Title: Improving Laplacian Pyramid Coding
1Improving Laplacian Pyramid Coding
- Sameh Zakhary, David Chen
- Stanford University
- EE 398A Final Project
2Outline
- 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
3LP Encoder and Decoder
encoder
(Burt, Adelson, 1983)
decoder
4LP with Quantization Noise
encoder
decoder
5Optimal Decoder for Noise Reduction
- Analysis matrix has more rows than columns
- Infinitely many synthesis matrices
1.5N
N
(Do, Vetterli, 2003)
(Burt, Adelson, 1983)
6Optimal Decoder for Noise Reduction
Lena, 512x512, 8 bpp
7Optimal Decoder for Noise Reduction
Lena, 512x512, 8 bpp
8Rate Allocation for Levels of the LP
- General Lagrangian minimization problem
- High-rate solution
(JPEG 2000, Ch. 5)
9Noise Processing at the Encoder
10Noise Processing at the Encoder
Lena, 512x512, 8 bpp, 9/7 filters
11Extensions 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)
-
12Pseudo-Wavelet Decomposition
9/7 wavelet
insert coarse
SPIHT Encoder
bitstream
13Pseudo-Wavelet Decomposition
Lena, 512x512, 8 bpp, 9/7 filters
14Summary 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