OPTIMZED SPIHT CODING

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: baboon lena

6. WAVELET TRANSFORM • Wavelet filters: 10/18 5/3

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

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

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) Qz(k) Qnz(k) R(k)

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

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)