Improving Laplacian Pyramid Coding

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Improving Laplacian Pyramid Coding

• Sameh Zakhary, David Chen
• Stanford University
• EE 398A Final Project

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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

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LP Encoder and Decoder
encoder
(Burt, Adelson, 1983)
decoder
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LP with Quantization Noise
encoder
decoder
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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)
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Optimal Decoder for Noise Reduction
Lena, 512x512, 8 bpp
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Optimal Decoder for Noise Reduction
Lena, 512x512, 8 bpp
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Rate Allocation for Levels of the LP

• General Lagrangian minimization problem
• High-rate solution

(JPEG 2000, Ch. 5)
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Noise Processing at the Encoder
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Noise Processing at the Encoder
Lena, 512x512, 8 bpp, 9/7 filters
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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)

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Pseudo-Wavelet Decomposition
9/7 wavelet
insert coarse
SPIHT Encoder
bitstream
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Pseudo-Wavelet Decomposition
Lena, 512x512, 8 bpp, 9/7 filters
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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