Multiple Description Image and Video Coding for Noisy Channels
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(65) yxyzs[©3qwzsap jms[PoP{ tkjmo ¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Üûrù wz{ko èî+ü n ío=prqjI3y èî9¨ ísa ÿiF3jwznmsap9 s q å o ikjmsaiQs¤nmoP{ Do=q å sA{ wxq å q å o Do=q å sA{ wxp ÷¤ù ÿ¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ü_û 8 wz{ko èî+ü n ío=prqjI3y èî9¨ ísa ÿiF3jwznmsap9 s q å o ikjmsaiQs¤nmoP{ Do=q å sA{ wxq å q å o Do=q å sA{ wxp xö©ú i ¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ü_û 8 ísa ÿikyzo=qmo ísA{ wxpk¥ å o= Do ¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Üûr÷ ä jI3p¢n saj vFanmoP{wx T3¥§oPs[{ wxpk¥DnI å o= Do¤¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ 83û wx T3¥§o PsA{koP{N3qÐú 9¨ 8vkikih¨Ðì ¼ å 3pkp¢o=yA3qÐú ¨ ú¤ú övQo=j©
(66) ¨ è î ù 5 ¨ û¢ö 85 wx T3¥§o PsA{koP{N3q ö¤¨ úvkikih¨Ðì ¼ å 3pkp¢o=yA3qÐú ¨ ú¤ú övQo=j©
(67) ¨ è î õ¤õ ¨ ÷ 5 {kì¨ ¨N¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ 85 wx T3¥§o PsA{koP{N3q ö¤¨ úvkikih¨Ðì ¼ å 3pkp¢o=yA3qÐú ¨ ú övQo=j©
(68) ¨ è î ù3û¢9¨ 55 {kì¨ ¨N¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ i¤ú \wx T3¥§oÆPsA{koP{É3qÆö¤¨ úãvkikih¨ 3t¢nmnw3pÉ å 3pkp¢o=yN3q ú ¨ ú ö\vQo=j©¨ è î ù 8 ¨ _û 5D{kì ¨ ¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ i¤ú wx T3¥§o Ps[{koP{ 3qTú 9¨ 8\vkikih¨ 3t¢nmnw3p å 3pkp¢o=y3q8ú ¨ ú¤ú ö`vQo=j©¨ è î õ ö¤¨ !ù hÿ{kì ¨ ¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ i ö wx T3¥§o Ps[{koP{ 3qö¤¨ ú\vkikih¨ 3t¢nmnw3p å 3pkp¢o=y3q8ú ¨ ú¤ú ö`vQo=j©¨ è î õ3û¢9¨ 5¤úD{kì ¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ i ö öPñ ñ ä nqjt¢=qtkjmot¢nwxpk¥ÿq å oyx w ]qwxpk¥Tnm å o= Do¤¨D¨¨¨¨¨N¨¨¨¨¨¨¨ i¤õ o©3p èî9óônÐ s ¢o©a å ]jI3 Do saj Psa ÿi(sap¢o=p[q/ s íê "!$#&%'()®Psayzsaj ü[wz{koPsPsa ÿikjmoPnmnmoP{9qmsù¤ú¤ú Avkwxqm$n *3+n õ¤ú ]jI3 DoP$n *3$n @¨ ä jI3p¢n ÿwznmnmwzsap.s<ü§o=j 3t¢nmnw3p å 3pkp¢o=yk3q ú ¨ ú¤ú övQo=j ê"" è %, - @hp¢s
(69) p¢sawznmo ¤ñ
(70) î % ìïhð é Bv @ jmsaiQs¤nmoP{ ñ . ïÐï ]/ @ ñ ¨`¨¨¨¨¨¨N¨¨¨¨¨¨¨ i8 1. 1. 2. 2. 0. i,j.
