id sid tid token lemma pos ispiv-90 1 1 14th 14th ADJ ispiv-90 1 2 international international ADJ ispiv-90 1 3 symposium symposium NOUN ispiv-90 1 4 on on ADP ispiv-90 1 5 particle particle NOUN ispiv-90 1 6 image image NOUN ispiv-90 1 7 velocimetry velocimetry NOUN ispiv-90 1 8 – – PUNCT ispiv-90 1 9 ispiv ispiv NOUN ispiv-90 1 10 2021 2021 NUM ispiv-90 1 11 august august PROPN ispiv-90 1 12 1 1 NUM ispiv-90 1 13 - - SYM ispiv-90 1 14 5 5 NUM ispiv-90 1 15 , , PUNCT ispiv-90 1 16 2021 2021 NUM ispiv-90 1 17 approximate approximate ADJ ispiv-90 1 18 bayesian bayesian NOUN ispiv-90 1 19 framework framework NOUN ispiv-90 1 20 for for ADP ispiv-90 1 21 3d 3d NOUN ispiv-90 1 22 reconstruction reconstruction NOUN ispiv-90 1 23 in in ADP ispiv-90 1 24 a a DET ispiv-90 1 25 volumetric volumetric NOUN ispiv-90 1 26 piv piv NOUN ispiv-90 1 27 / / SYM ispiv-90 1 28 ptv ptv PROPN ispiv-90 1 29 measurement measurement NOUN ispiv-90 1 30 sayantan sayantan PROPN ispiv-90 1 31 bhattacharya bhattacharya PROPN ispiv-90 1 32 * * PROPN ispiv-90 1 33 , , PUNCT ispiv-90 1 34 ilias ilias PROPN ispiv-90 1 35 bilionis bilionis NOUN ispiv-90 1 36 and and CCONJ ispiv-90 1 37 pavlos pavlo NOUN ispiv-90 1 38 p. p. PROPN ispiv-90 1 39 vlachos vlachos ADP ispiv-90 1 40 school school NOUN ispiv-90 1 41 of of ADP ispiv-90 1 42 mechanical mechanical ADJ ispiv-90 1 43 engineering engineering NOUN ispiv-90 1 44 , , PUNCT ispiv-90 1 45 purdue purdue PROPN ispiv-90 1 46 university university NOUN ispiv-90 1 47 , , PUNCT ispiv-90 1 48 west west PROPN ispiv-90 1 49 lafayette lafayette PROPN ispiv-90 1 50 , , PUNCT ispiv-90 1 51 in in ADP ispiv-90 1 52 47907 47907 NUM ispiv-90 1 53 , , PUNCT ispiv-90 1 54 usa usa PROPN ispiv-90 1 55 * * PUNCT ispiv-90 1 56 bhattac3@purdue.edu bhattac3@purdue.edu PROPN ispiv-90 1 57 abstract abstract ADJ ispiv-90 1 58 non non ADJ ispiv-90 1 59 - - ADJ ispiv-90 1 60 invasive invasive ADJ ispiv-90 1 61 flow flow NOUN ispiv-90 1 62 velocity velocity NOUN ispiv-90 1 63 measurement measurement NOUN ispiv-90 1 64 techniques technique NOUN ispiv-90 1 65 like like ADP ispiv-90 1 66 volumetric volumetric NOUN ispiv-90 1 67 particle particle NOUN ispiv-90 1 68 image image NOUN ispiv-90 1 69 velocimetry velocimetry NOUN ispiv-90 1 70 ( ( PUNCT ispiv-90 1 71 piv piv NOUN ispiv-90 1 72 ) ) PUNCT ispiv-90 1 73 ( ( PUNCT ispiv-90 1 74 elsinga elsinga ADV ispiv-90 1 75 et et PROPN ispiv-90 1 76 al al PROPN ispiv-90 1 77 . . PROPN ispiv-90 1 78 , , PUNCT ispiv-90 1 79 2006 2006 NUM ispiv-90 1 80 ; ; PUNCT ispiv-90 1 81 adrian adrian PROPN ispiv-90 1 82 and and CCONJ ispiv-90 1 83 westerweel westerweel NOUN ispiv-90 1 84 , , PUNCT ispiv-90 1 85 2011 2011 NUM ispiv-90 1 86 ) ) PUNCT ispiv-90 1 87 and and CCONJ ispiv-90 1 88 particle particle NOUN ispiv-90 1 89 tracking tracking NOUN ispiv-90 1 90 velocimetry velocimetry NOUN ispiv-90 1 91 ( ( PUNCT ispiv-90 1 92 ptv ptv INTJ ispiv-90 1 93 ) ) PUNCT ispiv-90 1 94 ( ( PUNCT ispiv-90 1 95 maas maas PROPN ispiv-90 1 96 , , PUNCT ispiv-90 1 97 gruen gruen PROPN ispiv-90 1 98 and and CCONJ ispiv-90 1 99 papantoniou papantoniou NOUN ispiv-90 1 100 , , PUNCT ispiv-90 1 101 1993 1993 NUM ispiv-90 1 102 ) ) PUNCT ispiv-90 1 103 use use VERB ispiv-90 1 104 multi multi ADJ ispiv-90 1 105 - - ADJ ispiv-90 1 106 camera camera ADJ ispiv-90 1 107 projections projection NOUN ispiv-90 1 108 of of ADP ispiv-90 1 109 tracer tracer NOUN ispiv-90 1 110 particle particle NOUN ispiv-90 1 111 motion motion NOUN ispiv-90 1 112 to to PART ispiv-90 1 113 resolve resolve VERB ispiv-90 1 114 threedimensional threedimensional ADJ ispiv-90 1 115 flow flow NOUN ispiv-90 1 116 structures structure NOUN ispiv-90 1 117 . . PUNCT ispiv-90 2 1 a a DET ispiv-90 2 2 key key ADJ ispiv-90 2 3 step step NOUN ispiv-90 2 4 in in ADP ispiv-90 2 5 the the DET ispiv-90 2 6 measurement measurement NOUN ispiv-90 2 7 chain chain NOUN ispiv-90 2 8 involves involve VERB ispiv-90 2 9 reconstructing reconstruct VERB ispiv-90 2 10 the the DET ispiv-90 2 11 3d 3d NUM ispiv-90 2 12 intensity intensity NOUN ispiv-90 2 13 field field NOUN ispiv-90 2 14 ( ( PUNCT ispiv-90 2 15 piv piv NOUN ispiv-90 2 16 ) ) PUNCT ispiv-90 2 17 or or CCONJ ispiv-90 2 18 particle particle NOUN ispiv-90 2 19 positions position NOUN ispiv-90 2 20 ( ( PUNCT ispiv-90 2 21 ptv ptv INTJ ispiv-90 2 22 ) ) PUNCT ispiv-90 2 23 given give VERB ispiv-90 2 24 the the DET ispiv-90 2 25 projected project VERB ispiv-90 2 26 images image NOUN ispiv-90 2 27 and and CCONJ ispiv-90 2 28 known know VERB ispiv-90 2 29 camera camera NOUN ispiv-90 2 30 correspondence correspondence NOUN ispiv-90 2 31 . . PUNCT ispiv-90 3 1 due due ADP ispiv-90 3 2 to to ADP ispiv-90 3 3 limited limited ADJ ispiv-90 3 4 number number NOUN ispiv-90 3 5 of of ADP ispiv-90 3 6 camera camera NOUN ispiv-90 3 7 - - PUNCT ispiv-90 3 8 views view NOUN ispiv-90 3 9 the the DET ispiv-90 3 10 projected project VERB ispiv-90 3 11 particle particle NOUN ispiv-90 3 12 images image NOUN ispiv-90 3 13 are be AUX ispiv-90 3 14 non non ADJ ispiv-90 3 15 - - ADJ ispiv-90 3 16 unique unique ADJ ispiv-90 3 17 making make VERB ispiv-90 3 18 the the DET ispiv-90 3 19 inverse inverse NOUN ispiv-90 3 20 problem problem NOUN ispiv-90 3 21 of of ADP ispiv-90 3 22 volumetric volumetric ADJ ispiv-90 3 23 reconstruction reconstruction NOUN ispiv-90 3 