-9436 93 13 only only ADV ajst-9436 93 14 blurs blur VERB ajst-9436 93 15 the the DET ajst-9436 93 16 image image NOUN ajst-9436 93 17 but but CCONJ ajst-9436 93 18 also also ADV ajst-9436 93 19 loses lose VERB ajst-9436 93 20 a a DET ajst-9436 93 21 lot lot NOUN ajst-9436 93 22 of of ADP ajst-9436 93 23 details detail NOUN ajst-9436 93 24 , , PUNCT ajst-9436 93 25 resulting result VERB ajst-9436 93 26 in in ADP ajst-9436 93 27 a a DET ajst-9436 93 28 large large ADJ ajst-9436 93 29 difference difference NOUN ajst-9436 93 30 in in ADP ajst-9436 93 31 brightness brightness NOUN ajst-9436 93 32 and and CCONJ ajst-9436 93 33 darkness darkness NOUN ajst-9436 93 34 . . PUNCT ajst-9436 94 1 comparing compare VERB ajst-9436 94 2 images image NOUN ajst-9436 94 3 8 8 NUM ajst-9436 94 4 , , PUNCT ajst-9436 94 5 10 10 NUM ajst-9436 94 6 , , PUNCT ajst-9436 94 7 12 12 NUM ajst-9436 94 8 , , PUNCT ajst-9436 94 9 and and CCONJ ajst-9436 94 10 14 14 NUM ajst-9436 94 11 , , PUNCT ajst-9436 94 12 it it PRON ajst-9436 94 13 can can AUX ajst-9436 94 14 be be AUX ajst-9436 94 15 seen see VERB ajst-9436 94 16 that that SCONJ ajst-9436 94 17 the the DET ajst-9436 94 18 overall overall ADJ ajst-9436 94 19 trend trend NOUN ajst-9436 94 20 of of ADP ajst-9436 94 21 pixel pixel ADJ ajst-9436 94 22 distribution distribution NOUN ajst-9436 94 23 before before ADP ajst-9436 94 24 and and CCONJ ajst-9436 94 25 after after ADP ajst-9436 94 26 denoising denoise VERB ajst-9436 94 27 using use VERB ajst-9436 94 28 haar haar PROPN ajst-9436 94 29 wavelet wavelet NOUN ajst-9436 94 30 basis basis NOUN ajst-9436 94 31 is be AUX ajst-9436 94 32 more more ADV ajst-9436 94 33 consistent consistent ADJ ajst-9436 94 34 in in ADP ajst-9436 94 35 figure figure NOUN ajst-9436 94 36 8 8 NUM ajst-9436 94 37 , , PUNCT ajst-9436 94 38 while while SCONJ ajst-9436 94 39 the the DET ajst-9436 94 40 consistency consistency NOUN ajst-9436 94 41 of of ADP ajst-9436 94 42 pixel pixel ADJ ajst-9436 94 43 distribution distribution NOUN ajst-9436 94 44 before before ADP ajst-9436 94 45 and and CCONJ ajst-9436 94 46 after after ADP ajst-9436 94 47 denoising denoise VERB ajst-9436 94 48 using use VERB ajst-9436 94 49 sym5 sym5 PROPN ajst-9436 94 50 wavelet wavelet NOUN ajst-9436 94 51 basis basis NOUN ajst-9436 94 52 is be AUX ajst-9436 94 53 slightly slightly ADV ajst-9436 94 54 poor poor ADJ ajst-9436 94 55 in in ADP ajst-9436 94 56 figure figure NOUN ajst-9436 94 57 10 10 NUM ajst-9436 94 58 . . PUNCT ajst-9436 95 1 figures figure NOUN ajst-9436 95 2 14 14 NUM ajst-9436 95 3 using use VERB ajst-9436 95 4 db3 db3 PROPN ajst-9436 95 5 wavelet wavelet NOUN ajst-9436 95 6 basis basis NOUN ajst-9436 95 7 are be AUX ajst-9436 95 8 worse bad ADJ ajst-9436 95 9 than than ADP ajst-9436 95 10 those those PRON ajst-9436 95 