Four Reconstruction Algorithms for Compressed Sensing

This article explores four reconstruction algorithms for compressed sensing: StOMP, BP, OMP, and block_omp. These algorithms are widely applied in signal processing domains. Notably, they enable signal compression while preserving critical information, facilitating efficient signal transmission and storage. The StOMP algorithm employs a stagewise thresholding approach to select multiple atoms per iteration, significantly accelerating convergence. BP implementation typically involves solving an L1-norm minimization problem using linear programming techniques. OMP operates through iterative greedy selection of dictionary atoms and orthogonal projection, making it suitable for sparse recovery problems. Block_omp extends OMP by processing signal blocks collectively, improving reconstruction efficiency for structured sparse signals. We will detail each algorithm's distinctive characteristics, implementation considerations, and applicable scenarios to help readers better understand and apply these methods in practical applications.