社内ゼミ用の資料です。 画像、音楽、動画、音声、データの圧縮に関する話。口頭での説明がないと伝わりにくいかもしれません。あしからず。

1. 2009.6.4 warawara@bug.co.jp

3. • ... JPEG, GIF, PNG, J2K, ...
• ... MPEG1/2/4, H.264,WMV, ...
• ... MP3, AAC, AppleLossless, ...
• ... μLaw, ADPCM, CELP, ...
• ... ZIP, LZH, CAB, 7z, bz2, ...

4. LOSSLESS LOSSY
Lossless
Lossy

6. ZeoSync
100 1

7. ZeoSync
100 1

8. Yes No

9. Yes No

10. 10bit = 1024 4bit = 16

11. 3
1
2
(Lossy )
3

12. 1 2

13. JPEG

15. RGB YCbCr
R G B
Y Cb Cr

17. 4:2:2
4:4:4
4: 1: 1

21. 100
75
50
25
0
1 11 21 31

22. 2
,

23. N
N
KLT

24. KLT
( )

25. KLT
DCT
, ρ→1

26. DCT
( )

27. 8x8 = 64

28. JPEG
,

29. 3
1
YCbCr, DCT
2
3

30. MP3

31. Speech
Audio

32. JPEG
MDCT
( DCT)

34. 3
1
MDCT
2
,
3

35. MPEG1/2

36. JPEG
MP3
MPEG Layer 1,2,3

38. I,P,B
I Frame: JPEG
P Frame:
B Frame:

39. 3
1
YCbCr, DCT
2
,
3

40. PCM,μLaw,ADPCM,CELP

42. Speech
Audio

43. bit
PCM ... 44kHz 16bit *2
μLaw ... 8kHz 8bit (ISDN 64+64=128)
ADPCM ... 8kHz 4bit (PHS)

44. ADPCM 32kbps
CELP 4 16kbps ( ,skype)

45. CELP
(Code excited linear prediction)
Volume
, Dictionary
, , Noise

46. 3
1
, , , , ,
2
3

47. RunLength,LZ77,LZ78,BWT,PPM

48. RunLength
AAAAAABBBCC A6B3C2
)JPGE, BMP

49. LZ77, LZSS
(Ziv,Lempel)
( )
(1 )
) ZIP,LZH,CAB(LZX),
7z(LZMA),PNG,...

50. 012340123012340123012340123
Sliding Window Input Output
1.
****************
012340123012340123012340123
2.
***************0 12340123012340123012340123 0
3.
**************01 2340123012340123012340123 01
4.
*************012 340123012340123012340123 012
5.
************0123 40123012340123012340123 0123
6.
***********01234 0123012340123012340123 01234
7.
*******012340123 012340123012340123 01234[5,4]
8.
2340123012340123 0123[5,4][9,18]

51. ) CAB(LZX), 7z(LZMA)

52. LZ78,LZW
) GIF
GIF

53. 012340123012340123012340123
w K wK
null 0 0
1. 1
0 1 01 01(256) [0]
2. ( w ) 1 2 12 12(257) [1]
2 3 23 23(258) [2]
3. ( K ) 3 4 34 34(259) [3]
4. w K (wK) 4 0 40 40(260) [4]
0 1 01
w wK 3 01 2 012 012(261) [256]
2 3 23
5. w
23 0 230 230(262) [258]
wK w K 3 0 1 01
01 2 012
012 3 0123 0123(263) [261]
3 4 34
34 0 340 340(264) [259]
(0-255) 0 1 01
01 2 012
012 3 0123
0123 0 01230 01230(265) [263]
0 1 01
01 2 012
012 3 0123
0123 4 01234 01234(266) [263]
4 0 40
40 1 401 401(267) [260]
1 2 12
12 3 123 123(268) [257]
3 --- --- [3]

54. Block Sorting
BWT
(M.Burrows & D.J.Wheeler)
MTF(Move To Front)
) bz2

55. ABRACADABRA

56. ABRACADABRA
ABRACADABRA
BRACADABRAA
RACADABRAAB
ACADABRAABR
CADABRAABRA
ADABRAABRAC
DABRAABRACA
ABRAABRACAD
BRAABRACADA
RAABRACADAB
AABRACADABR