11 using use VERB ajst-9436 95 12 sym5 sym5 PROPN ajst-9436 95 13 , , PUNCT ajst-9436 95 14 while while SCONJ ajst-9436 95 15 the the DET ajst-9436 95 16 pixel pixel NOUN ajst-9436 95 17 distribution distribution NOUN ajst-9436 95 18 before before ADP ajst-9436 95 19 and and CCONJ ajst-9436 95 20 after after ADP ajst-9436 95 21 denoising denoise VERB ajst-9436 95 22 using use VERB ajst-9436 95 23 coif3 coif3 NOUN ajst-9436 95 24 wavelet wavelet NOUN ajst-9436 95 25 basis basis NOUN ajst-9436 95 26 is be AUX ajst-9436 95 27 much much ADV ajst-9436 95 28 different different ADJ ajst-9436 95 29 . . PUNCT ajst-9436 96 1 4 4 X ajst-9436 96 2 . . X ajst-9436 96 3 conclusion conclusion NOUN ajst-9436 96 4 with with ADP ajst-9436 96 5 the the DET ajst-9436 96 6 rapid rapid ADJ ajst-9436 96 7 development development NOUN ajst-9436 96 8 of of ADP ajst-9436 96 9 modern modern ADJ ajst-9436 96 10 technology technology NOUN ajst-9436 96 11 , , PUNCT ajst-9436 96 12 image image NOUN ajst-9436 96 13 processing processing NOUN ajst-9436 96 14 technology technology NOUN ajst-9436 96 15 is be AUX ajst-9436 96 16 becoming become VERB ajst-9436 96 17 increasingly increasingly ADV ajst-9436 96 18 important important ADJ ajst-9436 96 19 . . PUNCT ajst-9436 97 1 denoising denoise VERB ajst-9436 97 2 images image NOUN ajst-9436 97 3 is be AUX ajst-9436 97 4 an an DET ajst-9436 97 5 important important ADJ ajst-9436 97 6 part part NOUN ajst-9436 97 7 of of ADP ajst-9436 97 8 image image NOUN ajst-9436 97 9 processing processing NOUN ajst-9436 97 10 . . PUNCT ajst-9436 98 1 images image NOUN ajst-9436 98 2 are be AUX ajst-9436 98 3 always always ADV ajst-9436 98 4 subject subject ADJ ajst-9436 98 5 to to ADP ajst-9436 98 6 interference interference NOUN ajst-9436 98 7 from from ADP ajst-9436 98 8 various various ADJ ajst-9436 98 9 signals signal NOUN ajst-9436 98 10 17 17 NUM ajst-9436 98 11 during during ADP ajst-9436 98 12 transmission transmission NOUN ajst-9436 98 13 , , PUNCT ajst-9436 98 14 and and CCONJ ajst-9436 98 15 at at ADP ajst-9436 98 16 this this DET ajst-9436 98 17 point point NOUN ajst-9436 98 18 , , PUNCT ajst-9436 98 19 they they PRON ajst-9436 98 20 become become VERB ajst-9436 98 21 noisy noisy ADJ ajst-9436 98 22 images image NOUN ajst-9436 98 23 . . PUNCT ajst-9436 99 1 image image NOUN ajst-9436 99 2 denoising denoising NOUN ajst-9436 99 3 is be AUX ajst-9436 99 4 a a DET ajst-9436 99 5 technique technique NOUN ajst-9436 99 6 for for ADP ajst-9436 99 7 removing remove VERB ajst-9436 99 8 the the DET ajst-9436 99 9 interference interference NOUN ajst-9436 99 10 noise noise NOUN ajst-9436 99 11 from from ADP ajst-9436 99 12 noisy noisy ADJ ajst-9436 99 13 images image NOUN ajst-9436 99 14 . . PUNCT ajst-9436 100 1 compared compare VERB ajst-9436 100 2 with with