Sparse Representation Orthogonal Matching Pursuit Algorithm MATLAB Source Code

This article provides a comprehensive exploration of the Sparse Representation Orthogonal Matching Pursuit (OMP) algorithm, an efficient technique widely used in signal processing for precise signal encoding and reconstruction. We present the complete MATLAB source code implementation, which includes key functions for atom selection, residual updating, and orthogonal projection operations. The core algorithm iteratively selects the most correlated atoms from the dictionary using matrix operations and solves least-squares problems at each step to update the signal approximation. We discuss practical applications in fields such as image processing, where OMP can be used for image compression and denoising, and speech recognition systems for feature extraction. The implementation demonstrates how to handle sparse recovery problems with optimized computational efficiency using MATLAB's built-in linear algebra functions. Additionally, we analyze the algorithm's advantages in convergence speed and reconstruction accuracy, while addressing limitations such as sensitivity to dictionary coherence and computational complexity for large-scale problems. Finally, we outline potential improvement directions including adaptive dictionary learning techniques and hybrid approaches combining OMP with other optimization methods to enhance performance in various signal processing scenarios.