(71) üAwxwxw. . û¢¨xö¤ö ©o 3p èî9óônÐs ¢o©a å ]jI3 Do sajÐðPsa ÿi(sap¢o=p[q/s íê "!$#&%'()®Psayzsaj ü[wz{koPsPsa ÿikjmoPnmnmoP{9qmsù¤ú¤ú Avkwxqmn$*3n+ õ¤ú ]jI3 DoPn$*3n$ @¨ ä jI3p¢n ÿwznmnmwzsap.s<ü§o=j 3t¢nmnw3p* å 3pkp¢o=yí3qú ¨ ú¤ú öDvQo=j ê"è"%ÿ®p¢s p¢sawznIo ñuî % ìïhðu jmsai(s¤nIoP{ ñ ïhï é ñ ¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ û¢¨xö©ù o©3p èî9óônÐ s ¢o©a å ]jI3 Do sajÐðPsa ÿi(sap¢o=p[q/s íê "!$#&%'()®Psayzsaj ü[wz{koPsPsa ÿikjmoPnmnmoP{9qmsù¤ú¤ú Avkwxqm$n *3+n õ¤ú ]jI3 DoP$n *3$n @¨ ä jI3p¢n ÿwznmnmwzsap.s<ü§o=j 3t¢nmnw3p* å 3pkp¢o=yí3qú ¨ ú¤ú öDvQo=j ê"" è %ÿ®p¢s p¢sawznIo ñuî % ìïhð u jmsai(s¤nIoP{ ñ ïhï é ñ ¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ û¢¨xö©õ íê !# % )Psayzsajü[wz{koPs9Psa ÿikjmoPnmnmoP{TqmsNù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap s<ü§o=j 3t¢nmnw3pë å 3pkp¢o=yD3q¼ú ¨ ú¤ú ö v(o=j©¨$ðnwxpk¥ q å o ñ
(72) ä ¨ ¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ û¢¨xö=û íê !# % )Psayzsajü[wz{koPs9Psa ÿikjmoPnmnmoP{TqmsNù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap`s<ü§o=j 3t¢nmnw3p` å 3pkp¢o=yh3q ú ¨ ú¤ú övQo=j©¨ ðnmwxpk¥9q å oikjms i(s¤nmoP{ ñ ¨ ¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ û¢¨xö 8 íê #Nü[wz{koPs9Psa ÿikjmoPnmnmoP{8qms9õ¤ú¤ú [vkwxqm$n *3n õ¤ú ]jI3 DoP$n *3$n @¨ ä jI3p¢n ÿwznmnwzsap^s<ü§o=j 3t¢nmnw3pZ å 3pkp¢o=y/3q
(73) ú ¨ ú¤ú öv(o=j©¨ðnwxpk¥Dq å o ñ
(74) ä ¨ û¢¨xö i íê #Nü[wz{koPs9Psa ÿikjmoPnmå nmoP{8qms9õ¤ú¤ú [vkwxqm$n *3n õ¤ú ]jI3 DoPå $n *3$n @¨ ä jI3p¢n ÿwznmnwzsapZs<ü§o=j 3t¢nInw3p^ 3pkp¢o=y3qú ¨ ú¤ú öNv(o=j©¨íðnmwxpk¥ÿq oikjmsaiQs¤nmoP{ ñ ¨Ã¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ û¢¨xö h o©3p èî9óônÿ s o©a å BjI3 Do ]saj ÖPsa ÿi(sap¢o=p[(q saj íê !$#&% ) Psayzsajü[wz{koPs`Psa ÿikjmoPnmnIoP{¼qmsù¤ú¤ú [vkwxqm$n *3n õ¤ú ]jI3 DoP$n *3$n @¨ ä jI3p¢n ÿwzn nwzsap s<ü§o=j.ð Zä ¦oP{koPnqjw3p% å 3pkp¢o=y3q9ú ¨ ú ö8vQo=j é ê""è % - @ 9p¢s p¢sawznmo ñuî % ìïhð ]/ @ jmsaiQs¤nmoP{ ñ ïhï ]{ @ ñ wxq å satkq å 3pkp¢o=y/Ps[{ wxpk¥ Fïhê ' ä ìïhð Bv @ ñ
(75) ä ¨ ¨¨¨¨¨ û¢¨xö©÷ o©3p èî9óônÿ s o©a å BjI3 Do ]sajÿðÜPsa ÿi(sap¢o=p[(q saj íê !$#&% ) Psayzsajü[wz{koPs`\äPsa ÿ ikjmoPnmnIoP{¼qmsù¤ú¤å ú [vkwxqm$n *3n õ¤ú ]jI3 DoP$n *3$n @¨ ä jI3p¢n ÿwzn nwzsap¬s<ü§o=j ð /oP{koPnqjw3p 3pkp¢o=y®3q ú ¨ ú öv(o=j êè %ÿ[p¢s9p¢sawznmo ñuî %Éìïhð
