Reconstruction Algorithms Comparison: OMP, SP, IRLS, CoSaMP and Their Performance Analysis

This article introduces several crucial reconstruction algorithms, including but not limited to OMP (Orthogonal Matching Pursuit), SP (Subspace Pursuit), IRLS (Iteratively Reweighted Least Squares), and CoSaMP (Compressive Sampling Matching Pursuit). These algorithms have gained widespread application in signal processing and image processing due to their ability to efficiently handle high-dimensional data while enhancing algorithm accuracy and reliability. From an implementation perspective, OMP operates by iteratively selecting the most correlated atoms from the measurement matrix and solving least squares problems. SP improves upon OMP by maintaining a fixed-size support set throughout iterations. IRLS addresses reconstruction through weighted least squares optimization with iteratively updated weights, while CoSaMP incorporates a pruning step to maintain sparsity constraints. We will analyze these algorithms' performance metrics, compare their respective advantages and limitations, and explore their application prospects across various domains. The implementation includes critical functions for sparse representation, residual calculation, and support set management. Ultimately, our research provides valuable references and guidance for scientists in both academic and industrial communities working with sparse signal reconstruction.