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Improving Laplacian Pyramid Coding

Improving Laplacian Pyramid Coding

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Improving Laplacian Pyramid Coding

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  1. Improving Laplacian Pyramid Coding Sameh Zakhary, David Chen Stanford University EE 398A Final Project

  2. Outline • Laplacian pyramid (LP) encoder and decoder • LP with quantization noise • Optimal decoder for noise reduction • Rate allocation for levels of the LP • Extensions of the LP structure • Noise processing at the encoder • Closed-loop encoder • Lifted pyramid • SVD-based transform • Pseudo-wavelet encoder with SPIHT S. Zakhary, D. Chen, EE 398A

  3. LP Encoder and Decoder encoder (Burt, Adelson, 1983) decoder S. Zakhary, D. Chen, EE 398A

  4. LP with Quantization Noise encoder decoder S. Zakhary, D. Chen, EE 398A

  5. Optimal Decoder for Noise Reduction • Analysis matrix has more rows than columns • Infinitely many synthesis matrices } 1.5N } N (Do, Vetterli, 2003) (Burt, Adelson, 1983) S. Zakhary, D. Chen, EE 398A

  6. Optimal Decoder for Noise Reduction “Lena”, 512x512, 8 bpp S. Zakhary, D. Chen, EE 398A

  7. Optimal Decoder for Noise Reduction “Lena”, 512x512, 8 bpp S. Zakhary, D. Chen, EE 398A

  8. Rate Allocation for Levels of the LP • General Lagrangian minimization problem • High-rate solution (JPEG 2000, Ch. 5) S. Zakhary, D. Chen, EE 398A

  9. Noise Processing at the Encoder S. Zakhary, D. Chen, EE 398A

  10. Noise Processing at the Encoder “Lena”, 512x512, 8 bpp, 9/7 filters S. Zakhary, D. Chen, EE 398A

  11. Extensions of the LP Structure • Closed-loop encoder • Uses feedback idea from predictive coding • 1 db improvement over open-loop at high rates (Ramchandran, 1994) • Lifted pyramid • Minimizes aliasing for video applications (Flierl, Vanderghyenst, 2005) • SVD-based transform • Critical representation of the LP (Rath, Guillemot, 2006) S. Zakhary, D. Chen, EE 398A

  12. Pseudo-Wavelet Decomposition 9/7 wavelet insert coarse SPIHT Encoder bitstream S. Zakhary, D. Chen, EE 398A

  13. Pseudo-Wavelet Decomposition “Lena”, 512x512, 8 bpp, 9/7 filters S. Zakhary, D. Chen, EE 398A

  14. Summary of Project Results • Compared performances of simple and optimal LP decoders • Constructed practical rate allocation algorithm for multiple levels of LP • Researched extensions of the basic LP structure • Noise processing at the encoder • Closed-loop encoder • Lifted pyramid • SVD-based transform • Pseudo-wavelet encoder with SPIHT S. Zakhary, D. Chen, EE 398A