(76) jmsaiQs¤nmoP{ ñ ïhï é ñ wxq å satkq å 3pkp¢o=y Ps[{ wxpk¥ ¢ïÐê ' ä ìïhð u ñ
(77) ä ¨ ¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ û¢¨xö 5 o©3p èî9óônÿ s o©a å BjI3 Do ]saj #~Psa ÿi(sap¢o=p[(q saj íê !$#&% ) Psayzsajü[wz{koPs`\äPsa ÿ ikjmoPnmnIoP{¼qmsù¤ú¤å ú [vkwxqm$n *3n õ¤ú ]jI3 DoP$n *3$n @¨ ä jI3p¢n ÿwzn nwzsap¬s<ü§o=j ð /oP{koPnqjw3p 3pkp¢o=y®3q ú ¨ ú öv(o=j êè %ÿ[p¢s9p¢sawznmo ñuî %Éìïhð
(78) jmsaiQs¤nmoP{ ñ ïhï é ñ wxq å satkq å 3pkp¢o=y Ps[{ wxpk¥ ¢ïÐê ' ä ìïhð u ñ
(79) ä ¨ ¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ û¢¨ ù¤ú ä íê !# % )Psayzsajü[wz{kZäoPs9P sa ÿikjmoPnmnmoP{¬å 3qù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$nå @¨ ñ jI3 p¢n ÿwxwzq nmå nmsawzsatkp\qs< åü§o=3jpkp¢ð o=y/Ps[{ wxêpkp¢¥¢{k¨âsAsa¨j
(80) ¨ ¨3¨Npkp¢¨o=¨y¨3q ¨ú ¨¨ ú ¨ö¨vQ¨o=j©¨N¨¨ð¨nwxpk¨¥8¨q ¨o¨¨ û¢¨ ù ö íê !# % )Psayzsajü[wz{koPs9P sa ÿikjmoPnmnmoP{¬3qù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap\s<ü§o=jð Zä êp¢{ksAsaj
(81) å 3pkp¢o=y3q ú ¨ ú övQo=j©¨ðnwxpk¥8q å o ñ
(82) ä ¨ ¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ û¢¨ ù¤ù íê !# % )Psayzsajü[wz{koPs9P sa ÿikjmoPnmnmoP{¬3qù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap\s<ü§o=jð Zä êp¢{ksAsaj
(83) å 3pkp¢o=y3q ú ¨ ú övQo=j©¨ðnwxpk¥8q å o ikjmsai(s¤nmoP{ ñ ¨u¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ û¢¨ ù¤õ íê !# % )Psayzsajü[wz{koPs9P sa ÿikjmoPnmnmoP{¬3qù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap¼s<ü§o=jð \ä ¦oP{koPnmqjw3p¼ å 3pkp¢o=y 3qú ¨ ú övQo=j©¨uðnwxpk¥ q å o ñ wxq å satkq
(84) å 3pkp¢o=y/Ps[{ wxpk¥¢¨ ¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨. . i8. ii. i!h. ¤÷ i. i5. aú h. Kû h. Kû h. h/8. h/i. hh. a÷ h. h/5.
(85) . w. . û¢¨ ù3û íê !# % )Psayzsajü[wz{koPs9P sa ÿikjmoPnmnmoP{¬3qù¤ú¤ú Avkwxqmn$*3n õ¤ú BjI3 DoPn*3n$ @¨ ä jI3p¢n ÿwznmnmwzsap¼s<ü§o=jð \ä ¦oP{koPnmqjw3p¼ å 3pkp¢o=y 3qú ¨ ú övQo=j©¨uðnwxpk¥ q å o ñ
(86) ä ¨ ¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ö÷¤ú û¢¨ ù 8 íê !# % )Psayzsajü[wz{koPs9P sa ÿikjmoPnmnmoP{¬3qù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap¼s<ü§o=jð \ä ¦oP{koPnmqjw3p¼ å 3pkp¢o=y 3qú ¨ ú övQo=j©¨uðnwxpk¥ q å oikjmsai(s¤nIoP{ ñ ¨±¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ö÷ ö û¢¨ ù i íê !# % )Psayzsajü[wz{koPs9Psa ÿikjmoPnmnmoP{¬3qù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap¬s<ü§o=jð Zä ¦oP{koPnqjw3p` å 3pkp¢o=y®3qú ¨ ú¤ú ö
