• Aucun résultat trouvé

A low-complexity video coder based on the Discrete Walsh Hadamard Transform

N/A
N/A
Protected

Academic year: 2022

Partager "A low-complexity video coder based on the Discrete Walsh Hadamard Transform"

Copied!
4
0
0

Texte intégral

(1)

N OQP%RTSU!PWVYXZOQ[]\_^`9acbd^.e;[fPgU!Phe;[i

j;kml7[enPWop`q;[srt^.lU]i[u`[wv kmO.lqyxzkme;kmV{kmi|ey}~ikmoZl7)PWi|V

€ƒ‚4„#…†‡&ˆH†D‰JˆH‰‹ŠŒ Ž]‘2’!“‡?”>‡&•–„ˆH†-— Šm˜!2€‡&•u™H„ˆH‰‹ŠŒš5›œž%‡#Ÿ?— Š]¡¢ž£uˆ¤…#„“Ÿ?— Š%‡&ˆ¥š¦§ž¨!— J ‡&ˆ¥&‰JˆH‰©

ª|«J¬­(®¯°0±²#³1¯´´Dµ¶©®ƒ·5­(¸&²±­ ¹²±º».¼7½½0«-»©¾2¶©µ¿¯C±´Dµ¹º!²(À‘Á5±µ¯´¹¯»#µíÄ|Å©Â0­(ƯC±µ²fÇÈ©».«IÉJÊ(ËÇ>ÌQÍÁ5±µ¯´¹¯»#«I¹­(ƺ

½0¬­(µÆ‹ÎH³1²Q´¹­.ϵЩƋÅÑ©¶©µ¿)Ź±µ¯´¹¯Åµ¹

Ò

«J¶´¹µ¹Ñ#¹¯²(ÀHӵó1±²(¹¯³Ô©¶©²Æ²®º».¾2¶©µ¿¯C±´Dµ¹º!²(À‘Õ2¯CѳԤ֭ ¹¯CƋ»×žÑ©¯|Ä|ÅÉJ·0ũر¯C®Ñ©¯1¹Ì#»&ÙڞÉÌ(ÈÈȧÕ2¯CѳԤ֭ ¹¯CƋ»Û.ܞµ¹ÝC¯C±Æí(¶Þ

ß]àá?â|ã]ß!ä4â

Á9Ô©µÃ´šÐ­(Ð&¯C±å±¯CÐ&²±D¹´m¹Ô©¯h±¯´Dѩƹ´š²¸#¹­(µ¶©¯Þæ²(À­(ЩЩƺ.µ¶©®

¹Ô©¯%¼µÃ´³1±¯1¹¯çm­(ÆôDÔ#ÉJÚ­Þ©­(¬­(±ÞWÁ5±­(¶´À²±¬é荼žçhÚÁ2ꃵ¶

­%¿.µÃÞ#¯C²ë³1²#Þ#µ¶©®m´³Ô©¯C¬ƒ¯Åë«I¹ƒÜžµÆÆ9¸&¯f´DÔ©² ܞ¶š¹Ô­ ¹§À²±§Æ² Ü

¸©µ¹±­ ¹¯­(ЩЩƵóC­ ¹µ²¶´H¹Ô©¯7¼žçhÚÁì³C­(¶!±¯­³ÔƒÐ&¯C±DÀ²±¬­(¶³1¯´

­(¶­(Ʋ®²Ñ´|¹²ë¹Ô©²Q´D¯²¸#¹­(µ¶©¯ÞWܞµ¹Ô–¹Ô©¯%¼µÃ´³1±¯1¹¯íÙ²Q´Dµ¶©¯

Á5±­(¶´À²±¬î荼ÙÁ2êfµ¶;¹¯C±¬´²(À³1²¬ƒÐ©±¯´´Dµ²¶_¯1ï!³1µ¯C¶³1º»

°Û#Õ×»7­(¶Þ_¿.µÃ´DÑ­(Æ4ðQÑ­(Ƶ¹ºÅñÁ9Ô©µÃ´í´DÑ©®®¯´¹´u¹Ô©¯åÑ´D¯å²(À

¹Ô©¯ƒ¼žçhÚÁ¢µ¶ë¿.µÃÞ#¯C²u³1²#Þ#µ¶©®f´Dº#´¹¯C¬´7ܞԩ¯C±¯4¹Ô©¯ƒ³1²¬ƒÐ©Ñ#É

¹­ ¹µ²¶­(Ƴ1²Q´¹4µÃ´4­fÀÑ©¶Þ©­(¬ƒ¯C¶Q¹­(Ƶô´DÑ©¯»‘®µ¿¯C¶ë¹Ô©¯!À­(±|Ư´´

³1²¬ƒÐ©Ñ#¹­ ¹µ²¶­(Æ.³1²¬ƒÐ©Æ¯1ò#µ¹º²(À©¹Ô©¯ž¼žçhÚÁåܞµ¹Ô§±¯´DÐ&¯³-¹¤¹²

¹Ô©¯|¼ÙÁÅ

óõô1ö

â|ã!÷øuùä4â

ô ÷ ö

¼Ñ©¯u¹²mµ¹´®².²#ÞåÐ&¯C±DÀ²±¬­(¶³1¯uµ¶W¹¯C±¬´ƒ²(À³1²¬ƒÐ©±¯´´Dµ²¶

¯1ï!³1µ¯C¶³1º»‘¹Ô©¯u¼ÙÁúÔ­´|¸&¯C¯C¶WܞµÃÞ#¯Cƺš­Þ#²Ð#¹¯Þšµ¶å¬­(¶.º

´¹­(¶Þ©­(±Þƒ³1²#Þ#µ¶©®4´³Ô©¯C¬ƒ¯´èÀ²±¯1ò©­(¬ƒÐ©Æ¯».ûQ°½ü§»Ó%°½ü§Ç»

