article_barseghyan.DVI Mathematical Problems of Computer Science 33, 73{82, 2010. Automated P AP Algor ithm for I nter fer ometr ic P hase Reconstr uction Y u r i A . B a r s e g h ya n Yerevan State University e-mail: yuri.barseghyan@gmail.com Abstract In this work the problem of interferometric phase reconstruction is considered. An automatic windows size selection algorithm is proposed which in combination with earlier developed PAP (pointwise approximation of phase) algorithm provides stable results even for bad quality of interferogramms. Experimental results show that com- bined algorithm demonstrates better performance in comparison with its original ver- sion. Refer ences [1 ] Gr a h a m L . C. \ S yn t h e t ic in t e r fe r o m e t e r r a d a r fo r t o p o g r a p h ic m a p p in g " . In P roceed- ings of the IE E E , 1 9 7 4 , v. 6 2 , p . 7 6 3 . [2 ] Go ld s t e in R . M., Ze b ke r H . A ., W e r n e r C. L . \ S a t e llit e r a d a r in t e r fe r o m e t r y: Two - d im e n s io n a l p h a s e u n wr a p p in g " . R adio Science, 1 9 9 7 , v. 2 3 , p . 7 1 3 . [3 ] Gh ig lia D . C., E ic h e l P . H . \ H ig h -r e s o lu t io n s yn t h e t ic a p e r t u r e r a d a r in t e r fe r o m e t r y: Te c h n o lo g y fo r p r e c is e t e r r a in e le va t io n m a p p in g " . D SP and M ultimedia Technology, 1 9 9 4 , v. 3 . [4 ] D . L . Fr ie d . \ L e a s t -s qu a r e s ¯ t t in g a wa ve -fr o n t d is t o r t io n e s t im a t e t o a n a r r a y o f p h a s e - d i®e r e n c e m e a s u r e m e n t s " . J ournal of the Optical Society of America, 6 7 ( 3 ) :3 7 0 -3 7 5 , Ma r c h 1 9 7 7 . [5 ] W . W . A r r a s m it h , M. C. R o g g e m a n n , B . M W e ls h . \ Op t im a l W a ve -fr o n t R e c o n s t r u c - t io n fo r a Co h e r e n t D i®r a c t e d Fie ld " . Applied Optics, 3 7 ( 2 0 ) :4 4 5 7 -4 4 6 7 , 1 9 9 8 . [6 ] R . J. N o ll. \ P h a s e e s t im a t e s fr o m s lo p e -t yp e wa ve -fr o n t s e n s o r s " . J ournal of the Optical Society of America, 6 8 ( 1 ) :1 3 9 -1 4 0 , Ja n u a r y 1 9 7 8 . [7 ] A . H e r m e n t , E . Mo u s s e a u x, O. Jo live t , A . D e Ce s a r e , F. Fr o u in , A . To d d -P o kr o p e k, J. B it t o u n . \ Im p r o ve d E s t im a t io n o f V e lo c it y a n d Flo w R a t e U s in g R e g u la r iz e d Th r e e - P o in t P h a s e -Co n t r a s t V e lo c im e t r y" . M agnetic R esonance in medicine, 4 4 :1 2 2 -1 2 8 , 2 0 0 0 . [8 ] M. H e d le y, D . R o s e n fe ld . \ A n e w Two -D im e n s io n a l P h a s e u n wr a p p in g A lg o r it h m fo r MR I Im a g e s " . M agnetic R esonance in M edicine, 2 4 :1 7 7 -1 8 1 , 1 9 9 2 . [9 ] G. H . Glo ve r , E . S c h n e id e r . \ Th r e e -P o in t D ixo n Te c h n iqu e fo r Tr u e W a t e r / Fa t d e - c o m p o s it io n wit h B0 In h o m o g e n e it y Co r r e c t io n " . M agnetic R esonance in M edicine, 1 2 :3 7 1 -3 8 3 , 1 9 9 1 . 