Representation and coding of images using wavelets

Abstract

Recently, there have been intense research activities in the theory of wavelets, driven by its application in a wide variety of areas, especially in image processing. This dissertation presents a body of work addressing the application aspects of wavelets in representation and coding of images.

We first introduce a novel space-frequency quantization (SFQ) scheme for wavelet image coding, which jointly optimizes scalar quantization and zerotree quantization using a rate-distortion optimization framework. The SFQ scheme can be viewed as a variant of Shapiro's embedded zerotree image coder (1) with impressive coding gain. We then extend SFQ from wavelet to wavelet packet (possibly space-varying) decompositions, achieving coding performance that is the best in the published literature.

We then examine the question of how to choose a space-varying wavelet packet tree representation that minimizes some additive cost function for an image. The idea is that for a practical cost function, some tree structures will perform better than others. We build new libraries of tree-structured bases for image representation with space-varying wavelet packets and devise fast algorithms for finding the best basis from the libraries. Using these algorithms to select the best tree-structured representation with a rate-distortion cost function gives very efficient adaptive compression schemes that are competitive with the best training-based schemes.