ADP ajst-9436 100 3 classical classical ADJ ajst-9436 100 4 denoising denoising NOUN ajst-9436 100 5 algorithms algorithm NOUN ajst-9436 100 6 , , PUNCT ajst-9436 100 7 wavelet wavelet NOUN ajst-9436 100 8 denoising denoise VERB ajst-9436 100 9 algorithms algorithm NOUN ajst-9436 100 10 can can AUX ajst-9436 100 11 better well ADV ajst-9436 100 12 preserve preserve VERB ajst-9436 100 13 image image NOUN ajst-9436 100 14 information information NOUN ajst-9436 100 15 in in ADP ajst-9436 100 16 the the DET ajst-9436 100 17 high high ADJ ajst-9436 100 18 - - PUNCT ajst-9436 100 19 frequency frequency NOUN ajst-9436 100 20 field field NOUN ajst-9436 100 21 , , PUNCT ajst-9436 100 22 and and CCONJ ajst-9436 100 23 do do AUX ajst-9436 100 24 not not PART ajst-9436 100 25 remove remove VERB ajst-9436 100 26 high high ADJ ajst-9436 100 27 - - PUNCT ajst-9436 100 28 frequency frequency NOUN ajst-9436 100 29 noise noise NOUN ajst-9436 100 30 and and CCONJ ajst-9436 100 31 information information NOUN ajst-9436 100 32 together together ADV ajst-9436 100 33 . . PUNCT ajst-9436 101 1 this this DET ajst-9436 101 2 article article NOUN ajst-9436 101 3 introduces introduce VERB ajst-9436 101 4 the the DET ajst-9436 101 5 wavelet wavelet NOUN ajst-9436 101 6 threshold threshold NOUN ajst-9436 101 7 algorithm algorithm NOUN ajst-9436 101 8 and and CCONJ ajst-9436 101 9 uses use VERB ajst-9436 101 10 matlab matlab PROPN ajst-9436 101 11 simulation simulation NOUN ajst-9436 101 12 to to PART ajst-9436 101 13 compare compare VERB ajst-9436 101 14 the the DET ajst-9436 101 15 denoising denoising NOUN ajst-9436 101 16 effects effect NOUN ajst-9436 101 17 of of ADP ajst-9436 101 18 the the DET ajst-9436 101 19 denoised denoise VERB ajst-9436 101 20 images image NOUN ajst-9436 101 21 obtained obtain VERB ajst-9436 101 22 by by ADP ajst-9436 101 23 using use VERB ajst-9436 101 24 fixed fix VERB ajst-9436 101 25 threshold threshold NOUN ajst-9436 101 26 method method NOUN ajst-9436 101 27 , , PUNCT ajst-9436 101 28 function function NOUN ajst-9436 101 29 method method NOUN ajst-9436 101 30 , , PUNCT ajst-9436 101 31 and and CCONJ ajst-9436 101 32 triple triple ADJ ajst-9436 101 33 standard standard ADJ ajst-9436 101 34 deviation deviation NOUN ajst-9436 101 35 method method NOUN ajst-9436 101 36 to to PART ajst-9436 101 37 obtain obtain VERB ajst-9436 101 38 the the DET ajst-9436 101 39 threshold threshold NOUN ajst-9436 101 40 , , PUNCT ajst-9436 101 41 haar haar PROPN ajst-9436 101 42 , , PUNCT ajst-9436 101 43 sym5 sym5 PROPN ajst-9436 101 44 , , PUNCT ajst-9436 101 45 db3 db3 PROPN ajst-9436 101 46 , , PUNCT ajst-9436 101 47 and and CCONJ ajst-9436 101 48 coif3 coif3 VERB ajst-9436 101 49 wavelet wavelet NOUN ajst-9436 101 50 bases basis NOUN ajst-9436 101 51 . . PUNCT ajst-9436 