7 3 7 4 Automated PAP Algorithm for Interferometric Phase Reconstruction [1 0 ] Y .A . B a r s e g h ya n \ P o in t wis e R e c o n s t r u c t io n o f In t e r fe r o m e t r ic P h a s e " . M athematical P roblems of Computer Science, vo l. 3 2 , p p . 4 8 -5 5 , 2 0 0 9 . [1 1 ] K a t ko vn ik V ., E g ia z a r ia n K ., A s t o la J. \ L o c a l a p p r o xim a t io n t e c h n iqu e s in s ig n a l a n d im a g e p r o c e s s in g " . SP IE P R E SS, B e llin g h a m , W a s h in g t o n , 2 0 0 6 . [1 2 ] K . H o a n d J. K a h n , \ E xa c t p r o b a b ilit y d e n s it y fu n c t io n fo r p h a s e m e a s u r e m e n t in t e r - fe r o m e t r y" . J . Opt. Soc. Amer. A, vo l. 1 2 , p p . 1 9 8 4 -1 9 8 9 , 1 9 9 5 . [1 3 ] J. L e e , K . H o p p e l, S . Ma n g o , a n d A . Mille r , \ In t e n s it y a n d p h a s e s t a t is t ic s o f m u lt ilo o k p o la r im e t r ic a n d in t e r fe r o m e t r ic S A R im a g e r y" . IE E E Trans. Geosci. R emote Sensing, vo l. 3 2 , p p . 1 0 1 7 -1 0 2 8 , 1 9 9 4 . [1 4 ] S . Ma d s e n , \ S p e c t r a l p r o p e r t ie s o f h o m o g e n e o u s a n d n o n h o m o g e n e o u s r a d a r im a g e s " , IE E E Trans. Aerosp. E lectron. Syst., vo l. A E S -2 3 , p p . 5 8 3 -5 8 8 , 1 9 8 7 . [1 5 ] C. R a t h je n , \ S t a t is t ic a l p r o p e r t ie s o f p h a s e -s h ift a lg o r it h m s " , J . Opt. Soc. Amer. A, vo l. 1 2 , p p . 1 9 9 7 -2 0 0 8 , 1 9 9 5 . [1 6 ] A . Go ld e n s h lu g e r a n d A . N e m ir o vs ki, \ On s p a t ia l a d a p t ive e s t im a t io n o f n o n p a r a m e t - r ic r e g r e s s io n " , M athematical M ethods of Statistic, vo l. 6 , p p . 1 3 5 -1 7 0 , 1 9 9 7 . [1 7 ] V . K a t ko vn ik, \ A n e w m e t h o d fo r va r yin g a d a p t ive b a n d wid t h s e le c t io n " , IE E E Trans- actions on Signal P rocessing, vo l. 4 7 , n o . 9 , p p . 2 5 6 7 -2 5 7 1 , 1 9 9 9 . ²íïáÙ³ï³óí³Í PAP ³É·áñÇÃÙ ÇÝï»ñý»ñáÙ»ïñÇÏ ÷áõÉÇ í»ñ³Ï³Ý·ÝÙ³Ý Ñ³Ù³ñ Ú. ´³ñë»ÕÛ³Ý ²Ù÷á÷áõÙ ²ß˳ï³ÝùáõÙ ùÝݳñÏíáõÙ ¿ ÇÝï»ñý»ñáÙ»ïñÇÏ³Ï³Ý ÷áõÉÇ í»ñ³Ï³Ý·ÝÙ³Ý ËݹÇñÁ: ²é³ç³ñÏíáõÙ ¿ å³ïáõѳÝÇ ã³÷ëÇ ÁÝïñÙ³Ý ³íïáÙ³ï³óí³Í ³É·áñÇÃÙ, áñÁ Ùdzíáñí³Í ÙÇÝã ³Û¹ ëï»ÕÍí³Í PAP ³É·áñÇÃÙÇ Ñ»ï ³å³ÑáíáõÙ ¿ ϳÛáõÝ ³ñ¹ÛáõÝùÝ»ñÁ ÝáõÛÝÇëÏ ÇÝï»ñý»ñ»ÝóÇáÝ å³ïÏ»ñÝ»ñÇ í³ï áñ³ÏÇ ¹»åùáõÙ: öáñÓ»ñÇ ³ñ¹ÛáõÝùÝ»ñÁ óáõÛó »Ý ï³ÉÇë, áñ Ùdzíáñí³Í ³É·áñÇÃÙÁ ¿ ѳٻٳï³Í ݳËÝ³Ï³Ý ³É·áñÇÃÙÇ Ñ»ï, ï³ÉÇë ¿ ÷áõÉÇ í»ñ³Ï³Ý·ÝÙ³Ý ×ßïáõÃÛ³Ý ½·³ÉÇ É³í³óáõÙÁ: