Orthogonal Matching Pursuit Algorithm

In computer science, the Orthogonal Matching Pursuit (OMP) algorithm is a greedy method used for sparse signal recovery. The core algorithmic principle involves iteratively selecting the most correlated basis vector by computing inner products with the residual error, then incorporating it into the current solution estimate. This selection-and-update process repeats until meeting specific convergence criteria. The algorithm typically implements orthogonalization through least-squares minimization at each iteration to ensure selected atoms remain perpendicular to the residual. OMP finds extensive applications in signal processing, image reconstruction, and machine learning domains due to its computational efficiency in handling large-scale datasets while maintaining high reconstruction quality. Key implementation considerations include stopping conditions based on residual thresholds or sparsity levels, with common optimizations involving precomputation of dictionary correlations and QR decomposition for efficient orthogonal projection.