CoSaMP, BP, and OMP Algorithms: Analysis and Error Comparison

This article examines the CoSaMP, Basis Pursuit (BP), and Orthogonal Matching Pursuit (OMP) algorithms, comparing their reconstruction errors under different signal-to-noise ratio (SNR) conditions. We explore their underlying principles and application domains, while evaluating performance variations through experimental simulations. The CoSaMP algorithm implements iterative signal estimation by maintaining a fixed support size and performing pruning operations to refine approximations. Basis Pursuit utilizes convex optimization techniques (typically solved via linear programming) to achieve sparse representations through L1-norm minimization. Orthogonal Matching Pursuit employs a greedy approach, incrementally selecting atoms from the dictionary that maximize correlation with the residual signal. By analyzing reconstruction errors across SNR levels, we demonstrate their relative strengths and limitations, providing practical guidance for algorithm selection in real-world applications.