Optimized Orthogonal Matching Pursuit Algorithm for Compressed Sensing Signal Recovery

This paper introduces an improved method for compressed sensing signal recovery, specifically enhancing the greedy iterative Orthogonal Matching Pursuit (OMP) algorithm. Traditional OMP selects non-optimal atoms during each iteration, resulting in suboptimal residual reduction. Our proposed Optimised_OMP algorithm guarantees that each newly selected atom remains orthogonal to the subspace formed by previously chosen atoms, achieved through orthogonal projection operations in the code implementation. This orthogonalization process ensures faster residual decline and accelerated convergence rates. The algorithm implementation includes correlation coefficient calculations between residuals and measurement matrix columns, followed by orthogonal projection updates using matrix operations. Furthermore, we conducted comparative analyses with other compressed sensing algorithms, demonstrating superior performance in both recovery accuracy and convergence speed. The MATLAB/Python implementation features key functions for atom selection, residual updates, and stopping criterion checks based on either sparsity level or residual threshold. This improved algorithm provides a novel approach and methodology for research in compressed sensing signal recovery applications.