The paper discusses the Orthogonal Matching Pursuit (OMP) algorithm for recovering a high-dimensional sparse signal from a small number of noisy linear measurements. OMP is an iterative greedy algorithm that selects at each step the column of the measurement matrix that is most correlated with the current residuals. The authors present a fully data-driven OMP algorithm with explicit stopping rules and show that under conditions on the mutual incoherence and the minimum magnitude of the nonzero components of the signal, the support of the signal can be recovered exactly with high probability. They also consider the problem of identifying significant components when some of the nonzero components are possibly small, demonstrating that OMP can still select all the significant components before possibly selecting incorrect ones. Additionally, with modified stopping rules, OMP can ensure that no zero components are selected. The paper compares the OMP algorithm with other methods, such as $\ell_1$ minimization, and shows that OMP has weaker conditions for recovery and is computationally simpler. The analysis is based on the Mutual Incoherence Property (MIP) and the Exact Recovery Condition (ERC), with detailed proofs provided in the supplementary material.The paper discusses the Orthogonal Matching Pursuit (OMP) algorithm for recovering a high-dimensional sparse signal from a small number of noisy linear measurements. OMP is an iterative greedy algorithm that selects at each step the column of the measurement matrix that is most correlated with the current residuals. The authors present a fully data-driven OMP algorithm with explicit stopping rules and show that under conditions on the mutual incoherence and the minimum magnitude of the nonzero components of the signal, the support of the signal can be recovered exactly with high probability. They also consider the problem of identifying significant components when some of the nonzero components are possibly small, demonstrating that OMP can still select all the significant components before possibly selecting incorrect ones. Additionally, with modified stopping rules, OMP can ensure that no zero components are selected. The paper compares the OMP algorithm with other methods, such as $\ell_1$ minimization, and shows that OMP has weaker conditions for recovery and is computationally simpler. The analysis is based on the Mutual Incoherence Property (MIP) and the Exact Recovery Condition (ERC), with detailed proofs provided in the supplementary material.