1. OPTIMZED SPIHT CODING 國立台北科技大學資工所 指導教授：楊士萱 研究生：廖武傑

2. OUTLINE  Wavelet Transform & Quantization  Bit rate & Quality  Future work

3. WAVELET TRANSFORM & QUANTIZATION

4. WAVELET TRANSFORM  Images  Wavelet filters  Scaling

5. WAVELET TRANSFORM  Images: lena baboon

6. WAVELET TRANSFORM  Wavelet filters: 10/185/3

7. WAVELET TRANSFORM  Scaling: – 5/3 filter h_subband*0.5 h_subband* h_subband*1.0

8. QUANTIZATION  Scalar Quantization – Step size  q  SPIHT – Decoding bit-rate  q – Zero-tree 0q

9. BIT RATE & QUALITY (R-D)  Coding bit rate(R) vs. Picture quality(D)  R-Q and D-Q functions(R(q),D(q)) characterize the R-D behavior.  R-D functions. (R-D curves)  Adjust the quantization setting and control the R and D.  Optimal Scaling for Best D(q) or R(q)

10. ρ DOMAIN R-D ANALYSIS  ρ: percentage of zeros among the quantized coefficients. (with a quantization parameter q)  ρ monotonically increases with q. – R(q)  R(ρ), – D(q)  D(ρ), – ρ domain R-D analysis

11. BIT RATE  R(q) = Qz(q) + Qnz(q) – Qz(q) : total bits required for representation of all zero coefficients – Qnz(q) : total bits required for representation of non-zero coefficients

12. BIT RATE(SQ,q=32,lena,5/3) Qnz(k) Qz(k) R(k)R(k)

13. BIT RATE(5/3 vs 9/7) Qz(k)Qnz(k) R(k)R(k) 5/3 9/7

14. QUALITY(SQ, q=32,lena) 5/3 9/7 PSNR

15. SCALING & R-D  Under Certain Quantization Parameter q: – Small scaling  High compression ratio – Large scaling  High image quality  Given a Quantization Parameter q and a Bit-rate R, We Can Find the Optimal Scaling for Best Image Quality.

16. OPTIMAL SCALING SPIHT SQ Lena, 5/3, 0.125 bpp

17. OPTIMAL SCALING  Quality Function : D(k, q)  Bit-rate Function : R(k, q) Where q is the size of Scalar Quantization step(fixed), k is the scaling factor of wavelet high frequency subband (variable). Cost Function F(k) = F(D(k), R(k))

18. FUTURE WORK  Find The Cost Function of SQ Accurately.  Use SPIHT Model Instead of SQ.  Modify SPIHT. (Probably)