24 underdetermined underdetermine VERB ispiv-90 3 25 . . PUNCT ispiv-90 4 1 moreover moreover ADV ispiv-90 4 2 , , PUNCT ispiv-90 4 3 higher high ADJ ispiv-90 4 4 particle particle NOUN ispiv-90 4 5 concentration concentration NOUN ispiv-90 4 6 ( ( PUNCT ispiv-90 4 7 > > X ispiv-90 4 8 0.05 0.05 NUM ispiv-90 4 9 ppp ppp NOUN ispiv-90 4 10 ) ) PUNCT ispiv-90 4 11 increases increase VERB ispiv-90 4 12 erroneous erroneous ADJ ispiv-90 4 13 reconstructions reconstruction NOUN ispiv-90 4 14 or or CCONJ ispiv-90 4 15 β€œ " PUNCT ispiv-90 4 16 ghost ghost NOUN ispiv-90 4 17 ” " PUNCT ispiv-90 4 18 particles particle NOUN ispiv-90 4 19 and and CCONJ ispiv-90 4 20 decreases decrease VERB ispiv-90 4 21 reconstruction reconstruction NOUN ispiv-90 4 22 accuracy accuracy NOUN ispiv-90 4 23 . . PUNCT ispiv-90 5 1 current current ADJ ispiv-90 5 2 reconstruction reconstruction NOUN ispiv-90 5 3 methods method NOUN ispiv-90 5 4 either either CCONJ ispiv-90 5 5 use use VERB ispiv-90 5 6 voxel voxel PROPN ispiv-90 5 7 - - PUNCT ispiv-90 5 8 based base VERB ispiv-90 5 9 representation representation NOUN ispiv-90 5 10 for for ADP ispiv-90 5 11 intensity intensity NOUN ispiv-90 5 12 reconstruction reconstruction NOUN ispiv-90 5 13 ( ( PUNCT ispiv-90 5 14 e.g. e.g. ADV ispiv-90 5 15 mart mart NOUN ispiv-90 5 16 ( ( PUNCT ispiv-90 5 17 elsinga elsinga X ispiv-90 5 18 et et PROPN ispiv-90 5 19 al al PROPN ispiv-90 5 20 . . PROPN ispiv-90 5 21 , , PUNCT ispiv-90 5 22 2006 2006 NUM ispiv-90 5 23 ) ) PUNCT ispiv-90 5 24 ) ) PUNCT ispiv-90 5 25 or or CCONJ ispiv-90 5 26 a a DET ispiv-90 5 27 particle particle NOUN ispiv-90 5 28 - - PUNCT ispiv-90 5 29 based base VERB ispiv-90 5 30 approach approach NOUN ispiv-90 5 31 ( ( PUNCT ispiv-90 5 32 e.g. e.g. ADV ispiv-90 5 33 ipr ipr PROPN ispiv-90 5 34 ( ( PUNCT ispiv-90 5 35 wieneke wieneke ADJ ispiv-90 5 36 , , PUNCT ispiv-90 5 37 2013 2013 NUM ispiv-90 5 38 ) ) PUNCT ispiv-90 5 39 ) ) PUNCT ispiv-90 5 40 for for ADP ispiv-90 5 41 3d 3d NUM ispiv-90 5 42 position position NOUN ispiv-90 5 43 estimation estimation NOUN ispiv-90 5 44 . . PUNCT ispiv-90 6 1 the the DET ispiv-90 6 2 former former ADJ ispiv-90 6 3 method method NOUN ispiv-90 6 4 is be AUX ispiv-90 6 5 computationally computationally ADV ispiv-90 6 6 intensive intensive ADJ ispiv-90 6 7 and and CCONJ ispiv-90 6 8 has have VERB ispiv-90 6 9 a a DET ispiv-90 6 10 lesser less ADJ ispiv-90 6 11 positional positional ADJ ispiv-90 6 12 accuracy accuracy NOUN ispiv-90 6 13 due due ADP ispiv-90 6 14 to to ADP ispiv-90 6 15 stretched stretch VERB ispiv-90 6 16 shape shape NOUN ispiv-90 6 17 of of ADP ispiv-90 6 18 the the DET ispiv-90 6 19 reconstructed reconstructed ADJ ispiv-90 6 20 particle particle NOUN ispiv-90 6 21 along along ADP ispiv-90 6 22 the the DET ispiv-90 6 23 line line NOUN ispiv-90 6 24 of of ADP ispiv-90 6 25 sight sight NOUN ispiv-90 6 26 . . PUNCT ispiv-90 7 1 the the DET ispiv-90 7 2 latter latter ADJ ispiv-90 7 3 compromises compromise VERB ispiv-90 7 4 triangulation triangulation NOUN ispiv-90 7 5 accuracy accuracy NOUN ispiv-90 7 6 ( ( PUNCT ispiv-90 7 7 maas maas PROPN ispiv-90 7 8 , , PUNCT ispiv-90 7 9 gruen gruen PROPN ispiv-90 7 10 and and CCONJ ispiv-90 7 11 papantoniou papantoniou NOUN ispiv-90 7 12 , , PUNCT ispiv-90 7 13 1993 1993 NUM ispiv-90 7 14 ) ) PUNCT ispiv-90 7 15 due due ADP ispiv-90 7 16 to to ADP ispiv-90 7 17 overlapping overlap VERB ispiv-90 7 18 particle particle NOUN ispiv-90 7 19 images image NOUN ispiv-90 7 20 for for ADP ispiv-90 7 21 higher high ADJ ispiv-90 7 22 particle particle NOUN ispiv-90 7 23 concentrations concentration NOUN ispiv-90 7 24 . . PUNCT ispiv-90 8 1 thus thus ADV ispiv-90 8 2 , , PUNCT ispiv-90 8 3 each each DET ispiv-90 8 4 method method NOUN ispiv-90 8 5 has have VERB ispiv-90 8 6 its its PRON ispiv-90 8 7 own own ADJ ispiv-90 8 8 challenges challenge NOUN ispiv-90 8 9 and and CCONJ ispiv-90 8 10 the the DET ispiv-90 8 11 error error NOUN ispiv-90 8 12 in in ADP ispiv-90 8 13 3d 3d PROPN ispiv-90 8 14 reconstruction reconstruction NOUN ispiv-90 8 15 significantly significantly ADV ispiv-90 8 16 affects affect VERB ispiv-90 8 17 the the DET ispiv-90 8 18 accuracy accuracy NOUN ispiv-90 8 19 of of ADP ispiv-90 8 20 the the DET ispiv-90 8 21 velocity velocity NOUN ispiv-90 8 22 measurement measurement NOUN ispiv-90 8 23 . . PUNCT ispiv-90 9 1 though though ADV ispiv-90 9 2 , , PUNCT ispiv-90 9 3 other other ADJ ispiv-90 9 4 methods method NOUN ispiv-90 9 5 like like ADP ispiv-90 9 6 maximum maximum ADJ ispiv-90 9 7 - - PUNCT ispiv-90 9 8 a a DET ispiv-90 9 9 - - PUNCT ispiv-90 9 10 posteriori posteriori NOUN ispiv-90 9 11 ( ( PUNCT ispiv-90 9 12 map map NOUN ispiv-90 9 13 ) ) PUNCT ispiv-90 9 14 estimation estimation NOUN ispiv-90 9 15 have have AUX ispiv-90 9 16 been be AUX ispiv-90 9 17 previously previously ADV ispiv-90 9 18 developed develop VERB ispiv-90 9 19 ( ( PUNCT ispiv-90 9 20 levitan levitan PROPN ispiv-90 9 21 and and CCONJ ispiv-90 9 22 herman herman PROPN ispiv-90 9 23 , , PUNCT ispiv-90 9 24 1987 1987 NUM ispiv-90 9 25 ; ; PUNCT ispiv-90 9 26 bouman bouman NOUN ispiv-90 9 27 and and CCONJ ispiv-90 9 28 sauer sauer NOUN ispiv-90 9 29 , , PUNCT ispiv-90 9 30 1996 1996 NUM ispiv-90 9 31 ) ) PUNCT ispiv-90 9 32 for for ADP ispiv-90 9 33 computed compute VERB ispiv-90 9 34 