Ó%°½üÌ#»|­(¶Þ¢Ú|ÅÌ(ý òê-»4Þ#¯´DЩµ¹¯åµ¹´ë´¹µÆƧ±¯CÆí ¹µ¿¯CƺdÔ©µ®Ô

³1²¬ƒÐ©Ñ#¹­ ¹µ²¶­(Æ?³1²Q´¹Å

Á9Ô©¯!¼žçhÚÁþµÃ´|­(¶m²±D¹Ô©²®²¶­(Ƥ¹±­(¶´À²±¬ÿܞԩ²Q´D¯ƒ¸­´DµÃ´

ÀÑ©¶³-¹µ²¶´ƒ³1²¶´DµÃ´¹ƒ²(À7­ë´D¯1¹ƒ²(À7±¯³-¹­(¶©®Ñ©Æí(±§Þ#µÃ´³1²¶Q¹µ¶.Ñ©²Ñ´

Ü9­>¿¯1À²±¬´¹Ô­ ¹7³C­(¶f¹­¯¹Ô©¯|¿ ­(ÆÑ©¯´9ÉÇ»&È©»­(¶ÞmÇÅ«I¹Ô­´

¸&¯C¯C¶ Æí(±®¯CƺåÑ´D¯ÞWÀ²±¬­(¶.ºWµ¬­(®¯fЩ±²#³1¯´´Dµ¶©®š­(ЩЩƵóC­ É

¹µ²¶´ÇHƵ¯|µ¬­(®¯4¯C¶©Ô­(¶³1¯C¬ƒ¯C¶Q¹»&¯Þ#®¯§Þ#¯1¹¯³-¹µ²¶?»+´DÐ&¯³-É

¹±­(Æ5­(¶­(ƺ#´DµÃ´C»Þ#µ®µ¹­(Æƹ¯C±µ¶©®!­(¶Þu¹²]´D²¬ƒ¯¯1ò.¹¯C¶Q¹µ¬­(®¯

³1²¬ƒÐ©±¯´´Dµ²¶?ÅÁ9Ô©¯§¬­(µ¶ë­Þ#¿ ­(¶Q¹­(®¯|²(À0¹Ô©¯ƒ¼žçhÚÁ¢µÃ´7µ¹´

Ʋ Ü;³1²¬ƒÐ©Ñ#¹­ ¹µ²¶­(Ƥ³1²¬ƒÐ©Æ¯1ò#µ¹º»&´Dµ¶³1¯|²¶©Æºf­!´D¬­(ÆÆ5¶.Ñ©¬§É

¸&¯C±ž²(ÀH­Þ©Þ#µ¹µ²¶´9µÃ´ž±¯ðQÑ©µ±¯Þ¹²!³1²¬ƒÐ©Ñ#¹¯µ¹Å

Á9Ô©¯7±¯´Dѩƹ´µ¶!¹Ô©µÃ´Ð­(Ð&¯C±9´DÔ©² Ü ¹Ô­ ¹9µ¶]¹Ô©¯³C­´D¯²(À?Ʋ Ü

¸©µ¹±­ ¹¯¿.µÃÞ#¯C²³1²#Þ#µ¶©®f¹Ô©¯Ð&¯C±DÀ²±¬­(¶³1¯ƒ²(À¹Ô©¯!¼žçhÚÁæµÃ´

³1²¬ƒÐ­(±­(¸©Æ¯¹²ƒ¹Ô­ ¹2²¸#¹­(µ¶©¯Þuܞµ¹Ôf¹Ô©¯|¼ÙÁ_µ¶u¹¯C±¬´ž²(À

³1²¬ƒÐ©±¯´´Dµ²¶?»)°Û#Õ×»+­(¶Þ%¿.µÃ´DÑ­(ÆHðQÑ­(Ƶ¹ºÅ|Á9Ô©µÃ´7µ¶Þ#µÃ³C­ ¹¯´

¹Ô­ ¹¤¹Ô©¯ž¼žçhÚÁW³C­(¶4¸&¯À­>¿²±­(¸©Æº7Ñ´D¯Þ|µ¶§Æ² ܚ¸©µ¹±­ ¹¯9­(Ð#É

ЩƵóC­ ¹µ²¶´C»5´Dµ¶³1¯ƒµ¹´Æ² Üæ³1²¬ƒÐ©Ñ#¹­ ¹µ²¶­(ÆH³1²Q´¹|³1²¶´¹µ¹Ñ#¹¯´

­(¶ƒ­Þ#¿ ­(¶Q¹­(®¯Üžµ¹Ô§±¯´DÐ&¯³-¹H¹²7¹Ô©¯ž´Dº#´¹¯C¬´¤¹Ô­ ¹­(±¯¸­´D¯Þ

²¶]¹Ô©¯|¼ÙÁÅ

ã äƒ÷ß!ä4â

ô ÷ ö

ã!÷ ãâ

ô

á

ó ø !#"$

Á9Ô©¯&%fÉIÐ&²µ¶Q¹|Ç1ÉJ¼¢¼žçhÚÁ_²(ÀH­Þ#µÃ´³1±¯1¹¯1ɋ¹µ¬ƒ¯´Dµ®¶­(Æ'¤è (5ê

µÃ´žÞ#¯¶©¯Þf­´Î

)

è+*©ê-,

Ç

%

.0/1

2

345

'¤è (5ê7698©è (5êܞµ¹Ô:*,hÈ<;CÇ=;?>>>;@%BA–Ç

ܞԩ¯C±¯C698#è (5êµÃ´¹Ô©¯çm­(ÆôDÔ]ÀÑ©¶³-¹µ²¶DÇ?²(À¤²±Þ#¯C±E*)»#ܞԩµÃ³Ô

µÃ´žÞ#¯¶©¯Þu±¯³1Ñ©±´Dµ¿¯Cƺ!­´CÎ

698F(GH, È À²±E(JI ȃ­(¶Þ(JKL%MA–Ç èÇ>ê

6 5 (GH, Ç À²±E(:,hÈ<;CÇ=;?>>>;@%BA–Ç

6ENO8F(GH,P698FÌQ(GFRhèSAÇ>ê

8

698FÌQ(A–Ç

6ENO8T

1 (GH,P698FÌQ(GUA èSAÇ>ê

8

698FÌQ(A–Ç

À²±*L, È<;CÇ=;?>>>;@%VA_ÇÅWÁ9Ô©¯f¶­ ¹Ñ©±¯u²(À2¹Ô©¯´D¯uÀÑ©¶³-¹µ²¶´

´DÑ©®®¯´¹´H¹Ô­ ¹¹Ô©¯7¼žçhÚÁh³C­(¶!¸&¯´DÑ©µ¹­(¸©Æ¯2À²±³1²#Þ#µ¶©®4µ¬§É

­(®¯´9ܞµ¹ÔfÔ©µ®ÔuÀ±¯ðQÑ©¯C¶³1º!À¯­ ¹Ñ©±¯´žÆµ¯¯Þ#®¯´ž²±2Þ#¯1¹­(µÆ¯Þ

¹¯1ò.¹Ñ©±¯ÌWIÅ

XY

ZQ[U\ìä]"$^`_a<b!#"$

מ¯³C­(ÆƵ¶©®í¹Ô­ ¹ƒÀ²±Æµ¶©¯­(±§¹±­(¶´À²±¬´|¹Ô©¯¯C¶©¯C±®ºmµ¶W¹Ô©¯

´DЭ ¹µÃ­(Æ0Þ#²¬­(µ¶ëµÃ´¯ðQÑ­(Ƒ¹²u¹Ô©¯¯C¶©¯C±®º%µ¶í¹Ô©¯ƒÀ±¯ðQÑ©¯C¶³1º

Þ#²¬­(µ¶_荰H­(±´D¯C¿ ­(Æ+c´§×ž¯CÆí ¹µ²¶&ê-»Ü¯uÔ­>¿¯f³1²¶´DµÃÞ#¯C±¯Þš¹Ü²

ÀÑ©¶³-¹µ²¶´!µ¶ì²±Þ#¯C±ƒ¹²å¯´¹µ¬­ ¹¯¹Ô©¯%¯C¶©¯C±®º–³1²¬ƒÐ­³-¹µ²¶

­(¸©µÆµ¹º!²(À¤¹Ô©¯|¼žçhÚÁÅ

d ²±¹Ô©µÃ´|Щѩ±Ð&²Q´D¯ƒÜ¯Ô­>¿¯ƒÐ©±²#³1¯´´D¯Þë­(¶mµ¶©Ð©Ñ#¹4µ¬­(®¯»

±´¹»(¸.º4Þ#µ¿.µÃÞ#µ¶©®µ¹0µ¶Q¹²e%gfh%fÉIЩµò#¯CÆ.¸©Æ²#³O#´‘­(¶Þ|¹Ô©¯C¶?»¸.º

¹±­(¶´À²±¬ƒµ¶©®f¯­³Ô븩Ʋ#³O%ܞµ¹Ôm¹Ô©¯]¼žçhÚÁŤÁ9Ô.Ñ´C»?¹Ô©¯´D¯

¹Ü²§ÀÑ©¶³-¹µ²¶´žÜžµÆÆ+¸&¯|Þ#¯¶©¯Þu²¶­§¸©Æ²#³OQÉI²(ÀÉIЩµò#¯CÆ)¸­´DµÃ´CÅ

Á9Ô©¯i±´¹4³1²¶´DµÃÞ#¯C±¯Þ%ÀÑ©¶³-¹µ²¶mµÃ´¹Ô©¯!½0¶©¯C±®ºí°0±²®±¯´É

´Dµ¿¯ d Ñ©¶³-¹µ²¶šè½° d ê-»#ܞԩµÃ³ÔfµÃ´9¯1ò#Щ±¯´´D¯Þu­´CÎ

½° d è (5êj,

Ç

k 5 3 2l

45 ) lN

ܞµ¹Ôm(:,ìÈ<;?>>>;@%

N

A–Ç=>

«I¹]±¯CЩ±¯´D¯C¶Q¹´ƒ¹Ô©¯%Ð&¯C±³1¯C¶Q¹­(®¯²(À¯C¶©¯C±®º–³1²¶Q¹­(µ¶©¯Þ µ¶

¹Ô©¯±´¹(h³1².¯1ï!³1µ¯C¶Q¹´4²(Àž¹Ô©¯]¹±­(¶´À²±¬ƒ¯Þm¸©Æ²#³O)»Hܞԩ¯C¶

²±Þ#¯C±¯Þµ¶m­íÇ1ÉJ¼þ¿¯³-¹²±7²(Àn%

N

¯CƯC¬ƒ¯C¶Q¹´­³C³1²±Þ#µ¶©®!¹²f­

ÝCµ®Ý­(®%´³C­(¶©¶©µ¶©®Å k 5

µÃ´¹Ô©¯!¯C¶©¯C±®ºë²(À9¹Ô©¯]¸©Æ²#³Oë­(¶Þ

) l

¹Ô©¯eo‹É‹¹Ô]¹±­(¶´À²±¬ƒ¯Þu³1².¯1ï!³1µ¯C¶Q¹Å

Á9Ô©¯í´D¯³1²¶Þì³1²¶´DµÃÞ#¯C±¯ÞWÀÑ©¶³-¹µ²¶hµÃ´¹Ô©¯ëÁ5±­(¶´À²±¬ƒ¯Þ

Ù².¯1ï!³1µ¯C¶Q¹´9Â0­(±µÃ­(¶³1¯èÁÙÂê9Þ#¯¶©¯Þf­´CÎ

ÁÙ§è (5êj, k è) 3 A ) ê N

?ܞµ¹Ôm(:,hÈ<;?>>>;@%

N

A–Ç

Published in 10th European Signal Processing Conference EUSIPCO, 1217-1220, 2000

which should be used for any reference to this work 1

(2)

