Orthogonal Matching Pursuit (OMP) Algorithm

The Orthogonal Matching Pursuit (OMP) algorithm is a sparse solution algorithm used for signal compression. This approach iteratively matches and tracks orthogonal bases of signals to achieve compression. The algorithm progressively reconstructs signals by selecting the most relevant orthogonal bases, enabling sparse signal representation. In signal processing applications, OMP is widely implemented in signal compression, image processing, and machine learning domains. From a code implementation perspective, OMP typically operates through iterative correlation calculations between the residual signal and dictionary atoms. Key algorithmic steps include: computing inner products to identify the most correlated atom, updating the support set through orthogonal projection using least squares, and recursively refining the residual. The MATLAB implementation commonly utilizes matrix operations for efficient orthogonal projections and employs QR decomposition for stable numerical solutions. The algorithm terminates when either reaching a predefined sparsity level or meeting residual error thresholds, making it particularly effective for compressed sensing recovery and sparse approximation problems.