tomography tomography NOUN ispiv-90 9 35 data datum NOUN ispiv-90 9 36 , , PUNCT ispiv-90 9 37 it it PRON ispiv-90 9 38 has have AUX ispiv-90 9 39 not not PART ispiv-90 9 40 been be AUX ispiv-90 9 41 explored explore VERB ispiv-90 9 42 for for ADP ispiv-90 9 43 piv/ piv/ NOUN ispiv-90 9 44 ptv ptv PROPN ispiv-90 9 45 3d 3d PROPN ispiv-90 9 46 reconstruction reconstruction NOUN ispiv-90 9 47 . . PUNCT ispiv-90 10 1 here here ADV ispiv-90 10 2 , , PUNCT ispiv-90 10 3 we we PRON ispiv-90 10 4 use use VERB ispiv-90 10 5 a a DET ispiv-90 10 6 map map NOUN ispiv-90 10 7 estimation estimation NOUN ispiv-90 10 8 framework framework NOUN ispiv-90 10 9 to to PART ispiv-90 10 10 model model VERB ispiv-90 10 11 and and CCONJ ispiv-90 10 12 solve solve VERB ispiv-90 10 13 the the DET ispiv-90 10 14 inverse inverse NOUN ispiv-90 10 15 problem problem NOUN ispiv-90 10 16 . . PUNCT ispiv-90 11 1 the the DET ispiv-90 11 2 cost cost NOUN ispiv-90 11 3 function function NOUN ispiv-90 11 4 is be AUX ispiv-90 11 5 optimized optimize VERB ispiv-90 11 6 using use VERB ispiv-90 11 7 a a DET ispiv-90 11 8 stochastic stochastic ADJ ispiv-90 11 9 gradient gradient NOUN ispiv-90 11 10 ascent ascent NOUN ispiv-90 11 11 ( ( PUNCT ispiv-90 11 12 sga sga PROPN ispiv-90 11 13 ) ) PUNCT ispiv-90 11 14 algorithm algorithm NOUN ispiv-90 11 15 . . PUNCT ispiv-90 12 1 such such DET ispiv-90 12 2 an an DET ispiv-90 12 3 optimization optimization NOUN ispiv-90 12 4 can can AUX ispiv-90 12 5 converge converge VERB ispiv-90 12 6 to to ADP ispiv-90 12 7 a a DET ispiv-90 12 8 better well ADJ ispiv-90 12 9 local local ADJ ispiv-90 12 10 maximum maximum NOUN ispiv-90 12 11 and and CCONJ ispiv-90 12 12 also also ADV ispiv-90 12 13 use use VERB ispiv-90 12 14 smaller small ADJ ispiv-90 12 15 image image NOUN ispiv-90 12 16 patches patch NOUN ispiv-90 12 17 for for ADP ispiv-90 12 18 efficient efficient ADJ ispiv-90 12 19 iterations iteration NOUN ispiv-90 12 20 . . PUNCT ispiv-90 13 1 our our PRON ispiv-90 13 2 method method NOUN ispiv-90 13 3 uses use VERB ispiv-90 13 4 a a DET ispiv-90 13 5 uniform uniform ADJ ispiv-90 13 6 prior prior ADJ ispiv-90 13 7 model model NOUN ispiv-90 13 8 for for ADP ispiv-90 13 9 the the DET ispiv-90 13 10 unknown unknown ADJ ispiv-90 13 11 3d 3d NUM ispiv-90 13 12 particle particle NOUN ispiv-90 13 13 positions position NOUN ispiv-90 13 14 ( ( PUNCT ispiv-90 13 15 π‘₯ π‘₯ NOUN ispiv-90 13 16 ) ) PUNCT ispiv-90 13 17 and and CCONJ ispiv-90 13 18 a a DET ispiv-90 13 19 forward forward ADJ ispiv-90 13 20 model model NOUN ispiv-90 13 21 ( ( PUNCT ispiv-90 13 22 𝑓 𝑓 X ispiv-90 13 23 ) ) PUNCT ispiv-90 13 24 of of ADP ispiv-90 13 25 the the DET ispiv-90 13 26 measurement measurement NOUN ispiv-90 13 27 chain chain NOUN ispiv-90 13 28 to to PART ispiv-90 13 29 estimate estimate VERB ispiv-90 13 30 the the DET ispiv-90 13 31 posterior posterior ADJ ispiv-90 13 32 distribution distribution NOUN ispiv-90 13 33 . . PUNCT ispiv-90 14 1 here here ADV ispiv-90 14 2 , , PUNCT ispiv-90 14 3 we we PRON ispiv-90 14 4 assume assume VERB ispiv-90 14 5 a a DET ispiv-90 14 6 uniform uniform ADJ ispiv-90 14 7 probability probability NOUN ispiv-90 14 8 distribution distribution NOUN ispiv-90 14 9 , , PUNCT ispiv-90 14 10 π‘₯𝑖 π‘₯𝑖 ADP ispiv-90 14 11 ∼ ∼ NOUN ispiv-90 14 12 π‘ˆ([π‘₯π‘šπ‘–π‘› π‘ˆ([π‘₯π‘šπ‘–π‘› NUM ispiv-90 14 13 , , PUNCT ispiv-90 14 14 π‘₯π‘šπ‘Žπ‘₯ π‘₯π‘šπ‘Žπ‘₯ NOUN ispiv-90 14 15 ] ] PUNCT ispiv-90 14 16 ) ) PUNCT ispiv-90 14 17 , , PUNCT ispiv-90 14 18 for for ADP ispiv-90 14 19 each each PRON ispiv-90 14 20 of of ADP ispiv-90 14 21 the the DET ispiv-90 14 22 𝑁 𝑁 PROPN ispiv-90 14 23 particle particle NOUN ispiv-90 14 24 positions position NOUN ispiv-90 14 25 within within ADP ispiv-90 14 26 the the DET ispiv-90 14 27 measurement measurement NOUN ispiv-90 14 28 domain domain NOUN ispiv-90 14 29 bounds bound NOUN ispiv-90 14 30 , , PUNCT ispiv-90 14 31 π‘₯π‘šπ‘–π‘› π‘₯π‘šπ‘–π‘› NOUN ispiv-90 14 32 and and CCONJ ispiv-90 14 33 π‘₯π‘šπ‘Žπ‘₯. π‘₯π‘šπ‘Žπ‘₯. VERB ispiv-90 14 34 the the DET ispiv-90 14 35 observations observation NOUN ispiv-90 14 36 𝑦1:𝑀 𝑦1:𝑀 NUM ispiv-90 15 1 = = SYM ispiv-90 15 2 ( ( PUNCT ispiv-90 15 3 𝑦1 𝑦1 PROPN ispiv-90 15 4 , , PUNCT ispiv-90 15 5 … … PUNCT ispiv-90 15 6 , , PUNCT ispiv-90 15 7 𝑦𝑀 𝑦𝑀 NOUN ispiv-90 15 8 ) ) PUNCT ispiv-90 15 9 are be AUX ispiv-90 15 10 recorded record VERB ispiv-90 15 11 images image NOUN ispiv-90 15 12 from from ADP ispiv-90 15 13 m m NOUN ispiv-90 15 14 cameras camera NOUN ispiv-90 15 15 with with ADP ispiv-90 15 16 image image NOUN ispiv-90 15 17 size size NOUN ispiv-90 15 18 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN ispiv-90 15 19 Γ— Γ— NOUN ispiv-90 15 20 𝑃𝑐 𝑃𝑐 PROPN ispiv-90 15 21 pixels pixel NOUN ispiv-90 15 22 . . PUNCT ispiv-90 16 1 we we PRON ispiv-90 16 2 define define VERB ispiv-90 16 3 the the DET ispiv-90 16 4 row row NOUN ispiv-90 16 5 and and CCONJ ispiv-90 16 6 column column NOUN ispiv-90 16 7 position position NOUN ispiv-90 16 8 of of ADP ispiv-90 16 9 a a DET ispiv-90 16 10 pixel pixel NOUN ispiv-90 16 11 using use VERB ispiv-90 16 12 π‘Ÿ π‘Ÿ NOUN ispiv-90 16 13 and and CCONJ ispiv-90 16 14 𝑐 𝑐 NOUN ispiv-90 16 15 respectively respectively ADV ispiv-90 16 16 . . PUNCT ispiv-90 17 1 the the DET ispiv-90 17 2 camera camera NOUN ispiv-90 17 3 calibration calibration NOUN