Compressive Sensing Reconstruction Algorithms for Image Signals

In this document, we explore compressive sensing reconstruction algorithms for image signals, along with comparative implementations containing both BP and OMP algorithms. Compressive sensing represents an emerging signal processing technique designed to reduce data storage and transmission costs through simultaneous sampling and compression. Throughout our discussion, we will examine the distinctions between these algorithms, including their respective advantages and limitations, along with their applicability across different scenarios. The Basis Pursuit (BP) algorithm typically employs linear programming or optimization techniques to find the sparsest solution that satisfies measurement constraints, while Orthogonal Matching Pursuit (OMP) operates as a greedy iterative algorithm that progressively selects the most correlated atoms from a dictionary. Furthermore, we will discuss practical applications of these algorithms and their potential uses in image processing and other domains, with particular attention to implementation considerations such as signal sparsity constraints, measurement matrix design, and reconstruction accuracy metrics.