Online compressed sensing

TL;DR

This paper introduces an online compressed sensing algorithm that efficiently recovers sparse signals with performance close to offline methods, balancing computational cost and accuracy in noisy environments.

Contribution

It proposes a novel online recovery algorithm based on mean field approximation, achieving near-optimal performance with linear computational complexity per update.

Findings

Online algorithm asymptotically matches offline optimal performance in noisy settings.

Computational cost impacts achievable performance in noiseless scenarios.

Algorithm operates with linear complexity relative to signal length.

Abstract

In this paper, we explore the possibilities and limitations of recovering sparse signals in an online fashion. Employing a mean field approximation to the Bayes recursion formula yields an online signal recovery algorithm that can be performed with a computational cost that is linearly proportional to the signal length per update. Analysis of the resulting algorithm indicates that the online algorithm asymptotically saturates the optimal performance limit achieved by the offline method in the presence of Gaussian measurement noise, while differences in the allowable computational costs may result in fundamental gaps of the achievable performance in the absence of noise.