Generating Functional Analysis of Iterative Algorithms for Compressed Sensing
Information Theory
2011-06-02 v1 Disordered Systems and Neural Networks
math.IT
Abstract
It has been shown that approximate message passing algorithm is effective in reconstruction problems for compressed sensing. To evaluate dynamics of such an algorithm, the state evolution (SE) has been proposed. If an algorithm can cancel the correlation between the present messages and their past values, SE can accurately tract its dynamics via a simple one-dimensional map. In this paper, we focus on dynamics of algorithms which cannot cancel the correlation and evaluate it by the generating functional analysis (GFA), which allows us to study the dynamics by an exact way in the large system limit.
Cite
@article{arxiv.1106.0086,
title = {Generating Functional Analysis of Iterative Algorithms for Compressed Sensing},
author = {Kazushi Mimura},
journal= {arXiv preprint arXiv:1106.0086},
year = {2011}
}
Comments
5 pages, 1 figure, to appear in Proc. of ISIT2011