102 1 the the DET ajst-9436 102 2 denoising denoise VERB ajst-9436 102 3 effect effect NOUN ajst-9436 102 4 of of ADP ajst-9436 102 5 the the DET ajst-9436 102 6 function function NOUN ajst-9436 102 7 method method NOUN ajst-9436 102 8 and and CCONJ ajst-9436 102 9 the the DET ajst-9436 102 10 fixed fix VERB ajst-9436 102 11 threshold threshold NOUN ajst-9436 102 12 method method NOUN ajst-9436 102 13 is be AUX ajst-9436 102 14 not not PART ajst-9436 102 15 much much ADV ajst-9436 102 16 different different ADJ ajst-9436 102 17 , , PUNCT ajst-9436 102 18 and and CCONJ ajst-9436 102 19 the the DET ajst-9436 102 20 denoising denoise VERB ajst-9436 102 21 effect effect NOUN ajst-9436 102 22 of of ADP ajst-9436 102 23 the the DET ajst-9436 102 24 triple triple ADJ ajst-9436 102 25 standard standard ADJ ajst-9436 102 26 deviation deviation NOUN ajst-9436 102 27 method method NOUN ajst-9436 102 28 is be AUX ajst-9436 102 29 the the DET ajst-9436 102 30 worst bad ADJ ajst-9436 102 31 , , PUNCT ajst-9436 102 32 and and CCONJ ajst-9436 102 33 the the DET ajst-9436 102 34 image image NOUN ajst-9436 102 35 is be AUX ajst-9436 102 36 also also ADV ajst-9436 102 37 unclear unclear ADJ ajst-9436 102 38 . . PUNCT ajst-9436 103 1 the the DET ajst-9436 103 2 denoising denoise VERB ajst-9436 103 3 effect effect NOUN ajst-9436 103 4 using use VERB ajst-9436 103 5 haar haar PROPN ajst-9436 103 6 wavelet wavelet NOUN ajst-9436 103 7 basis basis NOUN ajst-9436 103 8 is be AUX ajst-9436 103 9 better well ADJ ajst-9436 103 10 than than ADP ajst-9436 103 11 using use VERB ajst-9436 103 12 sym5 sym5 PROPN ajst-9436 103 13 , , PUNCT ajst-9436 103 14 db3 db3 PROPN ajst-9436 103 15 , , PUNCT ajst-9436 103 16 and and CCONJ ajst-9436 103 17 coif3 coif3 VERB ajst-9436 103 18 wavelet wavelet NOUN ajst-9436 103 19 basis basis NOUN ajst-9436 103 20 . . PUNCT ajst-9436 104 1 furthermore furthermore ADV ajst-9436 104 2 , , PUNCT ajst-9436 104 3 it it PRON ajst-9436 104 4 was be AUX ajst-9436 104 5 concluded conclude VERB ajst-9436 104 6 that that SCONJ ajst-9436 104 7 using use VERB ajst-9436 104 8 a a DET ajst-9436 104 9 fixed fix VERB ajst-9436 104 10 threshold threshold NOUN ajst-9436 104 11 method method NOUN ajst-9436 104 12 , , PUNCT ajst-9436 104 13 the the DET ajst-9436 104 14 denoising denoise VERB ajst-9436 104 15 effect effect NOUN ajst-9436 104 16 of of ADP ajst-9436 104 17 haar haar PROPN ajst-9436 104 18 wavelet wavelet NOUN ajst-9436 104 19 basis basis NOUN ajst-9436 104 20 is be AUX ajst-9436 104 21 better well ADJ ajst-9436 104 22 . . PUNCT ajst-9436 105 1 references reference NOUN ajst-9436 105 2 [ [ X ajst-9436 105 3 1 1 X ajst-9436 105 4 ] ] X ajst-9436 105 5 gunawan gunawan PROPN ajst-9436 105 6 d. d. PROPN ajst-9436 105 7 denoising denoise VERB ajst-9436 105 8 images image