(87) v(o=j©¨ðnwxpk¥ ñ wxq å satkq å 3pkp¢o=y/Ps[{ wxpk¥¢¨â¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ö÷¤ù û¢¨ !ù h íê !# % )Psayzsajü[wz{koPs9Psa ÿikjmoPnmnmoP{¬3qù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap¬s<ü§o=jð Zä ¦oP{koPnqjw3p` å 3pkp¢o=y®3qú ¨ ú¤ú ö
(88) v(o=j©¨ðnwxpk¥ ñ
(89) ä ¨ ¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ö÷¤õ û¢¨ ù¤÷ íê !# % )Psayzsajü[wz{koPs9Psa ÿikjmoPnmnmoP{¬3qù¤ú¤ú Avkwxqm$n *3n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap¬s<ü§o=jð Zä ¦oP{koPnqjw3p` å 3pkp¢o=y®3qú ¨ ú¤ú ö
(90) v(o=j©¨ðnwxpk¥ q å oikjmsai(s¤nIoP{ ñ ¨±¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ö÷3û û¢¨ ù 5 sA{ko=yÐ s q å oêp[qmo=jp¢o=q å 3pkp¢o=yX¨ nmqI3p¢{kn saj s[sA{ nqI3qmo3p¢{ì ]saj "ì a{ nqI3qmo¤¨ ¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ö÷ 8 û¢¨ õ¤ú o©3p èî9óônu s o©a å ]jI3 D"o ]saj Psa ÿi(sap¢o=p[q s íê PsayzsajíüAwz{koPs.Psa ÿå ikjmoPnmnmoP{ 3qù¤ú¤ú % vki¢n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap s©ü§o=jêp[qmo=jp¢o=q 3pkp¢o=yQnt ®o=jwxpk¥ ]jmsa ö©ú ¨ ÷ 5
(91) iFa §o=qyzs¤nmn<¨ î è - @ wxq å satkq jmo=qjI3p¢n ÿwznmnmwzsap
(92) ú iFa! §o=qyzs¤nm$n Q¦ü§o=jI3¥§ o èî Fõ¤ú ¨xö iD{kì ¨¢ìïhð , Bv @ jmsaiQs¤nmoP{ ñ ¢ Ðü§o=jI3¥§o èî9Fù ö¤¨ ha÷ {kì¨Fî ñ ]/ @ ðnwxpk¥ ñ ¢¦ü§o=jI3¥§ o èî9®ö hA9¨ i¤ùÿ{kì ¨ ¨¨¨¨¨¨Ö!÷ h û¢¨ õ ö o©3p èî9óônu s o©a å ]jI3 D"o ]saj Psa ÿi(sap¢o=p[q s íê PsayzsajíüAwz{koPs.Psa ÿikjmoPnmnmoP{ 3qù¤ú¤ú % vki¢n õ¤ú BjI3 DoPn *3$n @¨ ä jI3p¢n ÿwznmnmwzsap s©ü§o=jê"prqmo=jp¢o=q å 3pkp¢o=ynt ®o=jwxpk¥ Bjmsa 8
(93) iFa! §o=q yzs¤nmn<¨ î è - @ wxq å satkq jmo=qjI3p¢n ÿwznmnmwzsap
(94) ú iFa! §o=qyzs¤nm$n Q¦ü§o=jI3¥§ o èî Fõ¤ú ¨ ûrúD{kì ¨¢ìïhð , Bv @ jmsaiQs¤nmoP{ ñ ¢Ðü§o=jI3¥§o èî9Fù i ¨ hKû {kì¨Fî ñ ]/ @ ðnwxpk¥ ñ ¢¦ü§o=jI3¥§ o èî9¢ù ö¤¨ õ 8ÿ{kì ¨ ¨¨¨¨¨Ö!÷ h û¢¨ õ¤ù íê
(95) PsayzsajhüAwz{koPsuPsa ÿikjmoPnmnmoP{N3qÐù¤ú¤ú % vki¢
(96) n õ¤ ú ]jI3 DoP$n *3$n @¨ ä jI3p¢n ÿwznmnmwzsap.s<ü§o=j 3p.êp[qmo=jp¢o=q/nwx 9tky3qmsaj/nmt Qo=jwxpk¥ BjmsaJ 8 diFa §o=q yzs¤ nmn©¨Ãðnwxpk¥ ñ ¨ èîNù¤ú 9¨ 8¤úã{kì íð èî9íõ¤÷ 9¨ 53û%{kì # èî9kûrú 9¨ i¤ùÿ{kì ¨+¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ö÷¤÷ û¢¨ õ¤õ íê
