Performance Comparison of Various Greedy Algorithms in Compressed Sensing

This paper presents a comprehensive MATLAB simulation-based comparison of various greedy algorithms used in compressed sensing. The analyzed algorithms include Least Squares Matching Pursuit (LS-MP), which iteratively selects atoms based on least squares residual minimization; Orthogonal Matching Pursuit (OMP), known for its orthogonal projection step that ensures selected atoms remain in the solution subspace; Weak Matching Pursuit (WMP), a computationally efficient variant that uses weaker selection criteria; and Hard Thresholding algorithms that employ simple thresholding operations for sparse signal recovery. We conduct detailed performance evaluations of these algorithms, analyzing their applicability under different scenarios including varying sparsity levels, measurement matrix conditions, and noise environments. The MATLAB implementations feature key functions such as atom selection mechanisms, residual updates, and stopping criteria optimization. Performance metrics include reconstruction accuracy, computational complexity, and convergence rates. Furthermore, we examine the advantages and limitations of each algorithm: OMP provides high accuracy but suffers from computational overhead, while WMP offers faster execution at potential cost of precision. Hard thresholding methods demonstrate simplicity but may require careful parameter tuning. LS-MP balances between computational efficiency and reconstruction quality. Finally, we discuss potential future developments for these algorithms, including hybrid approaches, adaptive parameter selection methods, and hardware optimization techniques, aiming to advance their practical applications in compressed sensing domains such as medical imaging, wireless communications, and signal processing systems.