Wavelet Transform and SPIHT Coding

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Wavelet Transform and SPIHT Coding
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Outline

• Wavelet Transform
• SPIHT Coding
• Multiple Description Coding

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Wavelet Transform

• WHY Transform ?
• (1)energy compaction
• ???????????
• (2)decorrelation
• ???????????

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Wavelet Transform
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Discrete Wavelet Transformation
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Discrete Wavelet Transformation
???
???
LL1 HL1
LH1 HH1
LL2 HL2 HL1
LH2 HH2 HL1
LH1 LH1 HH1
???
HL2 HL1
HL2 HL1
LH2 LH2 HH2 HL1
LH1 LH1 LH1 HH1
LL3 HL3
LH3 HH3
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5/3 Lena 2-level
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??LL2??
PSNR29.2137dB
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Data Extension
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Period or Symmetric Extension
bpp 9/7 10/18 5/3 9/7M 5/11A 5/11C 13/7C 13/7T
0.125 30.06 /30.53 30.21 /30.69 29.61 /30.05 29.88 /30.32 29.73 /30.22 29.74 /30.25 30.07 /30.51 30.05 /30.50
0.25 33.22 /33.59 33.27 /33.76 32.61 /32.95 33.00 /33.36 32.84 /33.16 32.93 /33.27 33.16 /33.53 33.14 /33.50
0.5 36.53 /36.75 36.48 /36.88 35.91 /36.09 36.27 /36.56 36.12 /36.32 36.20 /36.43 36.42 /36.72 36.42 /36.70
1.0 39.77 /39.92 39.74 /39.95 39.15 /39.30 39.45 /39.60 39.31 /39.47 39.35 /39.51 39.62 /39.77 39.60 /39.74
Lena
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SPIHT Coding
DWT
SPIHT
IWT
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SPIHT Coding

• Proposed by Said and Pearlman in 1996
• Regard tree as the unit
• Idea of zerotree
• A. Said and W. A. Pearlman, A new, fast, and
  efficient image codec based on set partitioning
  in hierarchical trees, IEEE Trans. Circuits
  Syst. Video Technol., vol. 6, no. 3, pp. 243-250,
  June 1996.

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SPIHT Coding
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Two Type Zerotree
TYPE A
TYPE B
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SPIHT Coding
Initial threshold T
TT/2
LSP List of Significant Pixel
LIP List of Insignificant Pixel
LIS List of Insignificant Set
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Compression Performance with Various Filters
bpp D2 D4 D6 D8 9-tap 9/7 10/18 5/3 9/7M 5/11A 5/11C 13/7C 13/7T
0.125 27.53 28.99 29.39 29.50 30.37 30.53 30.69 30.05 30.32 30.22 30.25 30.51 30.50
0.25 30.21 31.88 32.37 32.54 33.39 33.59 33.76 32.95 33.36 33.16 33.27 33.53 33.50
0.5 33.50 35.27 35.75 35.87 36.57 36.75 36.88 36.09 36.56 36.32 36.43 36.72 36.70
1.0 37.45 38.94 39.27 39.36 39.78 39.92 39.95 39.30 39.60 39.47 39.51 39.77 39.74
Lena
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SPIHT?????

• ???????????????
• ??????????????

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Multiple Description Coding

• ?????????????????
• ?????????

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Multiple Description Coding
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Multiple Description Coding
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Multiple Description Coding
Lena 0.125bpp 10 packet lost
Unprotect PSNR14.29dB
MDC PSNR27.95dB