Optimization of multi-resolution source codes

Abstract

What is an optimal multi-resolution source code? This thesis studies the optimization of multi-resolution source codes. A multi-resolution source code is a data compression algorithm that generates a bit-stream that can be truncated at any point to reconstruct low-resolution representations of the original data. By progressively refining the description, these codes allow the receiver to get representations of progressively increasing quality from a single file. The optimization methods presented here are based on the minimization of a Lagrangian performance measure, which is a weighted sum of rates and distortions at the different resolutions of the multi-resolution code. The Lagrangian coefficients are the weights that parameterize the priorities assigned to the resolutions. The relative value of these parameters can be set according to the user's preferences regarding which rates are more important, the probability of decoding the file at each possible rate, or any other prioritization rationale. We present a method for converting design constraints into the corresponding Lagrangian parameters. We also use a Lagrangian analysis to investigate optimality properties of multiresolution codes. Specifically, we explore the characterization of the theoretically optimal output density functions of a two-resolution source code for any arbitrary set of priorities over the resolutions. Once the priority function has been identified, the goal is to design the multiresolution code that yields the best rate-distortion trade-off for those priorities. The minimization of the multi-resolution Lagrangian is somewhat specific to the frame work and type of multi-resolution code. We pursue this goal in several coding frameworks. The first framework is the multi-resolution vector quantizer (MRVQ) framework. Prior work on the topic described optimal MRVQ design for both fixed- and variable-rate systems but implemented only fixed-rate codes. The earliest portion of this thesis began with the implementation of the earlier described algorithm for variable-rate MRVQ for use as a testbed for understanding the important question of how to choose the Lagrangian parameters for multi-resolution codes to meet a collection of desired constraints. Armed with a new understanding of parameter choice in the MRVQ framework, we moved next to the more sophisticated coding framework of wavelet-based embedded bit-plane coders. New results in this framework include improvements on the Set Partitioning in Hierarchical Trees (SPIHT) and the Group Testing for Wavelets (GTW) algorithms that apply the lessons learned from MRVQ theory in these more sophisticated wavelet coding frameworks. Experimental results demonstrate the performance benefits associated with this approach.