(97) PsayzsajhüAwz{koPsuPsa ÿikjmoPnmnmoP{N3qÐù¤ú¤ú % vki¢
(98) n õ¤ ú ]jI3 DoP$n *3$n @¨ ä jI3p¢n ÿwznmnmwzsap.s<ü§o=j 3p.êp[qmo=jp¢o=q/nwx 9tky3qmsaj/nmt Qo=jwxpk¥ BjmsaJ 8 diFa §o=q yzs¤nmn©¨%ðnwxpk¥Æq å o`ikjmsai(s¤nIoP{ ñ ¨ èîN ù i ¨ h/iÆ{kì ð èî9 õ¤÷ ¨ ÷¤ùD{kì # èî9 ûrú 9¨ 8¤ùÿ{kì ¨ ¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨Ö÷ 5 8 ¨xö î
(99) o=ikjmoPnmo=p[qI3qwzsap s uq å o8q ís íñyxwxp¢o©3j.3jjI©þAn s éä 8q"þ[iQo aP¡rtkwznwxqwzsap\nþ nqmo= ¨Z¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ 5¤ù 8 ¨ ù ísa NvkwxpF3qwzsapd s \iF3wxjD s íñ~yxwxp¢o©3jT3jjI©þAnDwxp ¼¡rtkwxp¢=tkp 3j jI3pk¥§o= Do=prqƨ¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ 5¤õ 8 ¨ õ tkwxp¢=tkp NtkyxqwxjmoPnmsayxtkqwzsapÆ3pF3yxþAnmwzn©¨ ¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ 58 8 ¨ û ñ saju¡rtkwxp¢=tkp wx T3¥§oPn©¨ qI3p¢{¢3jm{ ñ â Do=q å sA{®¨ ¨¨¨¨¨¨¨ 5i 8 9¨ 8 ñ saju¡rtkwxp¢=tkp wx T3¥§oPn©¨ jmsai(s¤nIoP{ ñ Do=q å sA{®¨ ¨¨¨¨¨¨¨ 5!h 8 9¨ i yzsavF3yÐìíwxq
(100) yxyzs[©3qwzsap jms[PoP{ tkjmo ¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö©ú3û ä å jmoPo X¥§s[sA{`nqI3qmo¤£ nwxpk¥¤yzoo=jjmsaj nqI3qmo kjwxqm å T3p Ds[{ko=y saj 40 iFanmn©¨ö©ú 8 8 ¨ h ◦.
(101) . . . # !/wx T3¥§ouPsa ÿikjmoPnInmoP{ÿqmsNùvkiki( å o=p8P sap¢nwz{ko=jwxpk¥NqjI3p¢n ÿwznIå nwzsap 3 q3p¬o=yzo=üa3qwzsap 3pk¥¤yzo
(102) s 30 ú ¨ ú¤ú ö
(103) vQo=j$ @¨ qI3p¢{¢3jm{ ñ Do=q sA{®¨ wz{ko{koPPs[{ko=j9ö¤¨ ¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö©ú ¨ # /! wx T3¥§ouPsa ÿikjmoPnInmoP{ÿqmsNùvkiki( å o=p8P sap¢nwz{ko=jwxpk¥NqjI3p¢n ÿwznInwzsap 3 q3p¬o=yzo=üa3qwzsap 3pk¥¤yzo
(104) s 30 ú ¨ ú¤ú ö
(105) vQo=j$@ ¨ qI3p¢{¢3jm{ ñ Do=q å sA{®¨ wz{ko{koPPs[{ko=jù ¨ ¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö©ú ¨xö©ú # /! wx T3¥§ouPsa ÿikjmoPnInmoP{ÿqmsNùvkiki( å o=p8Psap¢nwz{ko=jwxpk¥NqjI3p¢n ÿwznInwzsap 3qí3p8o=yzo=ü¤3qwzsap¬3pk¥¤yzos 30 ú ¨ ú¤ú öv(o=j$@ ¨ jmsaiQs¤nmoP{ ñ Do=q å sA{®¨ wz{ko{koPPs[{ko=j9ö¤¨ ¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö¤ö©ú ¨xö¤ö # /! wx T3¥§ouPsa ÿikjmoPnInmoP{ÿqmsNùvkiki( å o=p8Psap¢nwz{ko=jwxpk¥NqjI3p¢n ÿwznInwzsap 3qí3p8o=yzo=ü¤3qwzsap¬3pk¥¤yzos 30 ú ¨ ú¤ú öv(o=j$@ ¨ jmsaiQs¤nmoP{ ñ Do=q å sA{®¨ wz{ko{koPPs[{ko=jù ¨ ¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö¤ö©ú ¨xö©ù # /! wx T3¥§ouPsa ÿikjmoPnInmoP{ÿqmsNùvkiki( å o=p8Psap¢nwz{ko=jwxpk¥NqjI3p¢n ÿwznInwzsap 3q3p¬o=yzo=üa3qwzsap 3pk¥¤yzo
