1. A Comprehensive Design Evaluation for SPIHT Coding 台北科技大學資工所指導教授：楊士萱學生：廖武傑 2003/06/05

2. Outline Transforms Transforms Energy distribution (DWT vs Spatial domain) Energy distribution (DWT vs Spatial domain) Arithmetic coding for SPIHT Arithmetic coding for SPIHT Future work Future work

3. Transforms Integer-to-integer transform : Integer-to-integer transform : Real-to-real transform : Real-to-real transform : Dot products between the two filter masks and the signal. Dot products between the two filter masks and the signal.

4. Transforms Integer-to-integer transform : Integer-to-integer transform : 5/3 9/7-M

5. Transforms Integer-to-integer transform : Integer-to-integer transform : 5/11-A 5/11-C

6. Transforms Integer-to-integer transform : Integer-to-integer transform : 13/7-T 13/7-C

7. Transforms Integer-to-integer transform : Integer-to-integer transform : 9/7-F

8. Transforms Integer-to-integer transform : Integer-to-integer transform : 9/7-F

9. Transforms Real-to-real (orthogonal)transform : Real-to-real (orthogonal)transform : Haar (Daubechies 2-tap ) Daubechies 4-tapDaubechies 6-tap index 00.7071060.4829630.332671 10.7071060.8365160.806892 20.2241440.459878 3-0.129410-0.135011 4-0.085441 50.035226

10. Transforms Real-to-real (biorthogonal)transform : Real-to-real (biorthogonal)transform : 9/7 index 00.8526990.788486 1,-10.3774020.418092 2,-2-0.110624-0.040689 3,-3-0.023849-0.064539 4,-40.037828 10/18 index 0,-10.7589080.623359 1,-20.0767900.163369 2,-3-0.157526-0.085661 3,-40.000082-0.013765 4,-50.0288520.308337 5,-6-0.002528 6,-7-0.009452 7,-8-0.000002 8,-90.000095

11. Computation Time required RWTIWT D2D4D69/710/1 8 5/39/7-F9/7- M 5/11 A 5/11- C 13/7 C 13/7- T 0.360.610.922.514.201.001.921.191.63 1.44 Relative ratio, 5/3 as 1

12. Outline Transforms Transforms Energy distribution (DWT vs Spatial domain) Energy distribution (DWT vs Spatial domain) Arithmetic coding for SPIHT Arithmetic coding for SPIHT Future work Future work

13. Testing data lena baboon pepper F16

14. Energy of LL subband( DWT domain coefficients) RWTIWT D2D4D69/710/185/39/7-F9/7-M5/11A5/11-C13/7C13/7-T Lena97.7997.3797.2897.9897.4278.2796.1282.1478.0977.7481.8882.10 Baboo n 98.8598.9698.9099.1898.6888.6998.4091.2188.5888.3991.6991.64 F1698.7798.7698.7498.9898.3388.6598.0691.1088.6088.4590.9190.10 Pepper94.7394.7294.0895.7194.2768.5392.1473.4668.7168.6272.5473.10 “ lena ”, 5-level decomposition, %

15. Energy of LL subband( Spatial domain pixels) RWTIWT D2D4D69/710/185/39/7-F9/7-M5/11A5/11-C13/7C13/7-T Lena94.5994.3895.5095.1695.6695.5095.7296.4195.5795.8096.1795.90 Baboo n 94.1594.3694.6294.6794.6495.3295.2095.8695.22 95.4895.33 F1696.5396.6996.9896.5796.9897.0697.0197.5397.0397.0897.1397.07 Pepper89.8294.8396.6495.6197.9494.6296.6196.5196.4697.1296.48 “ lena ”, 5-level decomposition, %

16. Compression performance(PSNR,dB) 5/39/7-F9/7-M5/11A5/11- C 13/7C13/7- T 10/189/7HaarD4D6 1/6429.7130.2529.7829.8429.7929.9429.9030.6830.5327.5328.9729.38 1/3232.6033.2432.8732.8132.8833.0433.0733.7533.5830.2131.8532.35 1/1635.7536.1735.9335.9235.8936.1436.1336.8636.7433.5035.2435.75 1/838.8738.8438.8038.8938.8039.0339.0039.9639.9237.4738.9239.26 5/39/7-F9/7-M5/11A5/11- C 13/7C13/7- T 10/189/7HaarD4D6 1/6420.9621.4220.8520.9220.8721.0520.9821.6021.4920.9721.2821.37 1/3222.2522.8022.1822.2322.1722.4022.3522.9722.8822.1422.5422.64 1/1624.2225.0724.2824.2524.2324.4924.4725.1325.1124.60 24.79 1/827.7128.3727.8027.7927.7628.0227.9828.6128.6227.97 28.21

17. Compression performance(PSNR dB) 5/39/7-F9/7-M5/11A5/11- C 13/7C13/7- T 10/189/7HaarD4D6 1/6428.3128.9528.4928.4128.3928.5628.5729.2629.2826.7827.9728.18 1/3231.4532.1431.8231.6631.7231.8531.8832.5632.5129.5730.9531.40 1/1635.2735.8535.7535.5535.6135.8435.8736.4536.4233.4534.7535.27 1/839.8439.6639.8239.8639.7439.99 40.92 38.4239.6139.59 5/39/7-F9/7-M5/11A5/11- C 13/7C13/7- T 10/189/7HaarD4D6 1/6428.3128.7728.3028.3628.3028.4428.4329.0129.0225.7827.2227.56 1/3230.6831.4231.0730.8330.8631.1931.1531.6731.7428.7630.2030.46 1/1633.0933.5133.1633.0732.9833.3333.3033.7833.8031.8132.9533.06 1/835.3835.8435.4835.3435.1835.6935.6636.2136.1835.0135.7135.77

18. Images recovered from lowest frequency component lena baboon pepper F16

19. Outline Transforms Transforms Energy distribution (DWT vs Spatial domain) Energy distribution (DWT vs Spatial domain) Arithmetic coding for SPIHT Arithmetic coding for SPIHT Future work Future work

20. Arithmetic coding for SPIHT

21. 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

22. Outline Transforms Transforms Energy distribution (DWT vs Spatial domain) Energy distribution (DWT vs Spatial domain) Arithmetic coding for SPIHT Arithmetic coding for SPIHT Future work Future work

23. Future work Implementation of Witten’s paper. Implementation of Witten’s paper. Improvement of arithmetic coding for SPIHT. Improvement of arithmetic coding for SPIHT.