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A Comprehensive Study of Wavelet Transforms for SPIHT

A Comprehensive Study of Wavelet Transforms for SPIHT. 台北科技大學資工所 指導教授：楊士萱 學生：廖武傑. 2003/03/27. Outline. Introduction Compression performance Scaling Finite length signal analysis Conclusion. Introduction. Transforms integer-to-integer (reversible) real-to-real(irreversibel) SPIHT

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A Comprehensive Study of Wavelet Transforms for SPIHT

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  1. A Comprehensive Study of Wavelet Transforms for SPIHT 台北科技大學資工所 指導教授：楊士萱 學生：廖武傑 2003/03/27

  2. Outline • Introduction • Compression performance • Scaling • Finite length signal analysis • Conclusion

  3. Introduction • Transforms integer-to-integer (reversible) real-to-real(irreversibel) • SPIHT wavelet domain coding zero-tree coding

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

  5. Wavelet filters for evaluation of coding • Integer-to-integer: 5/3, 9/7-M, 5/11-A, 5/11-C,13/7-T, 13/7-C, 9/7-F (biorthogonal) • Real-to-real: 9/7, 10/18 (biothogonal) Haar, Daubechies 4 taps, 6 taps(orthogonal)

  6. Complexity • Integer-to-integer: 5/3: 9/7-F:

  7. Complexity • Real-to-real: Haar: 9/7:

  8. SPIHT(set partitioning in hierarchical trees) • Zero-tree coding: ->inter-scaling correlation ->energy distribution

  9. Outline • Introduction • Compression performance • Scaling • Finite length signal analysis • conclusion

  10. Compression performance • Test images: lena F16 baboon pepper

  11. Compression performance

  12. Compression performance

  13. Energy of LL subband(%)

  14. Outline • Introduction • Compression performance • Scaling • Finite length signal analysis • Conclusion

  15. Scaling • Optimal scaling factor ->fixed scaling ->variable scaling • Modify SPIHT coding algorithm ->variable sorting threshold

  16. Fixed scaling • Optimal scaling factor for all wavelet decomposition is 1.41421 ,except 9/7-F(1.1496) • With proper scaling, the compression performance is much better for all wavelet filter.

  17. Coding with or without scaling (“Lena”) 5/3 9/7-F

  18. Coding with or without scaling (“Lena”) 13/7-T 13/7-C

  19. Coding with or without scaling (“Lena”) 5/11-A 5/11-C

  20. Finite length signal analysis • Optimal signal extension ->minimal the distortion of the reconstructive signal • Restriction of signal extension ->extension must match the filter-bank.

  21. Extensions for various filters • Odd symmetric extension for odd taps filter. • Even symmetric extension and anti-symmetric for even taps filter. • periodic extension for asymmetric filter. (circular convolution) • Only guarantee the forward-backward transform works.

  22. Extension affects performance Symmetric extension periodic extension

  23. Performance (with proper and improper extension )

  24. Outline • Introduction • Compression performance • Scaling • Finite length signal analysis • Conclusion

  25. Outline • Introduction • Compression performance • Scaling • Finite length signal analysis • Conclusion

  26. Conclusion • Coding performance associated with filter: • Properties of filter • Energy distribution of wavelet coefficients • Some issues of implementation • The differences between fixed and floating point filtering computation.

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