NOUN ajst-9436 105 9 using use VERB ajst-9436 105 10 wavelet wavelet NOUN ajst-9436 105 11 transform transform NOUN ajst-9436 105 12 [ [ X ajst-9436 105 13 a a X ajst-9436 105 14 ] ] X ajst-9436 105 15 . . PUNCT ajst-9436 106 1 in in ADP ajst-9436 106 2 : : PUNCT ajst-9436 106 3 proceedings proceeding NOUN ajst-9436 106 4 of of ADP ajst-9436 106 5 the the DET ajst-9436 106 6 ieee ieee PROPN ajst-9436 106 7 pacific pacific PROPN ajst-9436 106 8 rim rim PROPN ajst-9436 106 9 conference conference NOUN ajst-9436 106 10 on on ADP ajst-9436 106 11 communications communication NOUN ajst-9436 106 12 , , PUNCT ajst-9436 106 13 computers computer NOUN ajst-9436 106 14 and and CCONJ ajst-9436 106 15 signal signal VERB ajst-9436 106 16 processing[c processing[c PROPN ajst-9436 106 17 ] ] PUNCT ajst-9436 106 18 . . PUNCT ajst-9436 107 1 victoria victoria PROPN ajst-9436 107 2 bc bc PROPN ajst-9436 107 3 , , PUNCT ajst-9436 107 4 usa usa PROPN ajst-9436 107 5 , , PUNCT ajst-9436 107 6 1999:83 1999:83 NUM ajst-9436 107 7 - - SYM ajst-9436 107 8 85 85 NUM ajst-9436 107 9 . . PUNCT ajst-9436 108 1 [ [ X ajst-9436 108 2 2 2 X ajst-9436 108 3 ] ] X ajst-9436 108 4 ching ching NOUN ajst-9436 108 5 p p PROPN ajst-9436 108 6 c c NOUN ajst-9436 108 7 , , PUNCT ajst-9436 108 8 so so ADV ajst-9436 108 9 h h NOUN ajst-9436 108 10 c c NOUN ajst-9436 108 11 , , PUNCT ajst-9436 108 12 wu wu PROPN ajst-9436 108 13 s s PROPN ajst-9436 108 14 q. q. NOUN ajst-9436 108 15 on on ADP ajst-9436 108 16 wavelet wavelet NOUN ajst-9436 108 17 denoising denoising NOUN ajst-9436 108 18 and and CCONJ ajst-9436 108 19 its its PRON ajst-9436 108 20 applications application NOUN ajst-9436 108 21 to to ADP ajst-9436 108 22 tim tim PROPN ajst-9436 108 23 e e PROPN ajst-9436 108 24 delay delay NOUN ajst-9436 108 25 estimation[j estimation[j PROPN ajst-9436 108 26 ] ] PUNCT ajst-9436 108 27 . . PUNCT ajst-9436 109 1 ieee ieee PROPN ajst-9436 109 2 trans trans PROPN ajst-9436 109 3 . . PROPN ajst-9436 109 4 signal signal PROPN ajst-9436 109 5 processing processing NOUN ajst-9436 109 6 , , PUNCT ajst-9436 109 7 1999:2879 1999:2879 NUM ajst-9436 109 8 - - SYM ajst-9436 109 9 2882 2882 NUM ajst-9436 109 10 . . PUNCT ajst-9436 110 1 [ [ X ajst-9436 110 2 3 3 X ajst-9436 110 3 ] ] X ajst-9436 110 4 jansen jansen PROPN ajst-9436 110 5 m m PROPN ajst-9436 110 6 , , PUNCT ajst-9436 110 7 bultheel bultheel VERB ajst-9436 110 8 a. a. NOUN ajst-9436 110 9 multiple multiple PROPN ajst-9436 110 10 wavelet wavelet NOUN ajst-9436 110 11 thres thre NOUN ajst-9436 110 12 hold hold VERB ajst-9436 110 13 estimation estimation NOUN ajst-9436 110 14 by by ADP ajst-9436 110 15 generalized generalized ADJ ajst-9436 110 16 cross cross NOUN ajst-9436 110 17 validation validation NOUN ajst-9436 110 18 for for ADP ajst-9436 110 19 