RIP based condition for support recovery with A* OMP in the presence of noise

Abstract

A* orthogonal matching pursuit (A* OMP) aims at combination of best-first tree search with the OMP algorithm for the compressed sensing problem. In this study, the authors present a new analysis for the A* OMP algorithm using the restricted isometry property (RIP). The results show that if the sampling matrix A satisfies the RIP with δ K ⋆ < B/(K + B) (K ⋆ = max {2K, K + B}), then under some constraints on SNR, A* OMP accurately recovers the support of any K-sparse signal x from the samples y = Ax + e, where B is the number of child paths for each candidate in the algorithm. In addition, the proposed condition is an optimal condition that guarantees the success of A* OMP in the noise-free case.

Nearly optimal number of iterations for sparse signal recovery with orthogonal multi-matching pursuit *

“…As a popular greedy algorithm, OMP has the attractiveness of simplicity and low computational complexity. It has been well studied and many variants have been proposed, such as the stagewise OMP [13], regularized OMP [14], compressive sampling matching pursuit [15], subspace pursuit [16], A OMP [17,18], multipath matching pursuit [19], generalized covariance-assisted matching pursuit [20], and binary matching pursuit (BMP) [21].…”