Performance analysis of Orthogonal Matching Pursuit under general perturbations

As a canonical greedy algorithm, Orthogonal Matching Pursuit (OMP) is used for sparse approximation. Previous studies have mainly considered non-perturbed observations y = Φx, and focused on the exact recovery of x through y and Φ. Here, Φ is a matrix with more columns than rows, and x is a sparse signal to be recovered. This paper deals with performance of OMP under general perturbations - from both y and Φ. The main contribution shows that exact recovery of the support set of x can be guaranteed under suitable conditions. Such conditions are RIP-based, and involve the concept of sparsity, relative perturbation, and the smallest nonzero entry. In addition, certain conditions are given under which the support set of x can be reconstructed in the order of its entries' magnitude. In the end, it is pointed out that the conditions can be relaxed at the expense of a decrease in the accuracy of the recovery.