images image NOUN ajst-9436 110 20 with with ADP ajst-9436 110 21 correlated correlate VERB ajst-9436 110 22 noise[j noise[j NOUN ajst-9436 110 23 ] ] PUNCT ajst-9436 110 24 . . PUNCT ajst-9436 111 1 ieee ieee PROPN ajst-9436 111 2 trans trans PROPN ajst-9436 111 3 . . PUNCT ajst-9436 111 4 image image NOUN ajst-9436 111 5 processing processing NOUN ajst-9436 111 6 , , PUNCT ajst-9436 111 7 1999 1999 NUM ajst-9436 111 8 , , PUNCT ajst-9436 111 9 （ （ PUNCT ajst-9436 111 10 8οΌ‰:947 8οΌ‰:947 NUM ajst-9436 111 11 - - SYM ajst-9436 111 12 953 953 NUM ajst-9436 111 13 . . PUNCT ajst-9436 112 1 [ [ X ajst-9436 112 2 4 4 X ajst-9436 112 3 ] ] X ajst-9436 112 4 krim krim PROPN ajst-9436 112 5 h h PROPN ajst-9436 112 6 , , PUNCT ajst-9436 112 7 schick schick PROPN ajst-9436 112 8 i i PROPN ajst-9436 112 9 c. c. PROPN ajst-9436 112 10 minimaxdes minimaxde VERB ajst-9436 112 11 cription cription NOUN ajst-9436 112 12 length length NOUN ajst-9436 112 13 for for ADP ajst-9436 112 14 signal signal ADJ ajst-9436 112 15 denoising denoising NOUN ajst-9436 112 16 and and CCONJ ajst-9436 112 17 optimized optimize VERB ajst-9436 112 18 represent represent PROPN ajst-9436 112 19 ation[j ation[j PROPN ajst-9436 112 20 ] ] PUNCT ajst-9436 112 21 . . PUNCT ajst-9436 113 1 ieee ieee PROPN ajst-9436 113 2 trans trans PROPN ajst-9436 113 3 . . PUNCT ajst-9436 114 1 informati informati PROPN ajst-9436 114 2 on on ADP ajst-9436 114 3 theory theory NOUN ajst-9436 114 4 , , PUNCT ajst-9436 114 5 1999:898 1999:898 NUM ajst-9436 114 6 - - SYM ajst-9436 114 7 908 908 NUM ajst-9436 114 8 . . PUNCT ajst-9436 115 1 [ [ X ajst-9436 115 2 5 5 NUM ajst-9436 115 3 ] ] PUNCT ajst-9436 115 4 xu xu PROPN ajst-9436 115 5 yansun yansun PROPN ajst-9436 115 6 , , PUNCT ajst-9436 115 7 weaver weaver PROPN ajst-9436 115 8 j j PROPN ajst-9436 115 9 b b PROPN ajst-9436 115 10 , , PUNCT ajst-9436 115 11 healy healy PROPN ajst-9436 115 12 m m PROPN ajst-9436 115 13 j j PROPN ajst-9436 115 14 etal etal PROPN ajst-9436 115 15 . . PUNCT ajst-9436 116 1 wavelet wavelet NOUN ajst-9436 116 2 transform transform NOUN ajst-9436 116 3 domain domain NOUN ajst-9436 116 4 filters filter NOUN ajst-9436 116 5 : : PUNCT ajst-9436 116 6 a a DET ajst-9436 116 7 s s X ajst-9436 116 8 patially patially ADV ajst-9436 116 9 selective selective ADJ ajst-9436 116 10 noise noise NOUN ajst-9436 116 11 filtration filtration NOUN ajst-9436 116 12 technique[j technique[j PROPN ajst-9436 116 13 ] ] PUNCT ajst-9436 116 14 . . PUNCT ajst-9436 117 1 ieee ieee PROPN ajst-9436 117 2 trans trans PROPN ajst-9436 117 3 . . PUNCT ajst-9436 117 4 image image NOUN ajst-9436 117 5 processing processing NOUN ajst-9436 117 6 , , PUNCT ajst-9436 117 7 1994:743 1994:743 NUM ajst-9436 117 8 - - PUNCT ajst-9436 117 9 758 758 NUM ajst-9436 117 10 . . PUNCT