a comprehensive design evaluation for spiht coding...
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A Comprehensive Design A Comprehensive Design Evaluation for SPIHT CodingEvaluation for SPIHT Coding
台北科技大學資工所台北科技大學資工所指導教授：楊士萱指導教授：楊士萱學生：廖武傑學生：廖武傑
2003/06/05
OutlineOutline
TransformsTransforms Energy distribution (DWT vs Spatial domain)Energy distribution (DWT vs Spatial domain) Arithmetic coding for SPIHTArithmetic coding for SPIHT Future workFuture work
TransformsTransforms
Integer-to-integer transformInteger-to-integer transform::
Real-to-real transformReal-to-real transform:: Dot products between the two filter masks and the Dot products between the two filter masks and the
signal.signal.
2
)22()2()12()12(
nxnxnxny
4
2)12()12()2()2(
nynynxny
TransformsTransforms
Integer-to-integer transformInteger-to-integer transform::
5/3
9/7-M
TransformsTransforms
Integer-to-integer transformInteger-to-integer transform::
5/11-A
5/11-C
TransformsTransforms
Integer-to-integer transformInteger-to-integer transform::
13/7-T
13/7-C
TransformsTransforms
Integer-to-integer transformInteger-to-integer transform::
9/7-F
TransformsTransforms
Integer-to-integer transformInteger-to-integer transform::
9/7-F
TransformsTransforms
Real-to-real (orthogonal)transformReal-to-real (orthogonal)transform ::Haar (Daubechies 2-tap
)Daubechies 4-tap Daubechies 6-tap
index
0 0.707106 0.482963 0.332671
1 0.707106 0.836516 0.806892
2 0.224144 0.459878
3 -0.129410 -0.135011
4 -0.085441
5 0.035226
TransformsTransforms Real-to-real (biorthogonal)transformReal-to-real (biorthogonal)transform ::
9/7
index
0 0.852699 0.788486
1,-1 0.377402 0.418092
2,-2 -0.110624 -0.040689
3,-3 -0.023849 -0.064539
4,-4 0.037828
10/18
index
0,-1 0.758908 0.623359
1,-2 0.076790 0.163369
2,-3 -0.157526 -0.085661
3,-4 0.000082 -0.013765
4,-5 0.028852 0.308337
5,-6 -0.002528
6,-7 -0.009452
7,-8 -0.000002
8,-9 0.000095
Computation Time requiredComputation Time required
RWT IWT
D2 D4 D6 9/7 10/18
5/3 9/7-F 9/7-M
5/11A
5/11-C
13/7C
13/7-T
0.36 0.61 0.92 2.51 4.20 1.00 1.92 1.19 1.63 1.63 1.44 1.44
Relative ratio, 5/3 as 1
OutlineOutline
TransformsTransforms Energy distribution (DWT vs Spatial domain)Energy distribution (DWT vs Spatial domain) Arithmetic coding for SPIHTArithmetic coding for SPIHT Future workFuture work
Testing dataTesting data
lena
baboon
pepper
F16
Energy of LL subband( DWT domain cEnergy of LL subband( DWT domain coefficients)oefficients)
RWT IWT
D2 D4 D6 9/7 10/18 5/3 9/7-F 9/7-M 5/11A 5/11-C 13/7C 13/7-T
Lena 97.79 97.37 97.28 97.98 97.42 78.27 96.12 82.14 78.09 77.74 81.88 82.10
Baboon
98.85 98.96 98.90 99.18 98.68 88.69 98.40 91.21 88.58 88.39 91.69 91.64
F16 98.77 98.76 98.74 98.98 98.33 88.65 98.06 91.10 88.60 88.45 90.91 90.10
Pepper 94.73 94.72 94.08 95.71 94.27 68.53 92.14 73.46 68.71 68.62 72.54 73.10
“lena”, 5-level decomposition, %
Energy of LL subband( Spatial domain Energy of LL subband( Spatial domain pixels)pixels)
