Optimal Quantization for Compressive Sensing under Message Passing Reconstruction
Information Theory
2016-11-15 v2 math.IT
Abstract
We consider the optimal quantization of compressive sensing measurements following the work on generalization of relaxed belief propagation (BP) for arbitrary measurement channels. Relaxed BP is an iterative reconstruction scheme inspired by message passing algorithms on bipartite graphs. Its asymptotic error performance can be accurately predicted and tracked through the state evolution formalism. We utilize these results to design mean-square optimal scalar quantizers for relaxed BP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers.
Cite
@article{arxiv.1102.4652,
title = {Optimal Quantization for Compressive Sensing under Message Passing Reconstruction},
author = {Ulugbek Kamilov and Vivek K Goyal and Sundeep Rangan},
journal= {arXiv preprint arXiv:1102.4652},
year = {2016}
}
Comments
5 pages, 3 figures, submitted to IEEE International Symposium on Information Theory (ISIT) 2011; minor corrections in v2