0 20 40 60 0.94

0.95 0.96 0.97 0.98 0.99 1

Lena

Baboon

(a)

Energy Progressive Function

coefficient index

energy percentage

DCT WHT

0 20 40 60

0 10 20 30 40 50

Lena Baboon

(b)

Transformed Coefficients Variance

sorted coefficient index

variance (dB)

DCT WHT

0 20 40 60

0 0.2 0.4 0.6 0.8 1

30 fps

3 fps

(c)

Energy Progressive Function

coefficient index

energy percentage

DCT WHT

0 20 40 60

0 10 20 30 40 50

30 fps 3 fps

(d)

Transformed Coefficients Variance

sorted coefficient index

variance (dB)

DCT WHT

d µ®Ñ©±¯!ÇÎ2½0¶©¯C±®ºu³1²¬ƒÐ­³-¹µ²¶%¯1ï!³1µ¯C¶³1ºuÀ²±2¹Ô©¯ƒ¼žçhÚÁ

­(¶Þ!¹Ô©¯|¼ÙÁÅ

ܞԩ¯C±¯H¹Ô©¯¬­ ¹Ô©¯C¬­ ¹µÃ³C­(ÆQ¯1ò#Ð&¯³-¹­ ¹µ²¶|µÃ´+¹­¯C¶|² ¿¯C±5­(ÆÆ(¹Ô©¯

µ¬­(®¯¸©Æ²#³O#´CÅ5«I¹‘Ô­´¤¸&¯C¯C¶4±¯CÐ&²±D¹¯ÞÌ!#¹Ô­ ¹¤¹Ô©¯Æ¯´´D¯C±5¹Ô©¯

¿ ­(±µÃ­(¶³1¯»¹Ô©¯¸&¯1¹D¹¯C±u­ë¹±­(¶´À²±¬ ­(ЩЩ±²Q­³Ô©¯´4¹Ô©¯%²Ð#¹µÉ

¬­(Æ ­(±Ô.Ñ©¶©¯C¶#ÉJ·?².¯C¿¯žÁ5±­(¶´À²±¬~è ·#Á2ê‘À±²¬ ¹Ô©¯¯C¶©¯C±®º

³1²¬ƒÐ­³-¹µ²¶uÐ&²µ¶Q¹2²(À¤¿.µ¯CÜ©Ô©¯C¶³1¯»©¸&²(¹Ô³1²¶´DµÃÞ#¯C±¯ÞÀÑ©¶³-É

¹µ²¶´9®µ¿¯µ¶#À²±¬­ ¹µ²¶f­(¸&²Ñ#¹ž¯C¶©¯C±®º]³1²¬ƒÐ­³-¹µ²¶?Å

Á5²ë­(¶­(ƺ.ÝC¯¹Ô©¯]¯C¶©¯C±®ºm³1²¬ƒÐ­³-¹µ²¶åЩ±²Ð&¯C±D¹µ¯´|²(Àž¹Ô©¯

¼žçhÚÁ»Q­³1²¬ƒÐ­(±µÃ´D²¶4ܞµ¹Ôƒ¹Ô©¯2¼ÙÁ–Ô­´‘¸&¯C¯C¶¬­Þ#¯»¸.º

³1²¬ƒÐ©Ñ#¹µ¶©®f¹Ô©¯¹Ü²%­(¸&² ¿¯Þ#¯´³1±µ¸&¯ÞíÀÑ©¶³-¹µ²¶´À²±|¸&²(¹Ô

¹±­(¶´À²±¬´CÅ«J¬­(®¯´2Ô­>¿.µ¶©®!Þ#µ)¯C±¯C¶Q¹7´DÐ&¯³-¹±­(Ƥ³Ô­(±­³-¹¯C±DÉ

µÃ´¹µÃ³C´9Ƶ¯·?¯C¶­©»#Ø9­(¸&².²¶f­(¶Þu­ƒ´D¯C±µ¯´²(À¤Ð©±¯Þ#µÃ³-¹µ²¶u¯C±±²±

À±­(¬ƒ¯´²¸#¹­(µ¶©¯Þ%À±²¬ ¹Ô©¯!´D¯ðQÑ©¯C¶³1¯Ú­(ÆÆÉJÓ²¶©µ¹²±»?Ô­>¿¯

¸&¯C¯C¶fÑ´D¯Þu­´¹¯´¹2µ¬­(®¯´CÅ

d µ®ÅÇQ荭Qê)­(¶Þ d µ®ÅÇQè¸&ê+´DÔ©² Üí¹Ô©¯¬ƒ¯­(¶¿ ­(ÆÑ©¯´?²(À©½° d è (5ê

­(¶ÞƒÁÙƒè (5ꑲ¸#¹­(µ¶©¯Þ§À±²¬¢¹Ô©¯0% f]% ¸©Æ²#³O#´H²(À&¹Ô©¯µ¬§É

­(®¯´ƒ·?¯C¶­m­(¶Þ Ø9­(¸&².²¶?Å d µ®ÅÇQ荳ꃭ(¶ÞdÇQèÞ꧱¯CÐ&²±D¹ƒ¹Ô©¯

¬ƒ¯­(¶f¿ ­(ÆÑ©¯´9²¸#¹­(µ¶©¯Þ]À±²¬ ¹Ô©¯|¸©Æ²#³O#´9²(ÀH­(ÆÆ+¹Ô©¯Ð©±¯Þ#µÃ³-É

¹µ²¶¯C±±²±HÀ±­(¬ƒ¯´H²(À+¹Ô©¯´D¯ðQÑ©¯C¶³1¯Ú­(ÆÆÉJÓ²¶©µ¹²±»¬ƒ¯­´DÑ©±DÉ

µ¶©®§¹Ô©¯±¯´Dѩƹ´9²(À‘Ñ´Dµ¶©®§¹Ü²Þ#µ)¯C±¯C¶Q¹žÀ±­(¬ƒ¯±­ ¹¯´CÅ

Á9Ô©¯´D¯7±¯´Dѩƹ´µÆÆÑ´¹±­ ¹¯7¹Ô­ ¹9¹Ô©¯¼ÙÁhc´ž­(¶Þ]¼žçhÚÁhc´

Ð&¯C±DÀ²±¬­(¶³1¯»µ¶¹¯C±¬´?²(À#¯C¶©¯C±®º³1²¬ƒÐ­³-¹µ²¶?»µÃ´?¿¯C±º7´Dµ¬§É

µÆí(±7À²±¹Ô©¯µ¬­(®¯ƒØ9­(¸&².²¶m­(¶Þ%À²±¹Ô©¯Ð©±¯Þ#µÃ³-¹µ²¶ë¯C±±²±

À±­(¬ƒ¯´QܞԩµÆ¯2µ¶¹Ô©¯7³C­´D¯ž²(À+¹Ô©¯µ¬­(®¯2·?¯C¶­©»¹Ô©¯7¼žçhÚÁ

µÃ´9Ư´´9¯)¯³-¹µ¿¯¹Ô­(¶u¹Ô©¯|¼ÙÁÅ

Á9Ô©µÃ´|µÃ´4³1²¶´DµÃ´¹¯C¶Q¹4ܞµ¹Ôš¹Ô©¯]²¸´D¯C±¿ ­ ¹µ²¶m¬­Þ#¯]­ ¹|¹Ô©¯

¯C¶Þ ²(ÀåÛ.¯³-¹µ²¶ Ì#ÅÇZ­(¸&²Ñ#¹ ¹Ô©¯¢³Ô­(±­³-¹¯C±µÃ´¹µÃ³C´W²(Àí¹Ô©¯

¼žçhÚÁm¸­´DµÃ´)ÀÑ©¶³-¹µ²¶´C» ´Dµ¶³1¯H¹Ô©¯0µ¬­(®¯0·?¯C¶­žÔ­´?­žÆ¯´´D¯C±

Ô©µ®Ô#ɋÀ±¯ðQÑ©¯C¶³1º!³1²¶Q¹¯C¶Q¹ž¹Ô­(¶]¹Ô©¯µ¬­(®¯Ø9­(¸&².²¶?Å

â ø â ô1ö á?â ôZô ¢ß äƒ÷ø ô1ö

ó ä]"#[!b ^

Á5²4­(¶­(ƺ#´D¯¹Ô©¯Ð&¯C±DÀ²±¬­(¶³1¯ž²(À)¹Ô©¯7¼žçhÚÁ µ¶!´¹µÆƵ¬­(®¯

³1²#Þ#µ¶©®».­4³1²¬ƒÐ©±¯´´Dµ²¶´³Ô©¯C¬ƒ¯¸­´D¯Þ²¶¹Ô©¯7ûQ°½ü_´¹­(¶#É

0.2 0.4 0.6 0.8 1 1.2

25 30 35 40

Lena

Bits per pixel (bpp)

