Orthogonal Matching Pursuit with Tikhonov and Landweber Regularization

TL;DR

This paper introduces two regularized variants of Orthogonal Matching Pursuit that do not require prior sparsity knowledge, enabling efficient hardware implementation and effective compressed sensing with limited measurements.

Contribution

The paper proposes novel regularized OMP algorithms with no need for prior sparsity, suitable for real-world applications and hardware implementation.

Findings

Good performance with small number of measurements

Regularization improves robustness of OMP

Algorithms are hardware-efficient

Abstract

The Orthogonal Matching Pursuit (OMP) for compressed sensing iterates over a scheme of support augmentation and signal estimation. We present two novel matching pursuit algorithms with intrinsic regularization of the signal estimation step that do not rely on a priori knowledge of the signal's sparsity. An iterative approach allows for a hardware efficient implementation of our algorithm, and enables real-world applications of compressed sensing. We provide a series of numerical examples that demonstrate a good performance, especially when the number of measurements is relatively small.