ispiv-90 17 4 function function NOUN ispiv-90 17 5 ( ( PUNCT ispiv-90 17 6 β„‚π‘Ÿ β„‚π‘Ÿ PROPN ispiv-90 17 7 π‘š(π‘₯ π‘š(π‘₯ NOUN ispiv-90 17 8 ) ) PUNCT ispiv-90 17 9 , , PUNCT ispiv-90 17 10 ℂ𝑐 ℂ𝑐 PROPN ispiv-90 17 11 π‘š(π‘₯ π‘š(π‘₯ NOUN ispiv-90 17 12 ) ) PUNCT ispiv-90 17 13 ) ) PUNCT ispiv-90 17 14 provides provide VERB ispiv-90 17 15 the the DET ispiv-90 17 16 forward forward ADJ ispiv-90 17 17 mapping mapping NOUN ispiv-90 17 18 from from ADP ispiv-90 17 19 3d 3d NUM ispiv-90 17 20 particle particle NOUN ispiv-90 17 21 space space NOUN ispiv-90 17 22 ( ( PUNCT ispiv-90 17 23 π‘₯1:𝑁 π‘₯1:𝑁 NOUN ispiv-90 17 24 ) ) PUNCT ispiv-90 17 25 to to ADP ispiv-90 17 26 the the DET ispiv-90 17 27 image image NOUN ispiv-90 17 28 pixel pixel PROPN ispiv-90 17 29 coordinates coordinate NOUN ispiv-90 17 30 ( ( PUNCT ispiv-90 17 31 π‘Ÿ π‘Ÿ NOUN ispiv-90 17 32 , , PUNCT ispiv-90 17 33 𝑐 𝑐 NOUN ispiv-90 17 34 ) ) PUNCT ispiv-90 17 35 for for ADP ispiv-90 17 36 π‘šth π‘šth NOUN ispiv-90 17 37 camera camera NOUN ispiv-90 17 38 . . PUNCT ispiv-90 18 1 thus thus ADV ispiv-90 18 2 , , PUNCT ispiv-90 18 3 the the DET ispiv-90 18 4 projected project VERB ispiv-90 18 5 pixel pixel NOUN ispiv-90 18 6 intensity intensity NOUN ispiv-90 18 7 using use VERB ispiv-90 18 8 the the DET ispiv-90 18 9 forward forward ADJ ispiv-90 18 10 model model NOUN ispiv-90 18 11 is be AUX ispiv-90 18 12 written write VERB ispiv-90 18 13 as as ADP ispiv-90 18 14 , , PUNCT ispiv-90 18 15 π‘“π‘šπ‘Ÿπ‘(π‘₯1:𝑁 π‘“π‘šπ‘Ÿπ‘(π‘₯1:𝑁 PROPN ispiv-90 18 16 ) ) PUNCT ispiv-90 18 17 = = SYM ispiv-90 19 1 𝐼0 𝐼0 PROPN ispiv-90 19 2 2πœ‹πœŽπ‘‘ 2πœ‹πœŽπ‘‘ NUM ispiv-90 19 3 2βˆ‘ 2βˆ‘ NUM ispiv-90 19 4 exp⁑ exp⁑ X ispiv-90 20 1 ( ( PUNCT ispiv-90 20 2 βˆ’ βˆ’ PROPN ispiv-90 20 3 ( ( PUNCT ispiv-90 20 4 π‘Ÿβˆ’β„‚π‘Ÿ π‘Ÿβˆ’β„‚π‘Ÿ NOUN ispiv-90 20 5 π‘š(π‘₯𝑝 π‘š(π‘₯𝑝 NOUN ispiv-90 20 6 ) ) PUNCT ispiv-90 20 7 ) ) PUNCT ispiv-90 20 8 2 2 NUM ispiv-90 20 9 + + NOUN ispiv-90 20 10 ( ( PUNCT ispiv-90 20 11 π‘βˆ’β„‚π‘ π‘βˆ’β„‚π‘ NOUN ispiv-90 20 12 π‘š(π‘₯𝑝 π‘š(π‘₯𝑝 NOUN ispiv-90 20 13 ) ) PUNCT ispiv-90 20 14 ) ) PUNCT ispiv-90 20 15 2 2 NUM ispiv-90 20 16 2πœŽπ‘‘ 2πœŽπ‘‘ NOUN ispiv-90 20 17 2 2 NUM ispiv-90 20 18 ) ) PUNCT ispiv-90 20 19 𝑁 𝑁 PROPN ispiv-90 20 20 𝑝=1 𝑝=1 NOUN ispiv-90 20 21 ( ( PUNCT ispiv-90 20 22 1 1 NUM ispiv-90 20 23 ) ) PUNCT ispiv-90 20 24 . . PUNCT ispiv-90 21 1 in in ADP ispiv-90 21 2 equation equation NOUN ispiv-90 21 3 ( ( PUNCT ispiv-90 21 4 1 1 NUM ispiv-90 21 5 ) ) PUNCT ispiv-90 21 6 , , PUNCT ispiv-90 21 7 𝐼0 𝐼0 PROPN ispiv-90 21 8 , , PUNCT ispiv-90 21 9 πœŽπ‘‘ πœŽπ‘‘ PROPN ispiv-90 21 10 are be AUX ispiv-90 21 11 image image NOUN ispiv-90 21 12 parameters parameter NOUN ispiv-90 21 13 estimated estimate VERB ispiv-90 21 14 from from ADP ispiv-90 21 15 the the DET ispiv-90 21 16 optical optical ADJ ispiv-90 21 17 transfer transfer NOUN ispiv-90 21 18 function function NOUN ispiv-90 21 19 ( ( PUNCT ispiv-90 21 20 otf otf PROPN ispiv-90 21 21 ) ) PUNCT ispiv-90 21 22 of of ADP ispiv-90 21 23 particle particle NOUN ispiv-90 21 24 images image NOUN ispiv-90 21 25 . . PUNCT ispiv-90 22 1 the the DET ispiv-90 22 2 likelihood likelihood NOUN ispiv-90 22 3 of of ADP ispiv-90 22 4 all all DET ispiv-90 22 5 observed observed ADJ ispiv-90 22 6 data datum NOUN ispiv-90 22 7 conditioned condition VERB ispiv-90 22 8 on on ADP ispiv-90 22 9 particle particle NOUN ispiv-90 22 10 positions position NOUN ispiv-90 22 11 is be AUX ispiv-90 22 12 : : PUNCT ispiv-90 22 13 𝑝(𝑦1:𝑀| 𝑝(𝑦1:𝑀| VERB ispiv-90 22 14 π‘₯1:𝑁 π‘₯1:𝑁 NOUN ispiv-90 22 15 ) ) PUNCT ispiv-90 22 16 = = SYM ispiv-90 23 1 ∏ ∏ PROPN ispiv-90 23 2 ∏ ∏ PROPN ispiv-90 23 3 ∏ ∏ PROPN ispiv-90 23 4 𝑝(π‘¦π‘šπ‘Ÿπ‘|π‘“π‘šπ‘Ÿπ‘(π‘₯1:𝑁 𝑝(π‘¦π‘šπ‘Ÿπ‘|π‘“π‘šπ‘Ÿπ‘(π‘₯1:𝑁 NOUN ispiv-90 23 5 ) ) PUNCT ispiv-90 23 6 ) ) PUNCT ispiv-90 24 1 𝑃𝑐 𝑃𝑐 PROPN ispiv-90 24 2 𝑐=1 𝑐=1 PROPN ispiv-90 24 3 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN ispiv-90 24 4 π‘Ÿ=1 π‘Ÿ=1 PROPN ispiv-90 24 5 𝑀 𝑀 PROPN ispiv-90 24 6 π‘š=1 π‘š=1 X ispiv-90 24 7 ( ( PUNCT ispiv-90 24 8 2 2 NUM ispiv-90 24 9 ) ) PUNCT ispiv-90 24 10 , , PUNCT ispiv-90 24 11 where where SCONJ ispiv-90 24 12 , , PUNCT ispiv-90 24 13 each each DET ispiv-90 24 14 pixel pixel NOUN ispiv-90 24 15 is be AUX ispiv-90 24 16 considered consider VERB ispiv-90 24 17 as as ADP ispiv-90 24 18 an an DET ispiv-90 24 19 independent independent ADJ ispiv-90 24 20 observation observation NOUN ispiv-90 24 21 . . PUNCT ispiv-90 25 1 assuming assume VERB ispiv-90 25 2 a a DET ispiv-90 25 3 log log NOUN ispiv-90 25 4 - - PUNCT ispiv-90 25 5 normal normal ADJ ispiv-90 25 6 noise noise NOUN ispiv-90 25 7 the the DET ispiv-90 25 8 individual individual ADJ ispiv-90 25 9 pixel pixel NOUN ispiv-90 25 10 likelihood likelihood NOUN ispiv-90 25 11 is be AUX ispiv-90 25 12 defined define VERB ispiv-90 25 13 as as ADP ispiv-90 25 14 a a DET ispiv-90 25 15 normal normal ADJ ispiv-90 25 16 distribution distribution NOUN ispiv-90 25 17 𝒩(log 𝒩(log PUNCT ispiv-90 25 18 π‘¦π‘šπ‘Ÿπ‘| π‘¦π‘šπ‘Ÿπ‘| ADP ispiv-90 25 19 log log PROPN ispiv-90 25 20 π‘“π‘šπ‘Ÿπ‘(π‘₯1:𝑁 π‘“π‘šπ‘Ÿπ‘(π‘₯1:𝑁 PROPN ispiv-90 25 21 ) ) PUNCT ispiv-90 25 22 , , PUNCT ispiv-90 25 23 𝜎 𝜎 PROPN ispiv-90 25 24 2 2 NUM ispiv-90 25 25 ) ) PUNCT ispiv-90 25 26 , , PUNCT ispiv-90 25 27 with with ADP ispiv-90 25 28 noise noise NOUN ispiv-90 25 29 variance