Evaluation of SPIHT Coding Parameters Shih-Hsuan Yang and Wu-Jie Liao Department of Computer Science...
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Transcript of Evaluation of SPIHT Coding Parameters Shih-Hsuan Yang and Wu-Jie Liao Department of Computer Science...
Evaluation of SPIHT Coding Parameters
Shih-Hsuan Yang and Wu-Jie Liao
Department of Computer Science and Information Engineering
National Taipei University of Technology
Taipei, Taiwan, ROC
December 15, 2003December 15, 2003
Wavelet Transform (1D)
h0
h1
2
2
g0
g12
2
LPF LPF
HPF HPF
X(n) y(n)
If X(n) = y(n), this called perfect reconstruction
Effects of Wavelet Filters
Properties of wavelets:Desirable time-frequency localization.Compact support.Orthogonality.Smoothness, regularity, or vanishing moment
s.Symmetry (linear-phase constraint).
Wavelet Filters for Evaluation
Real to real transform : (irreversible)5/3, 9/7-F, 9/7-M, 5/11-A, 5/11-C, 13/7-T, 13/
7-C (biorthogonal) Integer to integer transform : (reversible)
Haar wavelet (D2, orthogonal)Daubechies 4 and 6 tap (D4, D6, orthogonal)9/7, 10/18 (biorthogonal)
Real to Real Transform(RWT)
Conventional transform (convolves the input signal with the wavelet filter kernel.)
Computational complexity is proportion to the length of filter kernel.
Real to Real Transform (RWT)index D2(h0) D4(h0) D6(h0)
0 0.7071 0.4830 0.332705
1 0.7071 0.8365 0.806915
2 0.2241 0.459877
3 -0.1294 -0.135011
4 -0.0854412
5 0.0352263
index 9/7(h0) 9/7(g0) 10/18(h0) 10/18(g0)
0 0.852699 0.788486 0.75890773 0.62335964
1 0.377402 0.418092 .07679049 0.163368
2 -0.110624 -0.040689 -0.157526 -0.0856619
3 -0.023849 -0.064539 0.0000824478 -0.013765
4 0.037828 0.0288525 0.03083373
5 -0.002528037
6 -0.0094524629
7 -0.00000272719
8 0.0009544
Integer to Integer Transform (IWT)
Fixed-point approximation to conventional transform (RWT).
Suitable for lossy and lossless coding. Computational complexity is proportion to l
ifting steps required.
Integer to Integer Transform (IWT)
Lifting step
5/3:
2
1])1[][(
4
1][][
])[]1[(2
1][][
0
000
ndndnsns
nsnsndnd
9/7-F:
2
1]))1[][(217(
4096
1][][
2
1]))[]1[(203(
128
1][][
1101
0001
ndndnsns
nsnsndnd
2
1]))1[][(1817(
4096
1][][
2
1]))[]1[(113(
128
1][][
111
011
ndndnsns
nsnsndnd
Computational complexity
RWT
D2 D4 D6 9/7 10/18
1.00 1.56 2.06 2.03 3.59
IWT
5/3 9/7-F 9/7-M 5/11A 5/11-C 13/7C 13/7-T
1.00 1.94 1.01 1.52 1.52 1.13 1.13
Relative computation time required for transformation
The simulation is conducted on Pentium-4 2.4GHz PC
Effects of Extension TypesPeriodic extension Odd-symmetric (for odd-tap filter)
even-symmetric (for even-tap filter) anti-symmetric (for even-tap filter)
SPIHT Quantization
Wavelet coefficients c[i] Bit plane of c[i]
Significant : | c[i] | >= k=0,1,2,…,n
n212 n
22 n
02
k2
SPIHT Quantization(cont.)Example of Parent-Offspring dependencies
(i,j) root
O(i,j) offspring of root
D(i,j) descendant of root
L(i,j) = D(i,j) - O(i,j)
Type A
Type B
SPIHT Algorithm
Sorting passRefinement
pass
LIS : list of insignificant sets
LIP : list of insignificant pixels
LSP : list of significant pixels
for LSPencoding symbol :
0 or 1
T/ 2
T : threshold
Initialization
Experiments
ImagesLena and baboon.