(106) s 30 ú ¨ ú¤ú ö
(107) vQo=j$@ ¨ qI3p¢{¢3jm{ ñ Do=q å sA{®¨ ío=prqjI3y¦ å 3pkp¢o=yX¨ ¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö¤ö¤ö ¨xö©õ # /! wx T3¥§ouPsa ÿikjmoPnInmoP{ÿqmsNùvkiki( å o=p8Psap¢nwz{ko=jwxpk¥NqjI3p¢n ÿwznInwzsap 3qí3p8o=yzo=ü¤å 3qwzsap¬3pk¥¤yzos 30 ú ¨ ú¤ú öv(o=j$@ ¨ jmsaiQs¤nmoP{ ñ Do=q å sA{®¨ ío=prqjI3y¦ 3pkp¢o=yX¨ ¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö¤ö¤ö ì ¨xö wx¥¤pF3y¦{ wxüAwznwzsap wxprqms8ntkv nwx¥¤pF3yznusaj jmsatki é wz=qtkjmoPn é
(108) ¨¨ö©õ¤ù ì ¨ ùñoPnI=jwxikqwzsap¢n
(109) jmoPntkyxqI3p[q ]jmsa ñ ì ¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö©õ¤õ ì ¨õ Í Psa ÿiQsap¢o=prq.s íê ¢sajmo= T3p+üAwz{koPs sajvkwxqjI3qmoPn ]jmsa ö©ú¤ú`qms ¤ú¤ú % vki¢n©¨uö©ú ikjmsavF3vkwxyxwxq"þs /iFa §o=q
(110) yzs¤nmn<¨ ¨¨¨¨¨N¨¨¨¨¨¨¨ö©õ ì ¨ ûÛ Psa ÿiQsap¢o=prqs íê ¢sajmo= T3pãüAwz{koPs^Psa ÿikjmoPnmnIoP{ 3q ¤ú¤ú % vki¢n ]saj { w®o=jmo=prquikjmsavF3vkwxyxwxqwzoPnus /iFa!§o=quyzs¤nIn B wX¨ôo¤¨ { wQo=jmo=p[q r ü¤3yxt¢oPn$@ ¨ å å ¨ ÷ 8. ◦. 5. 8 95. ◦. 5. 8. ◦. 8. ◦. 8. ◦. 8. ◦. 8. i. 8. ì ¨98. ¨xö ¨ ù ¨ õ ¨ û ¨98 ¨9i ¨ h. wxyzo=prq¼ü[D wz{ko©oP3sâp¢n Psa ÿwx¥ ikjmoPiFnmanm!oP§{o=q3yzqÆs¤nmù¤nmú¤oPú n©¨% ¨vk¨i¢n¼¨3¨Np¢¨{èq¨jI3¨p¢¨n ÿ¨wxq¨qmoP¨{ ¨Ns©¨ü§¨o=jƨ ¨¨ö©õ!h ð \ä nwx 9tky3qmsaj©¨Tïho ]qNPsayxtk ÿph wxq å satkq9jmoP{ tkp¢{¢3p¢=þãa{¢3ikqI3vkwxy wxqþ ¢îuwx¥ å q
(111) Psayxtk ÿph wxq å jmoP{ tkp¢{¢3p¢=þa{¢3ikqI3vkwxyxwxq"þ§¨ ¨N¨¨¨¨¨¨¨ö=ûrú n Twx T3¥§o¤¨ ¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨ö=ûrõ 512 × 512 ikw o=yz k i w. = o z y n íññö # $!wx T3¥§o¤¨(¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨ö=û¤û 352 × 360 352 × 360 ikw o=yzn íññù # $!wx T3¥§o¤¨(¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨ö=û¤û tkwxp¢=tkp # ! wx T3¥§o¤¨ ¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö=_û 8 íê !# % )íPsayzsajuüAwz{koPsk ¨ kjI3 DoPn©uö¤£Ðö¤ö¤£¢ù ö¤£Fõ ö¤£x¨x¨x¨¨¨N¨¨¨¨¨¨¨ö=_û i íê # üAwz{koPsk ¨ kjI3 DoPn©
(112) ö¤£hö¤ö¤£Fù ö¤£¢õ ö¤£h¨x¨x¨*¨¨¨¨¨¨N¨¨¨¨¨¨¨ö=.û h íê \Psayzsaj
(113) ü[wz{koPsk ¨ ¢jI3 DoPn©uö©ú £Fù¤ú £¢õ¤ú £x¨x¨x¨Î¨¨N¨¨¨¨¨¨¨ö=ûr÷ N. rN = 1.
(114) " .
