Universal multiresolution source codes

Abstract

A multiresolution source code is a single code giving an embedded source description that can be read at a variety of rates and thereby yields reproductions at a variety of resolutions. The resolution of a source reproduction here refers to the accuracy with which it approximates the original source. Thus, a reproduction with low distortion is a "high-resolution" reproduction while a reproduction with high distortion is a "low-resolution" reproduction. This paper treats the generalization of universal lossy source coding from single-resolution source codes to multiresolution source codes. Results described in this work include new definitions for weakly minimax universal, strongly minimax universal, and weighted universal sequences of fixed- and variable-rate multiresolution source codes that extend the corresponding notions from lossless coding and (single-resolution) quantization to multiresolution quantizers. A variety of universal multiresolution source coding results follow, including necessary and sufficient conditions for the existence of universal multiresolution codes, rate of convergence bounds for universal multiresolution coding performance to the theoretical bound, and a new multiresolution approach to two-stage universal source coding.