Orthogonal Matching Pursuit Algorithm for Sparse Signal Recovery

In this article, we explore the Orthogonal Matching Pursuit (OMP) algorithm, a powerful method for sparse signal recovery. The algorithm achieves signal reconstruction by representing signals as sparse vectors through an iterative greedy approach. We provide a comprehensive breakdown of the algorithm's underlying principles and implementation methodology, including key computational steps such as correlation calculation, support set expansion, and least-squares estimation. The implementation typically involves maintaining an active set of atoms from the dictionary matrix and solving a least-squares problem at each iteration to update the signal approximation. Through experimental demonstrations, we showcase the algorithm's effectiveness in recovering sparse signals from incomplete measurements. Additionally, we present a comparative analysis between OMP and other signal recovery algorithms, discussing their relative advantages and limitations in terms of reconstruction accuracy, computational complexity, and convergence properties. This article enables readers to understand OMP's practical applications in sparse signal recovery while gaining deep insights into the algorithm's operational mechanisms and performance characteristics through code-oriented explanations.