Number of Measurements in Sparse Signal Recovery

TL;DR

This paper investigates the asymptotic limits of sparse signal recovery from noisy measurements, extending existing results to broader measurement ensembles and establishing bounds on the number of measurements needed.

Contribution

It generalizes sparse recovery performance analysis to subgaussian and other ensembles, providing new achievable results and a converse bound using information theory concepts.

Findings

Extended analysis to subgaussian measurement ensembles.

Provided an achievable measurement bound in the linear sparsity regime.

Established a converse bound applicable to many measurement ensembles.

Abstract

We analyze the asymptotic performance of sparse signal recovery from noisy measurements. In particular, we generalize some of the existing results for the Gaussian case to subgaussian and other ensembles. An achievable result is presented for the linear sparsity regime. A converse on the number of required measurements in the sub-linear regime is also presented, which cover many of the widely used measurement ensembles. Our converse idea makes use of a correspondence between compressed sensing ideas and compound channels in information theory.