PSNR (dB)

dct Qk dwht Qu dwht Qk

0 0.5 1 1.5 2 2.5

20 25 30 35

Baboon

Bits per pixel (bpp)

PSNR (dB)

dct Qk dwht Qu dwht Qk

d µ®Ñ©±¯Ì#Î5×2­ ¹¯1ÉJÞ#µÃ´¹²±D¹µ²¶³1Ñ©±¿¯´+²¸#¹­(µ¶©¯ÞÀ±²¬_¯C¶³1²#Þ#µ¶©®

¹Ô©¯µ¬­(®¯´9·?¯C¶­­(¶ÞuØ9­(¸&².²¶?Å

¹Ô©¯À²ÆƲ ܞµ¶©®§Ð­(±­(®±­(ЩÔ?Å

Á9Ô©¯µ¶©Ð©Ñ#¹]µ¬­(®¯µÃ´!Þ#µ¿.µÃÞ#¯Þ–µ¶Q¹²:f ÉIЩµò#¯CÆ2¸©Æ²#³O#´

¯­³Ôm²(À9¹Ô©¯C¬ñµÃ´¹±­(¶´À²±¬ƒ¯Þm­(¶Þí¹Ô©¯C¶WðQÑ­(¶Q¹µÝC¯Þ+ÅfÁ9Ô©¯

ðQÑ­(¶Q¹µÝC¯Þ7¸©Æ²#³O7µÃ´)¹Ô©¯C¶|Э´´D¯Þ¹²­(¶¯C¶Q¹±²Ð.º7³1²#Þ#¯C±?ܞԩµÃ³Ô

±´¹¯1ò#¯³1Ñ#¹¯´|­uÝCµ®Ý­(®f´³C­(¶©¶©µ¶©®f² ¿¯C±7¹Ô©¯!ðQÑ­(¶Q¹µÝC¯Þm³1²(É

¯1ï!³1µ¯C¶Q¹µ¶ ²±Þ#¯C±§¹²m²¸#¹­(µ¶ ­mý(Ë(ÉIÐ&²µ¶Q¹fÇ1ÉJ¼ ¿¯³-¹²±­(¶Þ

¹Ô©¯C¶ëÐ&¯C±DÀ²±¬´­u±Ñ©¶#ÉIƯC¶©®(¹Ôë³1²#Þ#¯§¹²³1²¬ƒÐ­³-¹Æ²¶©®u±Ñ©¶´

²(ÀÝC¯C±²Q´CÅ5Á9Ô©¯Æí´¹‘²Ð&¯C±­ ¹µ²¶µÃ´5¹Ô©¯žÚ2Ñ)¬­(¶©¶4¯C¶³1²#Þ#µ¶©®7²(À

¹Ô©¯±¯´Dѩƹµ¶©®2´Dº.¬4¸&²Æô5­³C³1²±Þ#µ¶©®¹²ž¹Ô©¯¯´¹­(¸©ÆµÃ´DÔ©¯ÞûQ°½ü

´DÐ&¯³1µ&³C­ ¹µ²¶´CÅ

X

ã

d ²±5³1²¬ƒÐ­(±µÃ´D²¶Ð©Ñ©±Ð&²Q´D¯´+ܯ0Ô­>¿¯0³1²#Þ#¯Þ7¹Ô©¯0µ¬­(®¯´?·?¯C¶­

­(¶ÞØ9­(¸&².²¶%Ñ´Dµ¶©®¹Ô©¯§ðQÑ­(¶Q¹µÝ­ ¹µ²¶¬­ ¹±µòu¹Ô­ ¹7µÃ´Ð©±²(É

Ð&²Q´D¯Þfµ¶f¹Ô©¯4Ä2¶©¶©¯1ò Û.Ð&¯³1µ&³C­ ¹µ²¶²(À‘¹Ô©¯4ûQ°½üæÛQ¹­(¶#É

Þ©­(±Þ:ÊQIő«J¶!¹Ô©µÃ´Ð­(Ð&¯C±¹Ô©µÃ´¬­ ¹±µò!ܞµÆÆ)¸&¯7±¯1À¯C±±¯Þƒ¹²§­´

8QÅ

d µ®ÅÌf´DÔ©² Ü2´¹Ô©¯]±­ ¹¯1ÉJÞ#µÃ´¹²±D¹µ²¶m³1Ñ©±¿¯´²(À9¹Ô©¯]µ¬­(®¯´

·?¯C¶­m­(¶Þ Ø9­(¸&².²¶?»²¸#¹­(µ¶©¯Þ–¸.ºW¿ ­(±º.µ¶©®ë¹Ô©¯%´³C­(ƯuÀ­³-É

¹²±²(À?¹Ô©µÃ´9ðQÑ­(¶Q¹µÝ­ ¹µ²¶!¬­ ¹±µò!ܞµ¹Ô©µ¶!¹Ô©¯±­(¶©®¯]È<>F;WIÅ

Û.µ¶³1¯¬­ ¹±µò

8|µÃ´9¶©²(¹2²Ð#¹µ¬ƒµÝC¯Þ]À²±9¹Ô©¯|¼žçhÚÁ» d µ®ÅÌ

­(ÆôD²4Щ±¯´D¯C¶Q¹´0¹Ô©¯7±¯´Dѩƹµ¶©®4±­ ¹¯1ÉJÞ#µÃ´¹²±D¹µ²¶!³1Ñ©±¿¯´0À²±¹Ô©¯

¼žçhÚÁdðQÑ­(¶Q¹µÝC¯Þ]ܞµ¹Ôf­4Ñ©¶©µÀ²±¬ ¶©²±¬­(Ƶݭ ¹µ²¶!¬­ ¹±µò

»¤µ‹Å¯Å»‘­¬­ ¹±µòëܞԩ²Q´D¯!³1².¯1ï!³1µ¯C¶Q¹´Ô­>¿¯­(ÆÆH¹Ô©¯]´­(¬ƒ¯

¿ ­(ÆÑ©¯Å7Á9Ô©¯´D¯|¿ ­(ÆÑ©¯´Ô­>¿¯¸&¯C¯C¶ë­(ÆƲ ܯÞ]¹²]¿ ­(±º]À±²¬ ÇCË

¹²"!È©Å

«I¹|³C­(¶í¸&¯ƒ¶©²(¹¯Þ%¹Ô­ ¹¹Ô©¯¼ÙÁ¢µÃ´¬ƒ²±¯§¯1ï!³1µ¯C¶Q¹¹Ô­(¶

¹Ô©¯¼žçhÚÁ¢À²±¹Ô©¯ƒµ¬­(®¯ƒ·?¯C¶­uµ¶í¹¯C±¬´²(À9°Û#Õ×æ­(¶Þ

³1²¬ƒÐ©±¯´´Dµ²¶|±­ ¹µ²Å¤Õ2¯C¿¯C±D¹Ô©¯CƯ´´?¹Ô©¯9¿.µÃ´DÑ­(Æ#ðQÑ­(Ƶ¹º²(À©¹Ô©¯

±¯³1²¶´¹±Ñ³-¹¯Þ!µ¬­(®¯´9µÃ´ž´¹µÆÆ5³1²¬ƒÐ­(±­(¸©Æ¯Å

# ¶ ¹Ô©¯ ²(¹Ô©¯C± Ô­(¶Þ+» À²±¢¹Ô©¯ µ¬­(®¯ Ø9­(¸&².²¶ñ¹Ô©¯

¼žçhÚÁhc´?Ð&¯C±DÀ²±¬­(¶³1¯HµÃ´?¿¯C±º³1ƲQ´D¯‘¹²ž¹Ô©¯¼ÙÁhc´C»>¯C¿¯C¶µ¶

¹Ô©¯±­ ¹¯1ÉJÞ#µÃ´¹²±D¹µ²¶ƒ´D¯C¶´D¯Å‘Á9Ô©µÃ´±¯´Dѩƹ³1²¶F±¬´0­(®Q­(µ¶§¹Ô©¯

Щ±¯C¿.µ²Ñ´4²¸´D¯C±¿ ­ ¹µ²¶å±¯C®Q­(±Þ#µ¶©®¹Ô©¯f¯C¶©¯C±®ºš³1²¬ƒÐ­³-¹µ²¶

2

(3)

