Signal and Noise Statistics Oblivious Sparse Reconstruction using OMP/OLS

TL;DR

This paper introduces two new frameworks, TF-IGP and RRT-IGP, that enable OMP and OLS algorithms to perform effective sparse signal reconstruction without prior knowledge of signal sparsity or noise variance, expanding their practical applicability.

Contribution

The paper proposes computationally efficient methods, TF-IGP and RRT-IGP, that allow OMP and OLS to succeed in sparse recovery without needing prior estimates of sparsity or noise levels.

Findings

TF-IGP and RRT-IGP achieve successful recovery under restricted isometry conditions.

Numerical simulations show competitive performance compared to traditional methods.

Frameworks extend the applicability of OMP/OLS in practical scenarios.

Abstract

Orthogonal matching pursuit (OMP) and orthogonal least squares (OLS) are widely used for sparse signal reconstruction in under-determined linear regression problems. The performance of these compressed sensing (CS) algorithms depends crucially on the \textit{a priori} knowledge of either the sparsity of the signal ($k_0$) or noise variance ($\sigma^2$). Both $k_0$ and $\sigma^2$ are unknown in general and extremely difficult to estimate in under determined models. This limits the application of OMP and OLS in many practical situations. In this article, we develop two computationally efficient frameworks namely TF-IGP and RRT-IGP for using OMP and OLS even when $k_0$ and $\sigma^2$ are unavailable. Both TF-IGP and RRT-IGP are analytically shown to accomplish successful sparse recovery under the same set of restricted isometry conditions on the design matrix required for OMP/OLS with \textit{a priori} knowledge of $k_0$ and $\sigma^2$. Numerical simulations also indicate a highly competitive performance of TF-IGP and RRT-IGP in comparison to OMP/OLS with \textit{a priori} knowledge of $k_0$ and $\sigma^2$.