Collection of Common Compressed Sensing Algorithms

This article provides a comprehensive summary of prevalent compressed sensing algorithms, covering key methodologies such as L1-minimization, Orthogonal Matching Pursuit (OMP), and Gradient Projection (GP). Each algorithm presents distinct advantages and limitations, necessitating careful selection based on specific application requirements. In practical implementations, these algorithms typically involve solving underdetermined linear systems through optimization techniques like convex relaxation (L1), iterative greedy methods (OMP), or sparse reconstruction with gradient-based optimization (GP). Compressed sensing algorithms demonstrate extensive applications in signal processing domains including signal reconstruction and image processing. For researchers in related fields, understanding both the theoretical foundations and practical implementation nuances of these algorithms—such as regularization parameter tuning in L1 solvers or stopping criteria configuration in iterative methods—is crucial for effective deployment.