荭Qê²±µ®µ¶­(Æ è¸&ê9¼ÙÁ 荳ê9¼žçhÚÁ

d µ®Ñ©±¯Ê©ÎHמ¯C®µ²¶u²(À¤¹Ô©¯µ¬­(®¯Ø9­(¸&².²¶?Å

Э(±­(¸©Æ¯¹²%¹Ô©¯u¼ÙÁhc´4ܞԩ¯C¶W­(ЩЩƵ¯Þm¹²íÔ©µ®ÔšÀ±¯ðQÑ©¯C¶³1º

³1²¶Q¹¯C¶Q¹žµ¬­(®¯´C»©­´ž´DÔ©² ܞ¶]µ¶ d µ®ÅÊ©Å

d µ®ÅÊè¸&ê0­(¶Þ d µ®ÅÊ荳êH´DÔ©² ܖ¹Ô©¯7±¯³1²¶´¹±Ñ³-¹µ²¶ðQÑ­(Ƶ¹º

²(À­u±¯C®µ²¶%²(À0¹Ô©¯ƒµ¬­(®¯ƒØ9­(¸&².²¶?Å4Á9Ô©¯³1²¬ƒÐ©Æ¯1¹¯§µ¬­(®¯

Ü9­´§³1²¬ƒÐ©±¯´´D¯Þ Þ#¯³1²¬ƒÐ©±¯´´D¯Þmܞµ¹Ôå¹Ô©¯¼ÙÁ ­(¶Þš¹Ô©¯

¼žçhÚÁåܞµ¹Ô­7³1²#Þ#µ¶©®7¸©µ¹±­ ¹¯9²(À&È©Åýý2¸©Ð©Ðƒµ¶§¸&²(¹Ôƒ³C­´D¯´CÅ

«I¹³C­(¶%¸&¯§¶©²(¹¯Þ¹Ô­ ¹7¹Ô©¯§Æ² Ü9ɋÀ±¯ðQÑ©¯C¶³1ºuÝC²¶©¯´§è¯Å®Å»&¹Ô©¯

µ±µÃ´ê]­(±¯í¸&¯1¹D¹¯C±±¯³1²¶´¹±Ñ³-¹¯Þì¸.º ¹Ô©¯m¼ÙÁ»žÜžÔ©µÆ¯í¹Ô©¯

¼žçhÚÁdÐ&¯C±DÀ²±¬´9¸&¯1¹D¹¯C±2²¶]¹Ô©¯Ô©µ®Ô#ɋÀ±¯ðQÑ©¯C¶³1º!±¯C®µ²¶´CÅ

â ø â ô1öuô ø ÷ á ù 7ö ä äƒ÷ø

ô1ö

Á5²ë±¯Cµ¶#À²±³1¯!¹Ô©¯uÆí ¹D¹¯C±ƒ²¸´D¯C±¿ ­ ¹µ²¶?»0­íÆí(±®¯]¶.Ñ©¬4¸&¯C±ƒ²(À

Щ±¯Þ#µÃ³-¹µ²¶¯C±±²±‘À±­(¬ƒ¯´0Ô­´0¸&¯C¯C¶!³1²#Þ#¯ÞƒÀ²ÆƲ ܞµ¶©®¹Ô©¯±¯1É

Ð&²±D¹¯Þ§´³Ô©¯C¬ƒ¯2­(¶Þ4Ñ´Dµ¶©®¸&²(¹Ô§¹±­(¶´À²±¬´CÅ d µ®Å˱¯CÐ&²±D¹´

­4±¯CЩ±¯´D¯C¶Q¹­ ¹µ¿¯2¯1ò©­(¬ƒÐ©Æ¯7²(À?¹Ô©¯±¯´Dѩƹ´²¸#¹­(µ¶©¯Þ+ÅH«I¹ž³C­(¶

¸&¯7¶©²(¹¯Þ!¹Ô­ ¹¹Ô©¯¼žçhÚÁhc´±­ ¹¯1ÉJÞ#µÃ´¹²±D¹µ²¶!Ð&¯C±DÀ²±¬­(¶³1¯

µÃ´¿¯C±º%³1ƲQ´D¯§¹²f¹Ô­ ¹²¸#¹­(µ¶©¯Þë¸.º%Ñ´Dµ¶©®u¹Ô©¯!¼ÙÁÅ5Á9Ô©µÃ´

À­³-¹4´DÑ©®®¯´¹´¹²%­(¶­(ƺ.ÝC¯§¹Ô©¯!­(ЩЩƵóC­ ¹µ²¶m²(À¹Ô©¯!¼žçhÚÁ

¹²ƒ¯C¶³1²#Þ#¯Ð©±¯Þ#µÃ³-¹µ²¶u¯C±±²±À±­(¬ƒ¯´CÅ

ó ä]"#[åáb ^

Á9Ô©¯¬ƒ²(¹µ¿ ­ ¹µ²¶–²(ÀÑ´Dµ¶©®å¼žçhÚÁ~µÃ´§¹²m¹­¯­Þ#¿ ­(¶Q¹­(®¯

²(ÀHµ¹´2Ʋ ÜZ³1²¬ƒÐ©Ñ#¹­ ¹µ²¶­(Æ5³1²Q´¹Å9«J¶²±Þ#¯C±ž¹²¯C¯CÐf¹Ô©¯|Ʋ Ü

³1²¬ƒÐ©Æ¯1ò#µ¹º|¹­(±®¯1¹0µ¶¿.µÃÞ#¯C²|³1²#Þ#µ¶©®»Q­¿¯C±º4´Dµ¬ƒÐ©Æ¯´³Ô©¯C¬ƒ¯

Ô­´¸&¯C¯C¶fÑ´D¯Þ!¹²´¹ÑÞ#º!¹Ô©¯Ð&¯C±DÀ²±¬­(¶³1¯7²(À5¹Ô©¯|¼žçhÚÁÅ

Á9Ô©µÃ´ž´³Ô©¯C¬ƒ¯µÃ´ž¸­´D¯Þ]²¶fÓ²(¹µ²¶ûQ°½üúèÓ%ûQ°½üê-Å

Á9Ô©¯m±´¹!À±­(¬ƒ¯²(À7¹Ô©¯%¿.µÃÞ#¯C²å´D¯ðQÑ©¯C¶³1¯µÃ´µ¶Q¹±­ À±­(¬ƒ¯

³1²#Þ#¯Þ+»žµ‹Å¯Å»2µ¹uµÃ´u³1²#Þ#¯Þì­´]­(¶h²±Þ#µ¶­(±ºW´¹µÆÆ7µ¬­(®¯%Ñ´É

µ¶©®W¹Ô©¯šûQ°½ü ´¹­(¶Þ©­(±Þ+Å Á9Ô©¯m´DÑ©¸´D¯ðQÑ©¯C¶Q¹fÀ±­(¬ƒ¯´f­(±¯

µ¶Q¹¯C±DÀ±­(¬ƒ¯³1²#Þ#¯ÞW¸.º–­(ЩЩƺ.µ¶©®ë¹Ô©¯%ûQ°½ü ­(Æ®²±µ¹Ô©¬ ¹²

¹Ô©¯Ð©±¯Þ#µÃ³-¹µ²¶–¯C±±²±4À±­(¬ƒ¯´ƒÑ´Dµ¶©®š­ëÑ©¶©µÀ²±¬ ðQÑ­(¶Q¹µÝ­ É