variance NOUN ispiv-90 25 30 𝜎2.the 𝜎2.the DET ispiv-90 25 31 posterior posterior ADJ ispiv-90 25 32 𝑝(π‘₯1:𝑁 𝑝(π‘₯1:𝑁 PROPN ispiv-90 25 33 | | NOUN ispiv-90 25 34 𝑦1:𝑀 𝑦1:𝑀 NUM ispiv-90 25 35 ) ) PUNCT ispiv-90 25 36 is be AUX ispiv-90 25 37 expressed express VERB ispiv-90 25 38 as as ADP ispiv-90 25 39 a a DET ispiv-90 25 40 function function NOUN ispiv-90 25 41 of of ADP ispiv-90 25 42 the the DET ispiv-90 25 43 likelihood likelihood NOUN ispiv-90 25 44 and and CCONJ ispiv-90 25 45 the the DET ispiv-90 25 46 prior prior ADJ ispiv-90 25 47 and and CCONJ ispiv-90 25 48 finally finally ADV ispiv-90 25 49 , , PUNCT ispiv-90 25 50 the the DET ispiv-90 25 51 map map NOUN ispiv-90 25 52 estimate estimate NOUN ispiv-90 25 53 is be AUX ispiv-90 25 54 given give VERB ispiv-90 25 55 by by ADP ispiv-90 25 56 π‘₯𝑀𝐴𝑃 π‘₯𝑀𝐴𝑃 PROPN ispiv-90 26 1 = = PUNCT ispiv-90 26 2 argmax[log(𝑝(π‘₯1:𝑁 argmax[log(𝑝(π‘₯1:𝑁 PROPN ispiv-90 26 3 | | NOUN ispiv-90 26 4 𝑦1:𝑀 𝑦1:𝑀 NUM ispiv-90 26 5 ) ) PUNCT ispiv-90 26 6 ) ) PUNCT ispiv-90 26 7 , , PUNCT ispiv-90 26 8 which which PRON ispiv-90 26 9 we we PRON ispiv-90 26 10 solve solve VERB ispiv-90 26 11 using use VERB ispiv-90 26 12 stochastic stochastic ADJ ispiv-90 26 13 gradient gradient ADJ ispiv-90 26 14 descent descent NOUN ispiv-90 26 15 . . PUNCT ispiv-90 27 1 this this DET ispiv-90 27 2 framework framework NOUN ispiv-90 27 3 was be AUX ispiv-90 27 4 implemented implement VERB ispiv-90 27 5 using use VERB ispiv-90 27 6 pytorch pytorch NOUN ispiv-90 27 7 with with ADP ispiv-90 27 8 tensor tensor NOUN ispiv-90 27 9 formulations formulation NOUN ispiv-90 27 10 . . PUNCT ispiv-90 28 1 the the DET ispiv-90 28 2 adam adam PROPN ispiv-90 28 3 optimizer optimizer NOUN ispiv-90 28 4 was be AUX ispiv-90 28 5 used use VERB ispiv-90 28 6 with with ADP ispiv-90 28 7 varying vary VERB ispiv-90 28 8 learning learning NOUN ispiv-90 28 9 rates rate NOUN ispiv-90 28 10 ( ( PUNCT ispiv-90 28 11 0.001 0.001 NUM ispiv-90 28 12 to to PART ispiv-90 28 13 0.1 0.1 NUM ispiv-90 28 14 ) ) PUNCT ispiv-90 28 15 and and CCONJ ispiv-90 28 16 a a DET ispiv-90 28 17 polynomial polynomial ADJ ispiv-90 28 18 calibration calibration NOUN ispiv-90 28 19 function function NOUN ispiv-90 28 20 was be AUX ispiv-90 28 21 used use VERB ispiv-90 28 22 to to PART ispiv-90 28 23 build build VERB ispiv-90 28 24 the the DET ispiv-90 28 25 forward forward ADJ ispiv-90 28 26 model model NOUN ispiv-90 28 27 . . PUNCT ispiv-90 29 1 synthetic synthetic ADJ ispiv-90 29 2 piv piv NOUN ispiv-90 29 3 images image NOUN ispiv-90 29 4 of of ADP ispiv-90 29 5 size size NOUN ispiv-90 29 6 64x64 64x64 NUM ispiv-90 29 7 pixels pixel NOUN ispiv-90 29 8 were be AUX ispiv-90 29 9 generated generate VERB ispiv-90 29 10 with with ADP ispiv-90 29 11 varying vary VERB ispiv-90 29 12 particle particle NOUN ispiv-90 29 13 concentrations concentration NOUN ispiv-90 29 14 ( ( PUNCT ispiv-90 29 15 0.01 0.01 NUM ispiv-90 29 16 to to PART ispiv-90 29 17 0.1 0.1 NUM ispiv-90 29 18 ppp ppp NOUN ispiv-90 29 19 ) ) PUNCT ispiv-90 29 20 to to PART ispiv-90 29 21 validate validate VERB ispiv-90 29 22 the the DET ispiv-90 29 23 algorithm algorithm NOUN ispiv-90 29 24 . . PUNCT ispiv-90 30 1 figure figure NOUN ispiv-90 30 2 1a 1a NOUN ispiv-90 30 3 ) ) PUNCT ispiv-90 30 4 shows show VERB ispiv-90 30 5 better well ADJ ispiv-90 30 6 convergence convergence NOUN ispiv-90 30 7 with with ADP ispiv-90 30 8 increasing increase VERB ispiv-90 30 9 learning learning NOUN ispiv-90 30 10 rate rate NOUN ispiv-90 30 11 . . PUNCT ispiv-90 31 1 however however ADV ispiv-90 31 2 , , PUNCT ispiv-90 31 3 the the DET ispiv-90 31 4 initial initial ADJ ispiv-90 31 5 results result NOUN ispiv-90 31 6 with with ADP ispiv-90 31 7 random random ADJ ispiv-90 31 8 initializations initialization NOUN ispiv-90 31 9 show show VERB ispiv-90 31 10 lower low ADJ ispiv-90 31 11 particle particle NOUN ispiv-90 31 12 yield yield NOUN ispiv-90 31 13 across across ADP ispiv-90 31 14 the the DET ispiv-90 31 15 range range NOUN ispiv-90 31 16 of of ADP ispiv-90 31 17 seeding seed VERB ispiv-90 31 18 density density NOUN ispiv-90 31 19 ( ( PUNCT ispiv-90 31 20 figure figure NOUN ispiv-90 31 21 1b 1b NUM ispiv-90 31 22 ) ) PUNCT ispiv-90 31 23 ) ) PUNCT ispiv-90 31 24 . . PUNCT ispiv-90 32 1 the the DET ispiv-90 32 2 rms rm NOUN ispiv-90 32 3 error error NOUN ispiv-90 32 4 for for ADP ispiv-90 32 5 the the DET ispiv-90 32 6 valid valid ADJ ispiv-90 32 7 measurements measurement NOUN ispiv-90 32 8 were be AUX ispiv-90 32 9 close close ADJ ispiv-90 32 10 to to PART ispiv-90 32 11 0.2 0.2 NUM ispiv-90 32 12 pixels pixel NOUN ispiv-90 32 13 . . PUNCT ispiv-90 33 1 the the DET ispiv-90 33 2 sga sga PROPN ispiv-90 33 3 algorithm algorithm NOUN ispiv-90 33 4 was be AUX ispiv-90 33 5 also also ADV ispiv-90 33 6 tested test VERB ispiv-90 33 7 with with ADP ispiv-90 33 8 different different ADJ ispiv-90 33 9 batch batch NOUN ispiv-90 33 10 size size NOUN ispiv-90 33 11 , , PUNCT ispiv-90 33 12 and and CCONJ ispiv-90 33 13 suitable suitable ADJ ispiv-90 33 14 learning learning NOUN ispiv-90 33 15 rates rate NOUN ispiv-90 33 16 . . PUNCT ispiv-90 34 1 lower low ADJ ispiv-90 34 2 batch batch NOUN ispiv-90 34 3 size size NOUN ispiv-90 34 4 showed show VERB ispiv-90 34 5 higher high ADJ ispiv-90 34 6 oscillations oscillation NOUN ispiv-90 34 