Implementation of Signal Compressed Sensing using Orthogonal Matching Pursuit Algorithm

In the field of signal processing, compressed sensing technology has been widely adopted for signal compression and transmission applications. Among various approaches, Orthogonal Matching Pursuit (OMP) stands as a prominent compressed sensing technique that efficiently accomplishes signal reconstruction and recovery. This algorithm operates by iteratively selecting the most representative basis functions through identifying the maximum inner products with the residual signal. The implementation typically involves initializing a residual vector equal to the original signal, then recursively identifying the dictionary atom that has the highest correlation with the current residual. Each iteration updates the estimated signal representation using least squares minimization and orthogonalizes the residual against selected atoms. Through this greedy approach, OMP achieves effective signal compression and reconstruction while maintaining reconstruction accuracy. The method ensures computational efficiency through optimized matrix operations and orthogonal projections, making it suitable for real-time applications. Code implementation generally requires designing measurement matrices, computing correlations, solving least squares problems, and implementing stopping criteria based on either sparsity constraints or residual thresholds.