¹µ²¶u¬­ ¹±µò+Å

Á5²ƒ­(¶­(ƺ#´D¯¹Ô©¯¼žçhÚÁdÐ&¯C±DÀ²±¬­(¶³1¯».ܯ7Ô­>¿¯­(ЩЩƵ¯Þ

¸&²(¹Ôí¹±­(¶´À²±¬´µ¶ë¹Ô©µÃ´¿.µÃÞ#¯C²f³1²#Þ#µ¶©®f´³Ô©¯C¬ƒ¯­(¶Þí³1²¬§É

Э(±¯Þm¹Ô©¯u¬ƒ¯­(¶W°Û#Õ× ²(À7­(Æƹԩ¯]À±­(¬ƒ¯´4²(À2¹Ô©¯u±¯³1²¶#É

´¹±Ñ³-¹¯Þš´D¯ðQÑ©¯C¶³1¯´|²¸#¹­(µ¶©¯Þå­ ¹§Þ#µ)¯C±¯C¶Q¹§¸©µ¹±­ ¹¯´CÅíÁ9Ô©¯

Ù«

d

Ú­(ÆÆÉJÓ²¶©µ¹²±]´D¯ðQÑ©¯C¶³1¯Ô­´!¸&¯C¯C¶ìÑ´D¯Þì­´!­ë¹¯´¹

´D¯ðQÑ©¯C¶³1¯Å

çìÔ©¯C¶ë¹Ô©¯±´¹À±­(¬ƒ¯ƒ²(À¹Ô©¯!´D¯ðQÑ©¯C¶³1¯ƒµÃ´¯C¶³1²#Þ#¯ÞíÑ´É

µ¶©®4¹Ô©¯´­(¬ƒ¯7ðQÑ­(¶Q¹µÝ­ ¹µ²¶!¬­ ¹±µò

87À²±9¸&²(¹Ô!¹Ô©¯¼ÙÁ

­(¶Þ!¹Ô©¯¼žçhÚÁ»#¹Ô©¯³1²±±¯´DÐ&²¶Þ#µ¶©®§°Û#Õ×d²(À5¹Ô©¯±¯³1²¶#É

´¹±Ñ³-¹¯Þƒµ¬­(®¯´0­(±¯Þ#µ)¯C±¯C¶Q¹ÅHÛ.µ¶³1¯µ¶Ð©±¯Þ#µÃ³-¹µ¿¯³1²#Þ#µ¶©®

¹Ô©¯íðQÑ­(Ƶ¹ºå²(À¹Ô©¯m±´¹!±¯³1²¶´¹±Ñ³-¹¯ÞWÀ±­(¬ƒ¯µ¶Ñ©¯C¶³1¯´

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

30 30.2 30.4 30.6 30.8 31 31.2 31.4

Bits per pixel (bpp)

PSNR (dB)

R−D curves for an interframe

DCT−Q u DWHT−Q

u

d µ®Ñ©±¯ËÎ4×2­ ¹¯1ÉJÞ#µÃ´¹²±D¹µ²¶š³1Ñ©±¿¯´²¸#¹­(µ¶©¯Þm¸.ºë³1²#Þ#µ¶©®%­

´Dµ¶©®Æ¯¯C±±²±9Щ±¯Þ#µÃ³-¹µ²¶]À±­(¬ƒ¯Å

10 20 30 40 50 60 70

31 32 33 34 35 36 37 38 39 40 41

Mean bit rate (Kbit/s)

PSNR (dB)

R−D curves (uniform quantization)

DCT DWHT

d µ®Ñ©±¯ #Î Ù²#Þ#µ¶©®dÐ&¯C±DÀ²±¬­(¶³1¯š²(À¹Ô©¯–¼ÙÁ ­(¶Þ_¹Ô©¯

¼žçhÚÁhÀ²±9¹Ô©¯|Ú­(ÆÆÉJÓ²¶©µ¹²±2´D¯ðQÑ©¯C¶³1¯Å

¹²f¬­¯§­]À­(µ±³1²¬ƒÐ­(±µÃ´D²¶?»)µ¹Ô­´¸&¯C¯C¶m³Ô©²Q´D¯C¶%¹²f´¹­(±D¹

ܞµ¹Ôu­e±´¹±¯³1²¶´¹±Ñ³-¹¯ÞƒÀ±­(¬ƒ¯Ô­>¿.µ¶©®¹Ô©¯´­(¬ƒ¯7°Û#Õ×

À²±¸&²(¹Ôì³C­´D¯´CÅìÁ5²š­³C³1²¬ƒÐ©ÆµÃ´DÔW¹Ô©µÃ´ƒ¹­´ š¹Ü²šÞ#µ)¯C±¯C¶Q¹

ðQÑ­(¶Q¹µÝ­ ¹µ²¶§¬­ ¹±µÃ³1¯´HÔ­>¿¯9¸&¯C¯C¶Ñ´D¯Þ§µ¶§¹Ô©¯³1²#Þ#µ¶©®Ð©±²(É

³1¯´´²(À0¹Ô©¯]±´¹7À±­(¬ƒ¯Î 8ƒÀ²±¹Ô©¯ƒ¼ÙÁ¢­(¶Þ 8!´³C­(ƯÞ

¸.ºë­]À­³-¹²±|È©ÅÍÀ²±¹Ô©¯!¼žçhÚÁÅ5«J¶ë¹Ô©µÃ´|Ü9­>ºf¹Ô©¯]°Û#Õ×

²(À¹Ô©¯:±´¹u±¯³1²¶´¹±Ñ³-¹¯Þ µ¬­(®¯%µÃ´!¹Ô©¯ë´­(¬ƒ¯%À²±]¸&²(¹Ô

¹±­(¶´À²±¬´CÅ

X ã

d µ®Ñ©±¯ í´DÔ©² Ü2´|¹Ô©¯f±­ ¹¯1ÉJÞ#µÃ´¹²±D¹µ²¶W³1Ñ©±¿¯´4²¸#¹­(µ¶©¯Þå¸.º

Ñ´Dµ¶©®ë¼ÙÁ ­(¶ÞW¼žçhÚÁő«I¹!³C­(¶å¸&¯f¶©²(¹¯Þš¹Ô­ ¹§À²±ƒÆ² Ü

¸©µ¹±­ ¹¯¿ ­(ÆÑ©¯´íèÇÈ ÉÌ(È ¸©µ¹ ´ê§¹Ô©¯%Ð&¯C±DÀ²±¬­(¶³1¯fµÃ´!¿¯C±º

3

(4)