7 ( ( PUNCT ispiv-90 34 8 figure figure NOUN ispiv-90 34 9 1c 1c NOUN ispiv-90 34 10 ) ) PUNCT ispiv-90 34 11 ) ) PUNCT ispiv-90 34 12 in in ADP ispiv-90 34 13 mean mean ADJ ispiv-90 34 14 square square ADJ ispiv-90 34 15 loss loss NOUN ispiv-90 34 16 as as SCONJ ispiv-90 34 17 smaller small ADJ ispiv-90 34 18 random random ADJ ispiv-90 34 19 patches patch NOUN ispiv-90 34 20 from from ADP ispiv-90 34 21 different different ADJ ispiv-90 34 22 camera camera NOUN ispiv-90 34 23 images image NOUN ispiv-90 34 24 did do AUX ispiv-90 34 25 not not PART ispiv-90 34 26 contain contain VERB ispiv-90 34 27 the the DET ispiv-90 34 28 projections projection NOUN ispiv-90 34 29 of of ADP ispiv-90 34 30 the the DET ispiv-90 34 31 same same ADJ ispiv-90 34 32 particles particle NOUN ispiv-90 34 33 . . PUNCT ispiv-90 35 1 subsequently subsequently ADV ispiv-90 35 2 , , PUNCT ispiv-90 35 3 random random ADJ ispiv-90 35 4 image image NOUN ispiv-90 35 5 patches patch NOUN ispiv-90 35 6 corresponding correspond VERB ispiv-90 35 7 to to ADP ispiv-90 35 8 the the DET ispiv-90 35 9 same same ADJ ispiv-90 35 10 sub sub NOUN ispiv-90 35 11 - - NOUN ispiv-90 35 12 volume volume NOUN ispiv-90 35 13 resulted result VERB ispiv-90 35 14 in in ADP ispiv-90 35 15 better well ADJ ispiv-90 35 16 convergence convergence NOUN ispiv-90 35 17 . . PUNCT ispiv-90 36 1 the the DET ispiv-90 36 2 reconstructed reconstructed ADJ ispiv-90 36 3 positions position NOUN ispiv-90 36 4 for for ADP ispiv-90 36 5 a a DET ispiv-90 36 6 random random ADJ ispiv-90 36 7 initialization initialization NOUN ispiv-90 36 8 tended tend VERB ispiv-90 36 9 to to PART ispiv-90 36 10 get get AUX ispiv-90 36 11 trapped trap VERB ispiv-90 36 12 in in ADP ispiv-90 36 13 local local ADJ ispiv-90 36 14 minima minima NOUN ispiv-90 36 15 and and CCONJ ispiv-90 36 16 to to PART ispiv-90 36 17 avoid avoid VERB ispiv-90 36 18 such such ADJ ispiv-90 36 19 cases case NOUN ispiv-90 36 20 perturbed perturb VERB ispiv-90 36 21 stochastic stochastic ADJ ispiv-90 36 22 gradient gradient NOUN ispiv-90 36 23 ascent ascent NOUN ispiv-90 36 24 ( ( PUNCT ispiv-90 36 25 psga psga NOUN ispiv-90 36 26 ) ) PUNCT ispiv-90 36 27 ( ( PUNCT ispiv-90 36 28 jin jin NOUN ispiv-90 36 29 et et PROPN ispiv-90 36 30 al al PROPN ispiv-90 36 31 . . PROPN ispiv-90 36 32 , , PUNCT ispiv-90 36 33 2021 2021 NUM ispiv-90 36 34 ) ) PUNCT ispiv-90 36 35 was be AUX ispiv-90 36 36 also also ADV ispiv-90 36 37 implemented implement VERB ispiv-90 36 38 . . PUNCT ispiv-90 37 1 every every DET ispiv-90 37 2 100 100 NUM ispiv-90 37 3 iterations iteration NOUN ispiv-90 37 4 if if SCONJ ispiv-90 37 5 the the DET ispiv-90 37 6 change change NOUN ispiv-90 37 7 in in ADP ispiv-90 37 8 loss loss NOUN ispiv-90 37 9 function function NOUN ispiv-90 37 10 was be AUX ispiv-90 37 11 less less ADJ ispiv-90 37 12 than than ADP ispiv-90 37 13 1 1 NUM ispiv-90 37 14 % % NOUN ispiv-90 37 15 , , PUNCT ispiv-90 37 16 the the DET ispiv-90 37 17 gradients gradient NOUN ispiv-90 37 18 were be AUX ispiv-90 37 19 perturbed perturb VERB ispiv-90 37 20 by by ADP ispiv-90 37 21 a a DET ispiv-90 37 22 zero zero NUM ispiv-90 37 23 mean mean NOUN ispiv-90 37 24 normal normal ADJ ispiv-90 37 25 distribution distribution NOUN ispiv-90 37 26 with with ADP ispiv-90 37 27 varying vary VERB ispiv-90 37 28 standard standard ADJ ispiv-90 37 29 deviations deviation NOUN ispiv-90 37 30 . . PUNCT ispiv-90 38 1 the the DET ispiv-90 38 2 methodology methodology NOUN ispiv-90 38 3 is be AUX ispiv-90 38 4 also also ADV ispiv-90 38 5 tested test VERB ispiv-90 38 6 for for ADP ispiv-90 38 7 triangulation triangulation NOUN ispiv-90 38 8 - - PUNCT ispiv-90 38 9 based base VERB ispiv-90 38 10 initializations initialization NOUN ispiv-90 38 11 and and CCONJ ispiv-90 38 12 for for ADP ispiv-90 38 13 random random ADJ ispiv-90 38 14 corresponding corresponding ADJ ispiv-90 38 15 patches patch NOUN ispiv-90 38 16 for for ADP ispiv-90 38 17 each each DET ispiv-90 38 18 camera camera NOUN ispiv-90 38 19 image image NOUN ispiv-90 38 20 . . PUNCT ispiv-90 39 1 furthermore furthermore ADV ispiv-90 39 2 , , PUNCT ispiv-90 39 3 the the DET ispiv-90 39 4 sensitivity sensitivity NOUN ispiv-90 39 5 of of ADP ispiv-90 39 6 the the DET ispiv-90 39 7 optimization optimization NOUN ispiv-90 39 8 framework framework NOUN ispiv-90 39 9 to to ADP ispiv-90 39 10 different different ADJ ispiv-90 39 11 image image NOUN ispiv-90 39 12 noise noise NOUN ispiv-90 39 13 models model NOUN ispiv-90 39 14 ( ( PUNCT ispiv-90 39 15 e.g. e.g. ADV ispiv-90 39 16 , , PUNCT ispiv-90 39 17 bernoulli bernoulli NOUN ispiv-90 39 18 or or CCONJ ispiv-90 39 19 poisson poisson NOUN ispiv-90 39 20 distributions distribution NOUN ispiv-90 39 21 ) ) PUNCT ispiv-90 39 22 is be AUX ispiv-90 39 23 explored explore VERB ispiv-90 39 24 . . PUNCT ispiv-90 40 1 finally finally ADV ispiv-90 40 2 , , PUNCT ispiv-90 40 3 we we PRON ispiv-90 40 4 compare compare VERB ispiv-90 40 5 the the DET ispiv-90 40 6 current current ADJ ispiv-90 40 7 estimation estimation NOUN ispiv-90 40 8 of of ADP ispiv-90 40 9 the the DET ispiv-90 40 10 reconstruction reconstruction NOUN ispiv-90 40 11 error error NOUN ispiv-90 40 12 with with ADP ispiv-90 40 13 existing exist VERB ispiv-90 40 14 methods method NOUN ispiv-90 40 15 for for ADP ispiv-90 40 16 a a DET ispiv-90 