57. ABRACADABRA
AABRACADABR
R
ABRAABRACAD
D
ABRACADABRA
A
ACADABRAABR
R
ADABRAABRAC
C
BRAABRACADA
A
BRACADABRAA
A
CADABRAABRA
A
DABRAABRACA
A
RAABRACADAB
B
RACADABRAAB
B

58. ABRACADABRA
R
D
A
R
C RDARCAAAABB 3
A
A
A
A
B
B

59. RDARCAAAABB 3

60. RDARCAAAABB 3
R
D
A
R
C
A
A
A
A
B
B

61. RDARCAAAABB 3
A R
A D
A A
A R
A C
B A
B A
C A
D A
R B
R B

62. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A
B A B
B A B
C A C
D A D
R B R
R B R

63. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A
B A B
B A B
C A C
D A D
R B R
R B R

64. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A
B A B
B A B
C A C
D A D
R B R
R B R

65. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A
B A B
B A B
C A C
D A D
R B R
R B R

66. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A
B A B
B A B
C A C
D A D
R B R
R B R

67. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B
B A B
B A B
C A C
D A D
R B R
R B R

68. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B R
B A B
B A B
C A C
D A D
R B R
R B R

69. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B R A
B A B
B A B
C A C
D A D
R B R
R B R

70. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B R A C
B A B
B A B
C A C
D A D
R B R
R B R

71. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B R A C A
B A B
B A B
C A C
D A D
R B R
R B R

72. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B R A C A D
B A B
B A B
C A C
D A D
R B R
R B R

73. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B R A C A D A
B A B
B A B
C A C
D A D
R B R
R B R

74. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B R A C A D A B
B A B
B A B
C A C
D A D
R B R
R B R

75. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B R A C A D A B R
B A B
B A B
C A C
D A D
R B R
R B R

