TUTORIAL - B

Wavelet-Based Image Coding

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Michael T. Orchard

Dept. of Electrical Engineering

Princeton University

Princeton, NJ 08540 USA

orchard@ee.princeton.edu

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Wavelets have played a major role in advances in image coding over the past five years. All of today's best-performing lossy image coding algorithms are wavelet-based, and these algorithms significantly outperform the best block-transform algorithms. Yet, not all wavelet-based algorithms can claim such performance advantages. In fact, early wavelet-based algorithms appearing in the literature did not fully recognize the advantages offered by wavelets for image coding. A second generation of wavelet-based algorithms began appearing 3-4 years ago, and only in the last year or two have the mathematical foundations for their high performance become fully understood.

This tutorial will present an in-depth study of the role of wavelets in image coding. It will present historical perspectives on BW (before wavelets) image coding, and the various stages of evolution of wavelet-based image coding algorithms. It will present analytical insights into the statistical properties of natural images that account for the advantages of wavelets in image coding. This analysis will relate the approaches taken by state-of-the-art wavelet coders to results of nonlinear approximation theory from the mathematics community. The tutorial will detail and compare several of today's best performing wavelet-based image coding algorithms. Finally, the tutorial will sketch some promising directions and challenges for improvements in the application of wavelets to compression of both images and video.

The tutorial presentation will be a mixture of three kinds of material:

a) Theory and analytical tools - A firm understanding of the important issues in wavelet coding must be based on understanding and intuitions of basic principles in coding and information. Due to time constraints, these principles will be sketched in their simplest forms, but will be extensively illustrated with graphical interpretations and toy examples.

b) Literature review - The material covered in the tutorial was developed within the context of a broad range of research activity in image coding over the past 10 years. While most of this activity is well outside the scope of this tutorial, to fully understand the "what, how, and why?"'s in the evolution of wavelet coding, it will be important to have an overview of much of this work. This overview will be provided via literature citation and summary.

c) Experimentation - The important issues in the performance of any algorithm can often be obscured by the complex interaction of many independent issues. In any research, our best tool for understanding detailed functions within a complex system is the design of experiments that provide control of unwanted factors, while measuring desired relations. The tutorial will make extensive use of customized experiments to test and challenge the theories and conclusions that are presented. Besides the graphical results of these experiments, participants will be given access to the test data and C and Matlab code, allowing them to continue their own experimentation after the tutorial.

OUTLINE:

1) Coding Background:

• quantization, rate-distortion analysis, transform coding, bitrate allocation, entropy coding, basic arithmetic coding.

2) Traditional Image Coding Algorithms

• Transform coders (brief summary of JPEG)
• Subband coders
• Early wavelet coders

3) Space-frequency Wavelet-based Algorithms

• space-frequency energy compaction for efficient image coding
• Overview of zerotree-based wavelet algorithms: role of space-frequency compaction

4) Nonlinear Approximation: a mathematical framework for

• analyzing wavelet-based coding algorithms

5) State-of-the-art Wavelet-based Image coding

• a detailed review of several of today's best performing wavelet-based image coding algorithms
• performance will be analyzed from the perspective of the framework presented in 4).

6) Future Directions

• improved image coding
• wavelets for video coding?? Issues and bottlenecks.

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