40 17 synthetic synthetic ADJ ispiv-90 40 18 vortex vortex NOUN ispiv-90 40 19 ring ring NOUN ispiv-90 40 20 case case NOUN ispiv-90 40 21 . . PUNCT ispiv-90 41 1 figure figure NOUN ispiv-90 41 2 1 1 NUM ispiv-90 41 3 : : PUNCT ispiv-90 41 4 subplot subplot NOUN ispiv-90 41 5 ( ( PUNCT ispiv-90 41 6 a a X ispiv-90 41 7 ) ) PUNCT ispiv-90 41 8 shows show VERB ispiv-90 41 9 algorithm algorithm NOUN ispiv-90 41 10 convergence convergence NOUN ispiv-90 41 11 for for ADP ispiv-90 41 12 different different ADJ ispiv-90 41 13 learning learning NOUN ispiv-90 41 14 rate rate NOUN ispiv-90 41 15 for for ADP ispiv-90 41 16 a a DET ispiv-90 41 17 whole whole ADJ ispiv-90 41 18 image image NOUN ispiv-90 41 19 optimization optimization NOUN ispiv-90 41 20 . . PUNCT ispiv-90 42 1 subplot subplot NOUN ispiv-90 42 2 ( ( PUNCT ispiv-90 42 3 b b NOUN ispiv-90 42 4 ) ) PUNCT ispiv-90 42 5 shows show VERB ispiv-90 42 6 rms rm NOUN ispiv-90 42 7 error error NOUN ispiv-90 42 8 in in ADP ispiv-90 42 9 reconstructed reconstructed ADJ ispiv-90 42 10 positions position NOUN ispiv-90 42 11 for for ADP ispiv-90 42 12 valid valid ADJ ispiv-90 42 13 measurements measurement NOUN ispiv-90 42 14 and and CCONJ ispiv-90 42 15 % % NOUN ispiv-90 42 16 of of ADP ispiv-90 42 17 valid valid ADJ ispiv-90 42 18 measurements measurement NOUN ispiv-90 42 19 or or CCONJ ispiv-90 42 20 particle particle NOUN ispiv-90 42 21 yield yield NOUN ispiv-90 42 22 for for ADP ispiv-90 42 23 different different ADJ ispiv-90 42 24 particle particle NOUN ispiv-90 42 25 concentrations concentration NOUN ispiv-90 42 26 in in ADP ispiv-90 42 27 particles particle NOUN ispiv-90 42 28 per per ADP ispiv-90 42 29 pixel pixel NOUN ispiv-90 42 30 ( ( PUNCT ispiv-90 42 31 ppp ppp PROPN ispiv-90 42 32 ) ) PUNCT ispiv-90 42 33 . . PUNCT ispiv-90 43 1 subplot subplot NOUN ispiv-90 43 2 ( ( PUNCT ispiv-90 43 3 c c X ispiv-90 43 4 ) ) PUNCT ispiv-90 43 5 shows show VERB ispiv-90 43 6 variation variation NOUN ispiv-90 43 7 in in ADP ispiv-90 43 8 mean mean ADJ ispiv-90 43 9 square square ADJ ispiv-90 43 10 loss loss NOUN ispiv-90 43 11 for for ADP ispiv-90 43 12 the the DET ispiv-90 43 13 cost cost NOUN ispiv-90 43 14 function function NOUN ispiv-90 43 15 for for ADP ispiv-90 43 16 different different ADJ ispiv-90 43 17 batch batch NOUN ispiv-90 43 18 size size NOUN ispiv-90 43 19 . . PUNCT ispiv-90 44 1 references reference NOUN ispiv-90 44 2 adrian adrian PROPN ispiv-90 44 3 , , PUNCT ispiv-90 44 4 r. r. PROPN ispiv-90 44 5 j. j. PROPN ispiv-90 44 6 and and CCONJ ispiv-90 44 7 westerweel westerweel PROPN ispiv-90 44 8 , , PUNCT ispiv-90 44 9 j. j. PROPN ispiv-90 44 10 ( ( PUNCT ispiv-90 44 11 2011 2011 NUM ispiv-90 44 12 ) ) PUNCT ispiv-90 44 13 particle particle NOUN ispiv-90 44 14 image image NOUN ispiv-90 44 15 velocimetry velocimetry NOUN ispiv-90 44 16 , , PUNCT ispiv-90 44 17 cambridge cambridge PROPN ispiv-90 44 18 aerospace aerospace PROPN ispiv-90 44 19 series series PROPN ispiv-90 44 20 . . PUNCT ispiv-90 45 1 bouman bouman PROPN ispiv-90 45 2 , , PUNCT ispiv-90 45 3 c. c. PROPN ispiv-90 45 4 a. a. PROPN ispiv-90 45 5 and and CCONJ ispiv-90 45 6 sauer sauer PROPN ispiv-90 45 7 , , PUNCT ispiv-90 45 8 k. k. PROPN ispiv-90 45 9 ( ( PUNCT ispiv-90 45 10 1996 1996 NUM ispiv-90 45 11 ) ) PUNCT ispiv-90 46 1 β€˜ ' PUNCT ispiv-90 46 2 a a DET ispiv-90 46 3 unified unified ADJ ispiv-90 46 4 approach approach NOUN ispiv-90 46 5 to to ADP ispiv-90 46 6 statistical statistical ADJ ispiv-90 46 7 tomography tomography NOUN ispiv-90 46 8 using use VERB ispiv-90 46 9 coordinate coordinate NOUN ispiv-90 46 10 descent descent NOUN ispiv-90 46 11 optimization optimization NOUN ispiv-90 46 12 ’ ' PUNCT ispiv-90 46 13 , , PUNCT ispiv-90 46 14 ieee ieee NOUN ispiv-90 46 15 transactions transaction NOUN ispiv-90 46 16 on on ADP ispiv-90 46 17 image image NOUN ispiv-90 46 18 processing processing NOUN ispiv-90 46 19 , , PUNCT ispiv-90 46 20 5(3 5(3 NUM ispiv-90 46 21 ) ) PUNCT ispiv-90 46 22 , , PUNCT ispiv-90 46 23 pp pp ADP ispiv-90 46 24 . . PUNCT ispiv-90 47 1 480–492 480–492 NUM ispiv-90 47 2 . . PUNCT ispiv-90 48 1 doi doi NOUN ispiv-90 48 2 : : PUNCT ispiv-90 48 3 10.1109/83.491321 10.1109/83.491321 NUM ispiv-90 48 4 . . X ispiv-90 48 5 elsinga elsinga PROPN ispiv-90 48 6 , , PUNCT ispiv-90 48 7 g. g. PROPN ispiv-90 48 8 e. e. PROPN ispiv-90 48 9 et et PROPN ispiv-90 48 10 al al PROPN ispiv-90 48 11 . . PROPN ispiv-90 48 12 ( ( PUNCT ispiv-90 48 13 2006 2006 NUM ispiv-90 48 14 ) ) PUNCT ispiv-90 48 15 β€˜ ' PUNCT ispiv-90 48 16 tomographic tomographic ADJ ispiv-90 48 17 particle particle NOUN ispiv-90 48 18 image image NOUN ispiv-90 48 19 velocimetry velocimetry NOUN ispiv-90 48 20 ’ ' PUNCT ispiv-90 48 21 , , PUNCT ispiv-90 48 22 experiments experiment NOUN ispiv-90 48 23 in in ADP ispiv-90 48 24 fluids fluid NOUN ispiv-90 48 25 , , PUNCT ispiv-90 48 26 41(6 41(6 NOUN ispiv-90 48 27 ) ) PUNCT ispiv-90 48 28 , , PUNCT ispiv-90 48 29 pp pp ADP ispiv-90 48 30 . . PUNCT ispiv-90 49 1 933–947 933–947 NUM ispiv-90 49 2 . . PUNCT ispiv-90 50 1 doi doi NOUN ispiv-90 50 2 : : PUNCT ispiv-90 50 3 10.1007 10.1007 NUM ispiv-90 50 4 / / SYM ispiv-90 50 5 s00348 s00348 NOUN ispiv-90 50 6 - - PUNCT ispiv-90 50 7 006 006 NUM ispiv-90 50 8 - - PUNCT ispiv-90 50 9 0212 0212 NUM ispiv-90 50 10 - - PUNCT ispiv-90 50 11 