Sufficient conditions for generalized Orthogonal Matching Pursuit in noisy case

In compressive sensing, generalized Orthogonal Matching Pursuit (gOMP) algorithm generalizes OMP algorithm by selecting N(N≥1) atoms in each iteration. In this paper, we propose restricted isometry constant based sufficient conditions for gOMP algorithm to correctly recover the support of significant components of signal when both measurement dictionary and measurement signal are contaminated with noise. Bound of estimation error is also derived. Upper bound of restricted isometry constant could be relaxed if the original sparse signal is strong decaying. When sparsity of original sparse signal is unavailable, we give a stopping criterion of gOMP algorithm to ensure correct support recovery.