Generating Functional Analysis of Iterative Algorithms for Compressed Sensing

TL;DR

This paper applies generating functional analysis to study the dynamics of iterative algorithms in compressed sensing, especially those that cannot cancel correlations, providing an exact large-system limit analysis.

Contribution

It introduces the use of generating functional analysis to evaluate the dynamics of correlated iterative algorithms in compressed sensing, extending beyond state evolution methods.

Findings

GFA accurately characterizes algorithm dynamics with correlations.

Provides exact analysis in the large system limit.

Extends understanding of iterative algorithms in compressed sensing.

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.