(115) . ù ¨xö
(116) î oPPsap¢nqjt¢=qwzsap\Ps[{ko=vQs[s n saj ¢¥¤tkjmoNù ¨ õ ¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ ö=û ù ¨ ù ío=prqjI3yh3p¢{8nmwz{ko uóôn saj q å oPo=prqjI3y(iF3jqwxqwzsap s ¢¥¤tkjmoù ¨ õ.3p¢{ q å oPs[{ko=vQsAs Anus qI3vkyzoNù ¨xö訨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ ö8 û¢¨xö jm savF3vkwxyxwxqþZ3p¢{ZanmnmsA=w3qmoP{`wxprqmo=jü¤3y¦ s /o©a å nþA NvQsayX¨ã¨N¨¨¨¨¨¨¨ 88 û¢¨ ù èî üa3yxt¢ oP"n saj ÿwx T3¥§oÿPsa ÿikjmoPnmnmoP{\qmsú 9¨ 88vkikih£ å o=p+Psap nwz{ko=jwxpk¥8ì â å 3pkp¢o=yzn<¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ 8¤÷ û¢¨ õ o©3p èîÍjmoPntkyxqmn ]saj íê !# % )PsayzsajüAwz{koPs¼Psa ÿikjmoPnmnmoP{*qms ù¤ú¤ú [vkwxqm $n *3n õ¤ú ]jI3 DoP$n *3$n @£ å o=p å 3pkp¢o=yhqjI3p¢n ÿwznmnwzsap3q 0.001 v(o=j©¨[i3û û¢¨ û o©3p èî ]{kì jmoPnmtkyxqmn saj íê !$#&%'()PsayzsajüAwz{koPsNPsa ÿikjmoPnInmoP{ qmsù¤ú¤ú Avkwxqm$n *3n õ¤ú ]jI3 DoP$n *3$n @¨ ð \ä å 3pkp¢o=y¢qjI3p¢n ÿwznInwzsapT3q 0.01 v(o=j©¨ ¨N¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ haù û¢9¨ 8 o©3p èî ]{kì jmoPnmtkyxqmn saj íê !$#&%'()PsayzsajüAwz{koPsNPsa ÿikjmoPnInmoP{ qmsù¤ú¤ú [vkwxqm$n *3n õ¤ú ]jI3 DoP$n *3$n @¨ð \ä å 3pkp¢o=yqjI3p¢n ÿwznInwzsap¸3q 0.001 v(o=j©¨%¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨ haõ 8 ¨xö èîÃü¤3yxt¢oPn saj # $! wx T3¥§o å o=p¼Psap¢nwz{ko=jwxpk¥¬qjI3p¢n ÿwznmnwzsap¼3q 3p^ o=yzo=üa3qwzsap\3pk¥¤yzo s 40 ú ¨ ú¤ú¤ú 8å v(o=$j @¨Ì¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö©!ú h 8 ¨ ù èîÃü¤3yxt¢oPn saj # $! wx T3¥§o o=p¼Psap¢nwz{ko=jwxpk¥¬qjI3p¢n ÿwznmnwzsap¼3q 3p^o=yzo=üa3qwzsap\3pk¥¤yzo s 30 ú ¨ ú¤ú öv(o=$j @¨T¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö©ú¤÷ .¨xö~êp¢{ksAsaj
(117) ì 9tkyxqwxiF3q å å 3pkp¢o=yÐiF3jI3 Do=qmo=jmn©¨ ¨¨¨¨N¨¨¨¨¨¨¨ö©ù¤ù .¨ ù ¦oP{koPnqjw3p¼ ì 9tkyxqwxiF3q å å 3pkp¢o=yhiF3jI3 Do=qmo=j©¨¢¨¨¨N¨¨¨¨¨¨¨ö©ù¤õ å .¨ õ # o wz=tky3j ìâ NtkyxqwxiF3q å å 3pkp¢o=yÐiF3jI3 Do=qmo=jmn©¨ ¨¨¨N¨¨¨ ¨¨¨¨ö©ù¤õ .¨ ûìwxqjI3qmoD3p¢{¼ü§o=yzsA=wxqþ¼ å 3jIa=qmo=jwznmqwzPn saj o©a å qþAi(oÿ s ð \ä o=p ü[wxjmsapk Do=p[q©¨h¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö©ù3û .9¨ 8 ís å o=jmo=p¢PovF3p¢{^3p¢{ T wx T3yhp[tk NvQo=j s /nIo=iF3jI3vkyzoiF3q å n saj q å o õ qmoPnq Ds[{ko=yzn
(118) ð \ä o=prüAwxjmsapk Do=prq©¨F¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö©ù 8 ì ¨xöØñw ®o=jmo=prqíikjmo nqmsajmoP{8{koPnm=jwxikqwzsap¢ n ]saj3pTwxprqmo=jü¤3y:qwx Do s QüAwz{koPs saj é
(119) @¨9¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨¨¨N¨¨¨¨¨¨¨ö©õ¤õ ◦ ◦.