RWT IWT
D2 D4 D6 9/7 10/18 5/3 9/7-F 9/7-M 5/11A 5/11-C 13/7C 13/7-T
Lena 94.59 94.38 95.50 95.16 95.66 95.50 95.72 96.41 95.57 95.80 96.17 95.90
Baboon
94.15 94.36 94.62 94.67 94.64 95.32 95.20 95.86 95.22 95.22 95.48 95.33
F16 96.53 96.69 96.98 96.57 96.98 97.06 97.01 97.53 97.03 97.08 97.13 97.07
Pepper 89.82 94.83 96.64 95.61 97.94 94.62 96.61 96.51 96.46 97.12 96.48
“lena”, 5-level decomposition, %
Compression performance(PSNR,dB)Compression performance(PSNR,dB)5/3 9/7-F 9/7-M 5/11A 5/11-
C13/7C 13/7-
T10/18 9/7 Haar D4 D6
1/64 29.71 30.25 29.78 29.84 29.79 29.94 29.90 30.68 30.53 27.53 28.97 29.38
1/32 32.60 33.24 32.87 32.81 32.88 33.04 33.07 33.75 33.58 30.21 31.85 32.35
1/16 35.75 36.17 35.93 35.92 35.89 36.14 36.13 36.86 36.74 33.50 35.24 35.75
1/8 38.87 38.84 38.80 38.89 38.80 39.03 39.00 39.96 39.92 37.47 38.92 39.26
5/3 9/7-F 9/7-M 5/11A 5/11-C
13/7C 13/7-T
10/18 9/7 Haar D4 D6
1/64 20.96 21.42 20.85 20.92 20.87 21.05 20.98 21.60 21.49 20.97 21.28 21.37
1/32 22.25 22.80 22.18 22.23 22.17 22.40 22.35 22.97 22.88 22.14 22.54 22.64
1/16 24.22 25.07 24.28 24.25 24.23 24.49 24.47 25.13 25.11 24.60 24.60 24.79
1/8 27.71 28.37 27.80 27.79 27.76 28.02 27.98 28.61 28.62 27.97 27.97 28.21
Compression performance(PSNR dB)Compression performance(PSNR dB)5/3 9/7-F 9/7-M 5/11A 5/11-
C13/7C 13/7-
T10/18 9/7 Haar D4 D6
1/64 28.31 28.95 28.49 28.41 28.39 28.56 28.57 29.26 29.28 26.78 27.97 28.18
1/32 31.45 32.14 31.82 31.66 31.72 31.85 31.88 32.56 32.51 29.57 30.95 31.40
1/16 35.27 35.85 35.75 35.55 35.61 35.84 35.87 36.45 36.42 33.45 34.75 35.27
1/8 39.84 39.66 39.82 39.86 39.74 39.99 39.99 40.92 40.92 38.42 39.61 39.59
5/3 9/7-F 9/7-M 5/11A 5/11-C
13/7C 13/7-T
10/18 9/7 Haar D4 D6
1/64 28.31 28.77 28.30 28.36 28.30 28.44 28.43 29.01 29.02 25.78 27.22 27.56
1/32 30.68 31.42 31.07 30.83 30.86 31.19 31.15 31.67 31.74 28.76 30.20 30.46
1/16 33.09 33.51 33.16 33.07 32.98 33.33 33.30 33.78 33.80 31.81 32.95 33.06
1/8 35.38 35.84 35.48 35.34 35.18 35.69 35.66 36.21 36.18 35.01 35.71 35.77
Images recovered from lowest Images recovered from lowest frequency component frequency component
lena
baboon
pepper
F16
OutlineOutline
TransformsTransforms Energy distribution (DWT vs Spatial domain)Energy distribution (DWT vs Spatial domain) Arithmetic coding for SPIHTArithmetic coding for SPIHT Future workFuture work
Arithmetic coding for SPIHTArithmetic coding for SPIHT
Arithmetic coding for SPIHTArithmetic coding for SPIHT
1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1‧‧‧
Symbol 1 Symbol 3 。。。Symbol 2
Bit stream from SPIHT
encoded
OutlineOutline
TransformsTransforms Energy distribution (DWT vs Spatial domain)Energy distribution (DWT vs Spatial domain) Arithmetic coding for SPIHTArithmetic coding for SPIHT Future workFuture work
Future workFuture work
Implementation of Witten’s paper. Implementation of Witten’s paper. Improvement of arithmetic coding for SPIHT.Improvement of arithmetic coding for SPIHT.