z. z. PROPN ispiv-90 50 12 jin jin PROPN ispiv-90 50 13 , , PUNCT ispiv-90 50 14 c. c. PROPN ispiv-90 50 15 et et PROPN ispiv-90 50 16 al al PROPN ispiv-90 50 17 . . PROPN ispiv-90 50 18 ( ( PUNCT ispiv-90 50 19 2021 2021 NUM ispiv-90 50 20 ) ) PUNCT ispiv-90 50 21 β€˜ ' PUNCT ispiv-90 50 22 on on ADP ispiv-90 50 23 nonconvex nonconvex NOUN ispiv-90 50 24 optimization optimization NOUN ispiv-90 50 25 for for ADP ispiv-90 50 26 machine machine NOUN ispiv-90 50 27 learning learning NOUN ispiv-90 50 28 : : PUNCT ispiv-90 51 1 gradients gradient NOUN ispiv-90 51 2 , , PUNCT ispiv-90 51 3 stochasticity stochasticity NOUN ispiv-90 51 4 , , PUNCT ispiv-90 51 5 and and CCONJ ispiv-90 51 6 saddle saddle NOUN ispiv-90 51 7 points point NOUN ispiv-90 51 8 ’ ' PUNCT ispiv-90 51 9 , , PUNCT ispiv-90 51 10 j. j. PROPN ispiv-90 51 11 acm acm PROPN ispiv-90 51 12 . . PUNCT ispiv-90 52 1 new new PROPN ispiv-90 52 2 york york PROPN ispiv-90 52 3 , , PUNCT ispiv-90 52 4 ny ny PROPN ispiv-90 52 5 , , PUNCT ispiv-90 52 6 usa usa PROPN ispiv-90 52 7 : : PUNCT ispiv-90 52 8 association association NOUN ispiv-90 52 9 for for ADP ispiv-90 52 10 computing computing NOUN ispiv-90 52 11 machinery machinery NOUN ispiv-90 52 12 , , PUNCT ispiv-90 52 13 68(2 68(2 NOUN ispiv-90 52 14 ) ) PUNCT ispiv-90 52 15 . . PUNCT ispiv-90 53 1 doi doi NOUN ispiv-90 53 2 : : PUNCT ispiv-90 53 3 10.1145/3418526 10.1145/3418526 NUM ispiv-90 53 4 . . PUNCT ispiv-90 54 1 levitan levitan PROPN ispiv-90 54 2 , , PUNCT ispiv-90 54 3 e. e. PROPN ispiv-90 54 4 and and CCONJ ispiv-90 54 5 herman herman PROPN ispiv-90 54 6 , , PUNCT ispiv-90 54 7 g. g. PROPN ispiv-90 54 8 t. t. PROPN ispiv-90 54 9 ( ( PUNCT ispiv-90 54 10 1987 1987 NUM ispiv-90 54 11 ) ) PUNCT ispiv-90 54 12 β€˜ ' PUNCT ispiv-90 54 13 a a DET ispiv-90 54 14 maximum maximum NOUN ispiv-90 54 15 a a DET ispiv-90 54 16 posteriori posteriori NOUN ispiv-90 54 17 probability probability NOUN ispiv-90 54 18 expectation expectation NOUN ispiv-90 54 19 maximization maximization NOUN ispiv-90 54 20 algorithm algorithm NOUN ispiv-90 54 21 for for ADP ispiv-90 54 22 image image NOUN ispiv-90 54 23 reconstruction reconstruction NOUN ispiv-90 54 24 in in ADP ispiv-90 54 25 emission emission NOUN ispiv-90 54 26 tomography tomography NOUN ispiv-90 54 27 ’ ' PUNCT ispiv-90 54 28 , , PUNCT ispiv-90 54 29 ieee ieee NOUN ispiv-90 54 30 transactions transaction NOUN ispiv-90 54 31 on on ADP ispiv-90 54 32 medical medical ADJ ispiv-90 54 33 imaging imaging NOUN ispiv-90 54 34 , , PUNCT ispiv-90 54 35 6(3 6(3 NUM ispiv-90 54 36 ) ) PUNCT ispiv-90 54 37 , , PUNCT ispiv-90 54 38 pp pp ADP ispiv-90 54 39 . . PUNCT ispiv-90 55 1 185–192 185–192 NUM ispiv-90 55 2 . . PUNCT ispiv-90 55 3 doi doi NOUN ispiv-90 55 4 : : PUNCT ispiv-90 55 5 10.1109 10.1109 NUM ispiv-90 55 6 / / SYM ispiv-90 55 7 tmi.1987.4307826 tmi.1987.4307826 NUM ispiv-90 55 8 . . PUNCT ispiv-90 55 9 maas maas PROPN ispiv-90 55 10 , , PUNCT ispiv-90 55 11 h. h. PROPN ispiv-90 55 12 g. g. PROPN ispiv-90 55 13 , , PUNCT ispiv-90 55 14 gruen gruen PROPN ispiv-90 55 15 , , PUNCT ispiv-90 55 16 a. a. NOUN ispiv-90 55 17 and and CCONJ ispiv-90 55 18 papantoniou papantoniou NOUN ispiv-90 55 19 , , PUNCT ispiv-90 55 20 d. d. PROPN ispiv-90 55 21 ( ( PUNCT ispiv-90 55 22 1993 1993 NUM ispiv-90 55 23 ) ) PUNCT ispiv-90 55 24 β€˜ ' PUNCT ispiv-90 55 25 particle particle NOUN ispiv-90 55 26 tracking tracking NOUN ispiv-90 55 27 velocimetry velocimetry NOUN ispiv-90 55 28 in in ADP ispiv-90 55 29 three three NUM ispiv-90 55 30 - - PUNCT ispiv-90 55 31 dimensional dimensional ADJ ispiv-90 55 32 flows flow NOUN ispiv-90 55 33 ’ ' PUNCT ispiv-90 55 34 , , PUNCT ispiv-90 55 35 experiments experiment NOUN ispiv-90 55 36 in in ADP ispiv-90 55 37 fluids fluid NOUN ispiv-90 55 38 , , PUNCT ispiv-90 55 39 15(2 15(2 NUM ispiv-90 55 40 ) ) PUNCT ispiv-90 55 41 , , PUNCT ispiv-90 55 42 pp pp ADJ ispiv-90 55 43 . . PUNCT ispiv-90 56 1 133–146 133–146 NUM ispiv-90 56 2 . . PUNCT ispiv-90 57 1 doi doi NOUN ispiv-90 57 2 : : PUNCT ispiv-90 57 3 10.1007 10.1007 NUM ispiv-90 57 4 / / SYM ispiv-90 57 5 bf00190953 bf00190953 NOUN ispiv-90 57 6 . . PUNCT ispiv-90 58 1 wieneke wieneke PROPN ispiv-90 58 2 , , PUNCT ispiv-90 58 3 b. b. PROPN ispiv-90 58 4 ( ( PUNCT ispiv-90 58 5 2013 2013 NUM ispiv-90 58 6 ) ) PUNCT ispiv-90 58 7 β€˜ ' PUNCT ispiv-90 58 8 iterative iterative ADJ ispiv-90 58 9 reconstruction reconstruction NOUN ispiv-90 58 10 of of ADP ispiv-90 58 11 volumetric volumetric ADJ ispiv-90 58 12 particle particle NOUN ispiv-90 58 13 distribution distribution NOUN ispiv-90 58 14 ’ ' PUNCT ispiv-90 58 15 , , PUNCT ispiv-90 58 16 meas meas PROPN ispiv-90 58 17 . . PUNCT ispiv-90 59 1 sci sci PROPN ispiv-90 59 2 . . PROPN ispiv-90 59 3 technol technol PROPN ispiv-90 59 4 . . PUNCT ispiv-90 59 5 meas meas PROPN ispiv-90 59 6 . . PUNCT ispiv-90 60 1 sci sci PROPN ispiv-90 60 2 . . PROPN ispiv-90 60 3 technol technol PROPN ispiv-90 60 4 , , PUNCT ispiv-90 60 5 24(24 24(24 NUM ispiv-90 60 6 ) ) PUNCT ispiv-90 60 7 , , PUNCT ispiv-90 60 8 pp pp ADP ispiv-90 60 9 . . PUNCT ispiv-90 61 1 24008–14 24008–14 X ispiv-90 61 2 . . PUNCT ispiv-90 62 1 doi doi NOUN ispiv-90 62 2 : : PUNCT ispiv-90 62 3 10.1088/0957 10.1088/0957 NUM ispiv-90 62 4 - - SYM ispiv-90 62 5 0233/24/2/024008 0233/24/2/024008 NOUN ispiv-90 62 6 . . PUNCT