Comparative Analysis of MP, OMP, and CoSaMP Algorithms for 2D Signal Processing

In this paper, we implement and compare three prominent sparse signal recovery algorithms - Matching Pursuit (MP), Orthogonal Matching Pursuit (OMP), and Compressive Sampling Matching Pursuit (CoSaMP) - for processing two-dimensional signals. These greedy algorithms are particularly useful in sparse approximation and compressive sensing applications, where they iteratively select the most correlated dictionary atoms to reconstruct signals from limited measurements. Through MATLAB/Python implementations, we demonstrate how these algorithms handle 2D signals by extending their core functionality. MP employs a simple iterative approach that selects the best-matching atom at each step but may require more iterations for convergence. OMP improves upon MP by orthogonalizing the residual against all previously selected atoms through least squares minimization, typically implemented using QR decomposition or pseudo-inverse operations. CoSaMP enhances stability by selecting multiple atoms per iteration while maintaining a fixed sparsity level, utilizing matrix operations for batch atom selection and pruning. Our comparative analysis focuses on key performance metrics including reconstruction accuracy, computational efficiency, and convergence behavior when processing various 2D signals such as images and sensor data. The evaluation examines how each algorithm balances trade-offs between reconstruction quality and computational complexity, providing insights for selecting appropriate methods based on specific application requirements in signal processing and data analysis.