A Modified Multiple OLS (m$^2$OLS) Algorithm for Signal Recovery in Compressive Sensing

TL;DR

This paper introduces a refined version of the mOLS algorithm for sparse signal recovery in compressive sensing, reducing computational complexity while maintaining fast convergence and success probability.

Contribution

The paper proposes a modified mOLS algorithm that preselects submatrices to lower computational costs without sacrificing convergence speed or accuracy.

Findings

Reduced computational complexity compared to original mOLS

Convergence guarantees for noisy and noise-free models

Maintains fast convergence properties

Abstract

Orthogonal least square (OLS) is an important sparse signal recovery algorithm for compressive sensing, which enjoys superior probability of success over other well-known recovery algorithms under conditions of correlated measurement matrices. Multiple OLS (mOLS) is a recently proposed improved version of OLS which selects multiple candidates per iteration by generalizing the greedy selection principle used in OLS and enjoys faster convergence than OLS. In this paper, we present a refined version of the mOLS algorithm where at each step of the iteration, we first preselect a submatrix of the measurement matrix suitably and then apply the mOLS computations to the chosen submatrix. Since mOLS now works only on a submatrix and not on the overall matrix, computations reduce drastically. Convergence of the algorithm, however, requires ensuring passage of true candidates through the two stages of preselection and mOLS based selection successively. This paper presents convergence conditions for both noisy and noise free signal models. The proposed algorithm enjoys faster convergence properties similar to mOLS, at a much reduced computational complexity.