d µ®Ñ©±¯ ý©Î מ¯³1²¶´¹±Ñ³-¹¯Þ À±­(¬ƒ¯ ²(ÀZ´D¯ðQÑ©¯C¶³1¯ Ú­(ÆÆÉ

Ó²¶©µ¹²±Å

ø øä4â

¬ƒ¯1¹Ô©²#Þ ¬4ѩƹµÐ©ÆµÃ³C­ ¹µ²¶´ ­Þ©Þ#µ¹µ²¶´

Ä2±­(µ-ËI»?Ç1ÉJ¼úèòÌê È ËQý(Ë

·?µ¶©ÝC¯C±&WI»?Ç1ÉJ¼úèòÌê ÇýÈ ËÇý

ç쵶©²®±­Þ ýQI»&Ì>ÉJ¼ Ë ËQýQÌ

¼µ¬ƒµ¹±² ¿ Í! É ýÊý

ø ø â

¬ƒ¯1¹Ô©²#Þ ¬4ѩƹµÐ©ÆµÃ³C­ ¹µ²¶´ ­Þ©Þ#µ¹µ²¶´

Ó%­(¶©ÝQI»?Ç1ÉJ¼úèòÌê É Ê (Ë

Á¤­(¸©Æ¯¢ÇÎñÙ²¬ƒÐ©Ñ#¹­ ¹µ²¶­(Æu³1²Q´¹åÀ²±–¿ ­(±µ²Ñ´W¼ÙÁ ­(¶Þ

¼žçhÚÁ_­(Æ®²±µ¹Ô©¬´CÅ

Á9Ô©¯±¯³1²¶´¹±Ñ³-¹¯Þ|´D¯ðQÑ©¯C¶³1¯´¤Ü¯C±¯­(ÆôD²¯C¿ ­(ÆÑ­ ¹¯ÞÀ±²¬

­|¿.µÃ´DÑ­(Æ+ðQÑ­(Ƶ¹ºƒÐ&²µ¶Q¹ž²(À5¿.µ¯CÜő«I¹9Ü9­´0À²Ñ©¶Þ!¹Ô­ ¹¹Ô©¯±¯1É

´Dѩƹµ¶©®]¼ÙÁhc´­(¶Þf¼žçhÚÁhc´±¯³1²¶´¹±Ñ³-¹¯Þ]À±­(¬ƒ¯´žÜ¯C±¯

¶©¯­(±Æºµ¶Þ#µÃ´¹µ¶©®Ñ©µÃ´DÔ­(¸©Æ¯Å d µ®Ñ©±¯ý2´DÔ©² Ü2´5­ž±¯³1²¶´¹±Ñ³-¹¯Þ

À±­(¬ƒ¯!²(À9¹Ô©¯u´D¯ðQÑ©¯C¶³1¯]Ú­(ÆÆÉJÓ²¶©µ¹²±4²¸#¹­(µ¶©¯Þm¸.ºëÑ´Dµ¶©®

¸&²(¹Ô|¹±­(¶´À²±¬´CÅ5Á9Ô©¯´D¯±¯´Dѩƹ´5µ¶Þ#µÃ³C­ ¹¯¹Ô­ ¹¤¹Ô©¯9¼žçhÚÁ

³1²Ñ©ÆÃÞ¸&¯À­>¿²±­(¸©Æº4Ñ´D¯Þ!µ¶]­|¿.µÃÞ#¯C²§³1²#Þ#µ¶©®ƒ´³Ô©¯C¬ƒ¯»Q¯´DÐ&¯1É

³1µÃ­(Æƺ4ܞԩ¯C¶Ô©µ®Ô!³1²¬ƒÐ©±¯´´Dµ²¶ƒ±­ ¹µ²Q´0­(±¯ž±¯ðQÑ©µ±¯Þ§µ¶Ô©µ®Ô

À±¯ðQÑ©¯C¶³1º]³1²¶Q¹¯C¶Q¹9À±­(¬ƒ¯´CÅ

äƒ÷ùuâßâ

ô ÷ ö ß

äƒ÷

j ]ô âe

Á9Ô©µÃ´2´D¯³-¹µ²¶³1²¶´DµÃÞ#¯C±´¹Ô©¯4³1²¬ƒÐ©Ñ#¹­ ¹µ²¶­(Æ?³1²¬ƒÐ©Æ¯1ò#µ¹º]²(À

¹Ô©¯¼ÙÁš­(¶Þ¹Ô©¯¼žçhÚÁ»>µ¶¹¯C±¬´?²(À­Þ©Þ#µ¹µ²¶´5­(¶Þ¬4Ñ©ÆÉ

¹µÐ©ÆµÃ³C­ ¹µ²¶´9±¯ðQÑ©µ±¯Þ!¹²³1²¬ƒÐ©Ñ#¹¯¹Ô©¯|Þ#¯´Dµ±¯Þ!¹±­(¶´À²±¬fÅ

Á5²³1²¬ƒÐ©Ñ#¹¯¹Ô©¯n%fÉIÐ&²µ¶Q¹9Ç1ÉJ¼ ¼žçhÚÁ嬭(¶.º7À­´¹‘¬ƒ¯1¹Ô#É

²#Þ©´0Ô­>¿¯ž¸&¯C¯C¶!Þ#¯´Dµ®¶©¯Þ+ÅHÓ²Q´¹0²(À+¹Ô©¯C¬æЩ±¯´D¯C¶Q¹0¹Ô©¯´­(¬ƒ¯

³1²¬ƒÐ©Ñ#¹­ ¹µ²¶­(Ƴ1²Q´¹4²(À0%=N% ­Þ©Þ#µ¹µ²¶´ÇI»0­(¶Þm¹Ô©¯Cº

­(±¯f­(ÆÆ2³Ô­(±­³-¹¯C±µÝC¯Þå¸.ºš¹Ô©¯Cµ±±¯C®Ñ©Æí(±Æºš´¹±Ñ³-¹Ñ©±¯Þ–­Þ.É

Þ#µ¹µ²¶–´³Ô©¯C¬ƒ¯ÅšÁ9Ô©¯Cµ±ƒ¬­(µ¶WÞ#µ)¯C±¯C¶³1¯uµÃ´§±­ ¹Ô©¯C±§²¶š¹Ô©¯

²Ñ#¹Ð©Ñ#¹§²±Þ#¯C±|²(À9¹Ô©¯!¹±­(¶´À²±¬ƒ¯Þm³1².¯1ï!³1µ¯C¶Q¹´CÅ%Á9Ô©¯uÌ>ÉJ¼

¼žçhÚÁæ³C­(¶í¸&¯²¸#¹­(µ¶©¯Þíܞµ¹Ôí¹Ô©¯!³1Æí´´DµÃ³C­(Ƥ±² Ü9ÉJ³1²ÆÑ©¬ƒ¶

­(ЩЩ±²Q­³Ô!±¯ðQÑ©µ±µ¶©®!Ì%

N

=N?%ñ­Þ©Þ#µ¹µ²¶´CÅ

Á5²m³1²¬ƒÐ©Ñ#¹¯]¹Ô©¯%fÉIÐ&²µ¶Q¹fÇ1ÉJ¼ À­´¹!¼ÙÁ ¬­(¶.ºš­(Æ®²(É

±µ¹Ô©¬´uÔ­>¿¯í¸&¯C¯C¶dЩ±²Ð&²Q´D¯Þ+ÅúÁ¤­(¸©Æ¯–Ç뱯CÐ&²±D¹´u­W´DÔ©²±D¹

´DÑ©±¿¯Cº²(ÀH´DѳÔu¬ƒ¯1¹Ô©²#Þ©´CÅ

ðQÑ©µ±¯7­(¶.ºƒ¬4ѩƹµÐ©ÆµÃ³C­ ¹µ²¶u­(¶Þ!µ¹9µ¶.¿²Æ¿¯´­|Ư´´D¯C±¶.Ñ©¬4¸&¯C±

²(À+­Þ©Þ#µ¹µ²¶´‘¹Ô­(¶§¹Ô©²Q´D¯ž¶©¯Þ#¯C¯Þƒ¸.º§­(¶.º|²(À)¹Ô©¯2¼ÙÁhc´HÀ­´¹

´³Ô©¯C¬ƒ¯´C»QܞԩµÃ³Ôu­´Ð&²µ¶Q¹¯Þ!²Ñ#¹¸&¯1À²±¯»#´DÔ©² Ü2´0¹Ô©¯­Þ#¿ ­(¶#É

¹­(®¯²(À+¹Ô©¯¼žçhÚÁ À±²¬ ­4³1²¬ƒÐ©Ñ#¹­ ¹µ²¶­(Æ&Ð&²µ¶Q¹²(À5¿.µ¯CÜÅ

äƒ÷

ö ä ùá

ô ÷ ö á

Á9Ô©µÃ´4Э(Ð&¯C±ƒÐ©±¯´D¯C¶Q¹¯Þë¹Ô©¯uÐ&¯C±DÀ²±¬­(¶³1¯´4²(Àž¹Ô©¯f¼žçhÚÁ

ܞԩ¯C¶h­(ЩЩƵ¯Þ–¹²å­š¿.µÃÞ#¯C²å³1²#Þ#µ¶©®å´³Ô©¯C¬ƒ¯Å_«I¹]Ô­´¸&¯C¯C¶

´DÔ©² ܞ¶¹Ô­ ¹‘µ¶4Ʋ ܚ¸©µ¹±­ ¹¯9³1²#Þ#µ¶©®»>¹Ô©¯Ð&¯C±DÀ²±¬­(¶³1¯²(À#¹Ô©¯

¼žçhÚÁdµÃ´2³1²¬ƒÐ­(±­(¸©Æ¯¹²§¹Ô­ ¹2²¸#¹­(µ¶©¯Þ]ܞµ¹Ôu¹Ô©¯|¼ÙÁÅ

Á9Ô.Ñ´C»(Þ#Ñ©¯0¹²7µ¹´¤®².²#Þ|³1²#Þ#µ¶©®¯1ï!³1µ¯C¶³1ºµ¶4¿.µÃÞ#¯C²7³1²#Þ#µ¶©®

­(¶Þ¹²ƒµ¹´Æ² Üd³1²¬ƒÐ©Ñ#¹­ ¹µ²¶­(Æ+³1²Q´¹»Q¹Ô©¯¼žçhÚÁd³1²Ñ©ÆÃÞ!¸&¯

¯1ï!³1µ¯C¶Q¹ÆºÑ´D¯Þ|µ¶4Ʋ Ü帩µ¹±­ ¹¯¿.µÃÞ#¯C²7³1²#Þ#µ¶©®´³Ô©¯C¬ƒ¯´C»>¹Ô­ ¹

Þ#¯C¬­(¶ÞƒÆ² Ü ³1²¬ƒÐ©Æ¯1ò#µ¹º4µ¬ƒÐ©Æ¯C¬ƒ¯C¶Q¹­ ¹µ²¶´CÅ d Ñ©±D¹Ô©¯C±¬ƒ²±¯»