Wavelet filters IWT and RWT.
Extension types Periodic and symmetric.
Test images & Visual Quality Measurement (MSE, PSNR)
MSE
2
10
255log10PSNR
MSE
2
10
255log10PSNR
MSE
2
10
255log10PSNR
M
iii yx
M 1
2)(1
MSE
lena baboon
Compression Results (“lena”)bpp
RWT
D2 D4 D6 9/7 10/18
0.125 27.53 28.97 29.38 30.53 30.68
0.25 30.21 31.85 32.35 33.58 33.75
0.5 33.50 35.24 35.75 36.74 36.86
1.0 37.47 38.92 39.26 39.92 39.96
bppIWT
5/3 9/7F 9/7M 5/11A 5/11C 13/7C 13/7T
0.125 29.71 30.25 29.78 29.84 29.79 29.94 29.90
0.25 32.60 33.24 32.87 32.81 32.88 33.04 33.07
0.5 35.75 36.17 35.93 35.92 35.89 36.14 36.13
1.0 38.87 38.84 38.80 38.89 38.80 39.03 39.00
Compression Results (“baboon”)
bppRWT
D2 D4 D6 9/7 10/18
0.125 20.97 21.28 21.37 21.49 21.60
0.25 22.14 22.54 22.64 22.88 22.97
0.5 24.08 24.60 24.79 25.11 25.13
1.0 27.31 27.97 28.21 28.62 28.61
bppIWT
5/3 9/7F 9/7M 5/11A 5/11C 13/7C 13/7T
0.125 20.96 21.42 20.85 20.92 20.87 21.05 20.98
0.25 22.25 22.80 22.18 22.23 22.17 22.40 22.35
0.5 24.22 25.07 24.28 24.25 24.23 24.49 24.47
1.0 27.71 28.37 27.80 27.79 27.76 28.02 27.98
Energy Compaction (“lena”)
RWT IWT
D2 D4 D6 9/7 10/18 5/3 9/7-F 9/7-M 5/11A 5/11C 13/7C 13/7T
97 97 97 97 97 78 96 82 78 77 81 82
Energy percentage of DC subband (%,5 level decomposition)
9/7-F 5/3
Energy Compaction (“baboon”)
RWT IWT
D2 D4 D6 9/7 10/18 5/3 9/7-F 9/7-M 5/11A 5/11C 13/7C 13/7T
98 98 98 99 98 88 98 91 88 88 91 91
Energy percentage of DC subband (%,5 level decomposition)
9/7-F 5/3
Compression Results for Period/Symmetric Extension (lena)bpp RWT
D2 D4 D6 9/7 10/18
0.125 27.53 28.97 29.38 30.06/30.53 30.20/30.68
0.25 30.21 31.85 32.35 33.21/33.58 33.58/33.75
0.5 33.50 35.24 35.75 36.52/36.74 36.46/36.86
1.0 37.47 38.92 39.26 39.77/39.92 39.75/39.96
bpp IWT
5/3 9/7F 9/7M 5/11A 5/11C 13/7C 13/7T
0.125 29.20/29.71
29.86/30.25
29.40/29.78
29.33/29.84
29.32/29.79
29.53/29.94
29.53/29.90
0.25 32.12/32.60
32.88/33.24
32.53/32.87
32.36/32.81
32.41/32.88
32.70/33.04
32.69/33.07
0.5 35.50/35.75
35.96/36.17
35.73/35.93
35.72/35.92
35.72/35.89
35.90/36.14
35.89/36.13
1.0 38.76/38.87
38.74/38.84
38.71/38.80
38.78/38.89
38.70/38.80
38.92/39.03
38.88/39.00
Conclusions
9/7 and 10/18 biothogonal wavelets with symmetric extension provide the best compression performance, but highest complexity.
5/3 filter may be reasonably choice for low complexity codecs.