(120) wxw . . .
(121) . . . . . . . tkvkvF3p¢{®óFnuprtk NvQo=j©¨ t¢saqwzo=p[q s q å on7w 6©os q å ontkvkvF3p¢{{ wxüAwz{koP{ v[þ8q å onmw76©o¤¨ s q å o å sayzowx T3¥§o ]o¤¨ ¥¢¨x£ a = wxp q å o{ þra{ wz©anmo/ @¨. å 3pkp¢o=y 3iFa=wxqþ§¨ é ikqwzsapF3y o=wx¥ å q saj BjmoP¡[t¢o=p¢=þ¬nIo=yzoP=qwzsaph¨ ∆ ñwznqmsajqwzsaph¨ D ñwznqmsajqwzsap\anmnmsA=w3qmoP{ wxq å q å oPo=prqjI3y/{koPPs[{ko=j©¨ D ñwznqmsajqwzsap\anmnmsA=w3qmoP{ wxq å q å o noPnwx å 3pkp¢o=yX¨ D ñwznqmsajqwzsap å o=pZÿvkwxq jI3qmo s R ¨ D(R) å D , (i, j ∈ N) ñwznmqmsajqwzsapZanmnmsA=w3qmoP{ wxq ntkvkvF3p¢{ i £¢3p¢{{koPnm=jwxikqmsaj j ¨ satkjmPoo=p[qjmsairþ§¨ H(x) ísap¢{ wxqwzsapF3y¦o=p[qjmsairþsaj
(122) oP¡[tkwxü§sA©3qwzsaph¨ H (x) tF3prq7w 6<3qwzsap¼nqmo=i^anmnmsA=w3qmoP{ wxq å ntkvkvF3p¢{ i £¢3p¢{{koPnm=jwxikqmsaj j ¨ q , (i, j ∈ N) o=q
(123) s pF3qtkjI3yhp[tk NvQo=jmn©¨ N î oP{ tkp¢{¢3p¢=þ`iF3jI3 Do=qmo=j©¨ r o=q
(124) s jmo©3yhp[tk NvQo=jmn©¨ R í ì wxqujI3qmo¤¨ R ìíwxqujI3qmoanInms[=w3qmoP{ wxq å q å o nXq å å 3pkp¢o=yX¨ R ìíwxqujI3qmo å o=pZÿ{ wznmqmsajqwzsap^ s D ¨ R(D) å R , (i, j ∈ N) ìwxq
(125) jI3qmoanmnmsA=w3qmoP{ wxq ntkvkvF3p¢{ i £¢3p¢{^{koPnm=jwxikqmsaj j ¨ nqI3p¢{¢3jm{^{ko=ü[w3qwzsaph¨ σ ¤ ü 3jw3p¢Po¤¨ σ bd\ \Ee +. 1 w p[tk NvQo=j s ö¤óôn wxp^ sajm{®¨ ç e\] \ +. 1 w = ÿwxp {w (c)|c ∈ C, c 6= 0} bd\ \Ee
(126) ^(-bd0!+ äå o*prtk 9v(o=j+ s Tvkwxqmn å wz å { w Qo=j¼vQo=q oPo=pq sdvkwxpF3jþ nmqjwxpk¥§n©¨ sajm"o ]saj T3yxyxþ§£ d (a, b) = w (a ⊕ b) )g3 H(X) = P p(x)log ¨ P * 0bd'B+. T)g3 H (X) = p(x, y)log(p(x, y)/p(x)p(y)) ¨ +_ bT+ ç 0 0bd' C \EbH( I(X; Y ) = H(X) − H (x) = H(Y ) − H (Y ) ¨ 1bd+.' bQ)bQ_( 3 C = max(H(x) − H (x)) ¨ #SB ai. i. 1 22i. i. 0. n,n∈N i,j y. i,j N. n,n∈N i,j. 2. H. min. H. H. H. 1 2 p(x). y. x,y. y. p(x). y. x.
(127) wxü. . . '+ '+_+_ +.'e( 3 d(xn , xˆn ) = 1 Pn d(xi , xˆi ) ¨ i=1 n 0bQ +_ +_ *(- T ( 2¨ Z.
(128) . d(x, xˆ) = (x − x ˆ). 2. 10log10 MσSE .. £ å o=jmo dyn wzn.q å o`vkwxqmnprtk 9v(o=jDo©a å ikw o=ywznPs[{koP{®¨ ìíþ`{ko 3tkyxq oPsap¢nwz{ko=j dyn = 8 ¨.
(129) . dyn. −1 10log10 2M SE.
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