¹Ô©¯9±¯C®Ñ©Æí(±µ¹º7²(Àµ¹´¤À­´¹H­(Æ®²±µ¹Ô©¬´¤³C­(¶§­(ÆôD²¸&¯9¯1ò#ЩƲµ¹¯Þ

¹²Þ#¯´Dµ®¶]±¯Þ#ѳ1¯Þ.ÉJÞ#µ¯1ÉJ­(±¯­|Â7·¤Û.«µ¬ƒÐ©Æ¯C¬ƒ¯C¶Q¹­ ¹µ²¶´CÅ0°H­(±DÉ

¹µÃ³1Ñ©Æí(±|­(ЩЩƵóC­ ¹µ²¶´²(À9µ¶Q¹¯C±¯´¹µ¶³1ÆÑÞ#¯¹¯CƯ1ÉJ´DÑ©±¿¯CµÆÆí(¶³1¯

´Dº#´¹¯C¬´­(¶Þƒ¿.µÃÞ#¯C²4³1²#Þ#µ¶©®À²±¬ƒµ¶©µÃ­ ¹Ñ©±¯2¬ƒ²¸©µÆ¯´Dº#´¹¯C¬´CÅ

ßb"! "#[$ ^ G

Á9Ô©¯±´¹|­(Ñ#¹Ô©²±­³O.¶©² ܞƯÞ#®¯´2¹Ô©¯´DѩЩÐ&²±D¹±¯³1¯Cµ¿¯Þ%¸.º

Ù #

Û#Á_Ì Ëƒµ¶u¹Ô©¯À±­(¬ƒ¯²(ÀH­Û.Ô©²±D¹2Á5¯C±¬ Û#³1µ¯C¶Q¹µ&³ÓµÃ´É

´Dµ²¶?»#­(¶Þ!¸.º§¹Ô©¯|Û.ܞµÃ´´

d

¯Þ#¯C±­(Æ

#

ï!³1¯2À²±ž½Þ#ѳC­ ¹µ²¶]­(¶Þ

Û#³1µ¯C¶³1¯Ñ©¶Þ#¯C±7ü7±­(¶Q¹

# d

½ÛfÙ !.Í.ÅÈÈ (È©Å

ã!"ZQ b=

Ç Åü§Å‘د­(ѳԭ(¬ƒÐ?»$#Ä2ЩЩƵóC­ ¹µ²¶´|²(Àçm­(ÆôDÔW­(¶Þåמ¯1É

Æí ¹¯Þ d Ñ©¶³-¹µ²¶´&%©»Ä³C­Þ#¯C¬ƒµÃ³d°0±¯´´C»f·?²¶Þ#²¶?»f¾ »

Ç! (ËÅ

ÌW|Õ|ÅÛ)Å2ûQ­>ºQ­(¶Q¹u­(¶Þd°‘ÅžÕ2²ÆÆ#¼µ®µ¹­(Ƴ1²#Þ#µ¶©®–²(À4Ü9­>¿¯1É

À²±¬´&%©»0°0±¯C¶Q¹µÃ³1¯1ÉJÚ­(ÆƋ»H½0¶©®Æ¯Cܲ.²#ޖÙƵ+´C»Õû»H¾7Û#Ä|»

Ç! (ËÅ

ÊQ«Áž¾žÉJÁ מ¯³1²¬ƒ¬ƒ¯C¶Þ©­ ¹µ²¶ ÁÅ©Ç»#¼µ®µ¹­(Æ!Ù²¬ƒÐ©±¯´É

´Dµ²¶W­(¶Þ Ù²#Þ#µ¶©®í²(ÀÙ²¶Q¹µ¶.Ñ©²Ñ´É‹¹²¶©¯uÛQ¹µÆÆ9«J¬­(®¯´&%©»

Û.¯CÐ#¹Å?Ç! !QÌ#Å

Ë('§Å?Ä2±­(µ‹»+ÁÅ+Ä2®Ñ©µH­(¶ÞíӚÅ+Õ­ ­*)µ¬­©»+#Ä d ­´¹¼ÙÁÉ

Û Û#³Ô©¯C¬ƒ¯9À²±«J¬­(®¯´&%©»Á5±­(¶´CÅ(²(À&¹Ô©¯«½0«Ù½2» ÂH²Æ‹ÅQ½

Í.Ç»©Õ2²Å+ÇÇ»#ЩÐ?Å?ÇÈ ! >ÉÇÈ !.Í.»QÕ2² ¿)Å+Ç! ©Å

W|½2Ń·?µ¶©ÝC¯C± ­(¶Þ ½2Å d ¯Cµ®»,#Õ2¯CÜ ´³C­(Æ¯Þ ¼ÙÁ ­(Æ®²(É

±µ¹Ô©¬´À²±ÀÑ´D¯Þ%¬4ѩƹµÐ©Æº ­Þ©Þ%­(±³Ô©µ¹¯³-¹Ñ©±¯´&%©»)°0±²#³(Å

«ÙÄ7Û©Û#°HÉ!©Ç»Ð©Ð?Å+ÌÌ(È©Ç1ÉÌÌ(È(Ë»#Á5²±²¶Q¹²»

#

¶Q¹Å»?Ù­(¶­Þ©­©»

Ó%­>º%Ç! !©ÇÅ

ýQ|½2Å d ¯Cµ®f­(¶ÞëÛ)Å+ç쵶©²®±­Þ+»-#d ­´¹Ä2Æ®²±µ¹Ô©¬´À²±¹Ô©¯

¼µÃ´³1±¯1¹¯§Ù²Q´Dµ¶©¯Á5±­(¶´À²±¬.%©».«½½½–Á5±­(¶´CÅ#²¶Û.µ®¶­(Æ

°0±²#³1¯´´Dµ¶©®»CÂH²Æ‹ÅCËQÈ©»>Õ2²Å!©»>ЩÐ?Å>Ì#Ç Í>Ë(ÉÌ#Ç!Ê©»CÛ.¯CÐ#¹ÅQÇ! !QÌ#Å

Í!Â4ÅÛ)޼µ¬ƒµ¹±² ¿)»ü§ÅÄ|Å2ûÑ©ÆƵ¯C¶_­(¶ÞhçZÅÙŞӵÆƯC±»/#Ä

¶©¯CÜì¼ÙÁì­(Æ®²±µ¹Ô©¬ ¸­´D¯Þƒ²¶¯C¶³1²#Þ#µ¶©®|­(Æ®¯C¸©±­(µÃ³9µ¶#É

¹¯C®¯C±´&%©»)«ÙÄ7Û©Û#°HÉ! ©»¤Ç>Ì>ÉÇÓ%­>ºšÇ! ! ©»+Û.¯­ ¹D¹Æ¯»+çíÄ|»

¾7Û#Ä|Å

Q|ûÅçZÅìÓ%­(¶©Ý»0#ÄsÛ.¯ðQÑ©¯C¶³1ºQÉ # ±Þ#¯C±¯Þ d ­´¹ çm­(ÆôDÔ

Á5±­(¶´À²±¬.%©»9«½½½úÁ5±­(¶´CŲ¶hÄ2ÑÞ#µ²–­(¶Þh½0Ư³-¹±²Q­ É

³1²Ñ´¹µÃ³C´C»QÂH²Æ‹Å#оžÉÌ(È©».Õ2²Å.Ê©».ЩÐ?Å#Ì(È(Ë(ÉÌ(Èý©»Ä2Ñ©®Å)Ç!.Í(Ì#Å

4

Références

Documents relatifs

Fig. Comparative results, compression rate =30.. 5) Entropy coding: In coding systems, symbols are finally losslessly encoded by entropy coders. The principle of these coders

Several methods were used to lter the noisy image: thresholding of the undecimated wavelet transform (Figure 11b), thresholding of supercover DART (Figure 11c), thresholding of

The carried out experiments on a 1.1-kW induction generator based test bench have proved that a technique based on variance and energy analysis of wavelet decomposition

In this paper we study the relationship between the Eu- clidean and the discrete world thru two operations based on the Eu- clidean scaling function: the discrete smooth scaling and

Two parameters: the threshold (Thr) for the quadtree partitioning and quqp for the quantization process in (2), which are introduced in Section III, enable the Flat codec to obtain

An approximated quantisation multipliers matrix (Q) and its combination with one transform matrix (ST16 + Q) were also assessed in HEVC reference software, HM- 13.0, using

In addition, discrete wavelet transform (DWT) also stimulates particular research interest, since it trans- forms an image into various frequency bands, and natural images often

Secondly, we consider a specific modulation based on the sparse Walsh-Hadamard transform (WHT) that fulfills the EGC and considerably reduces the complexity of the symplectic