76. RDARCAAAABB 3
A R A
A D A
A A A
A R A
A C A A B R A C A D A B R A
B A B
B A B
C A C
D A D
R B R
R B R

77. BWT Example
Welcome to B.U.G., Inc. B.U.G. is a major player in the area of developing both of software and hardware and also supplier of systems solutions for the next generation of
computing, networking, digital video and database publishing system. SUCCESS IS MUTUAL This is our corporate motto. It means we should not compete, we should
collaborate and live together. Speculatively, * Turn the customer needs into a reality * Use each other's abilities to have a good business relationship * Universal society through
technology * Make the engineers self-realize the happiness of development For customers, societies, environments, employees.......... This means success for everything, all people
and things related to BUG. Overview B.U.G. is a major player in the area of developing both of software and hardware and also supplier of systems solutions for the next
generation of computing, networking, digital video and database publishing system. Thanks to its expertise in rich experience of technical development in them, its line of products
and services have been accepted and highly recognized by from much kind of industries. With this strong technical presence, B.U.G. has been contracted for a lot of commissioned
manufacturing and has developed a multi-platform application software such as a database application, Adobe PostScript RIP, and a network software, meanwhile it has dedicated to
development of an embedded system software, driver software, and firmware. B.U.G. also provides a full range of enhanced services, including marketing, maintenance, sales and
multi-vender technical support as well as technical development. B.U.G. has offered its customers turnkey solutions, making most of its strength in marketing research in order to
create technological breakthroughs and achieve competitive advantage and innovation. Also it forecasts of new customer and markets needs to quickly change its product line,
taking technical advantage in developing a full line of innovative products. B.U.G. has more than 100 employees at its headquarters in Sapporo and is proud of its engineers all
skilled and having wide ranges of knowledge and advanced technical abilities. B.U.G. was founded by four Hokkaido University students in 1977 and has made a rapid growth in
the last twenty years. B.U.G.'s ultimate goal is to meet various customers needs, from end-user to businesses with its advanced and leading edge technology.
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lstdas,aa,dngdst,osgemadrssa,,feedttnnaasededtssehhrresnhslrrlsfesoeeoleaayssgn,sddeel,lffnrmkssyssyseooldggff,dgfsgreheennneenrrndhyedrrdsssseststll.,ssgsyr.
yne.gPeggessssmgseggeseeifdinestcssoGmmysr.GGGGGGGGG........sUUUUUUUUUBBBBBBBBB01 791U UCC U......... R A I SIE t U .........TSBM ee
ttt l e rfmee ttkmmmMmtecccccocscttsee h nvhv hrrheevvmerh Sehhwwwwwwwww vmmmeu hhhwhhh bbblc dddrmrelclrrccvlvlhhhllaaaom aauua
niiiiiiieiiiaunnnnnnciicuirua aeeeeeeeeeooine l Suauuae ennnnneeeoeelnnneinnnnnnnnennennlnuneeeneen eaind uiinri eee auiAa
eeeooonaaaarrbvdvgrrrrgtlshhvvhshthgslghthhgnncvssdwwrtgrkzmvcrrrcntrrr lhrrrmmmsyrrtttttttttrppltcdztrncdcttbl deeennnbbnnyymrrWswvvvvvvvvvthtt tteetis vgg r
mmmmdmw ddpcmyymiivdsdhhnnfpetmemmvvpssvvdlecgisiciierrcnnnepgikkpknnniidddddddd in nnkoooooooooooooooooooolufo t oooooo
nnnnnnnnnnnnnnnnnnndaannd nouiuonniio nnoocctcttcttcgttncT tttttttt tttc wssttsTTtgcccccccccssttgttnngnnnndllvvrupwvvvarlltttrcchvhddhbbkt k
lllggpssprppddkthhkvhkkttth a tttttsttttrhrfv hh h tllm ggwWllt lsttltrnnlnaarkarrrns aarroc naaalaaaallallaaaal epeuppeuupi lwaepppp bbiia aeuauaoioooeeeeeeee
ppAaaauuucoookherooeeee ieo ppppnooooomo ooeeooee raiieeiaiooiioiiriiooeIeeaaaaiaaaaaaaaaaaaaaaaaaaaiaaeueiiiio iieeiii
iiiiiiiiiiioiiiiiiiaaaeeieehhhhhhUUgraoiihhh nnkooaaooeeeeaaiioeeeaeattdteerttttsttstsstgdssorrr sssssstlcllHcnnnsssrrctttttccccciiiiiirriiiicgllllellllfFfjjffbp
mfwwwfpcpmPnlbb mrrrhhff innrnrlliSo xxmmapooo- oppppmmoooorppaaauuau ie mmd uoeuooeeeeeooeeooeeeet ooeeaoaaaaaaaoaaaaaab -co e t p
etuacdoaaaoooiuuopppfftiphhpgoeeeeeeaeeoaeeeeeaeii'trheteautaattsnnaettrditaiatrsetaitigsrmmtinaekidr'naetedenrtereer aUiaae eu siin uusr llll eeeeioaoyyyyyuuuuu u a
nproixxinacInossensaaann iiaaaae pcaasssssnragwiooi oey kllieileeuuaaaaauuuareiaa n t sssssnsssiciiiiniesiincosc ffffff eeeiienqppssmdddotlnooqcooffmm
osssootTto-bbcccccdppllldddd ooaiaeiieeeeeeeei-iiiOerr oraneeddttttttm tn otttoeeeegtlbbletttlg ooaasssssrii

78. PPM
(Prediction by Partial Matching)
Microsof[?] iPhon[?]
) RAR, 7z(PPMd)

79. 3

81. bit
A or B
A or B or C or D
A or B or C
10%

82. bit
A or B
A or B or C or D
A or B or C
10%
log2(1/p) bit

83. Huffman
bit
) ZIP,LZH,JPEG

84. DAEBCBACBBBC
bit/ bit bit
B
C
A
D
E

85. DAEBCBACBBBC
bit/ bit bit
B 5 0.417 1.263 6.315 0 5
C 3 0.250 2.000 6.000 10 6
A 2 0.167 2.585 5.170 110 6
D 1 0.083 3.585 3.585 1110 4
E 1 0.083 3.585 3.585 1111 4
12 1.000 13.018 24.655 25

86. ) JPEG2000
RangeCoder
) 7z(LZMA)

87. abacab
0.32291... 0.32523...

88. abacab
Huffman
bit/ bit bit
a 3 0.500 1.000 3.000 0 3
b 2 0.333 1.585 3.170 10 4
c 1 0.167 2.585 2.585 11 2
6 1.000 5.170 8.755 9

90. 3
1
2
(Lossy )
3

91. ( )
→

92. Q & A