Encoding the /spl lscr//sub p/ ball from limited measurements

Abstract

We address the problem of encoding signals which are sparse, i.e. signals that are concentrated on a set of small support. Mathematically, such signals are modeled as elements in the /spl lscr//sub p/ ball for some p < 1. We describe a strategy for encoding elements of the /spl lscr//sub p/ ball which is universal in that 1) the encoding procedure is completely generic, and does not depend on p (the sparsity of the signal), and 2) it achieves near-optimal minimax performance simultaneously for all p < 1. What makes our coding procedure unique is that it requires only a limited number of nonadaptive measurements of the underlying sparse signal; we show that near-optimal performance can be obtained with a number of measurements that is roughly proportional to the number of bits used by the encoder. We end by briefly discussing these results in the context of image compression.

Cite this paper

@article{Candes2006EncodingT, title={Encoding the /spl lscr//sub p/ ball from limited measurements}, author={E . Candes and J. Romberg}, journal={Data Compression Conference (DCC'06)}, year={2006}, pages={33-42} }