An improved RIP based condition for support recovery with NR-A⋆OMP in the presence of general perturbation.

Nonlinear regression A⁎ orthogonal matching pursuit (NR-A⁎OMP), as a new algorithm, has been proposed for recovering the sparse signal in the filed of compressed sensing. In this paper, we consider the general perturbed model y ˜ = Φ x + b , Φ ˜ = Φ + E , where x is K -sparse and E is the perturbation matrix. Assume that the matrix Φ ˜ satisfies the RIP of order K ⋆ with δ K ⋆ < B K + B (K ⁎ = max ⁡ { 2 K , K + B }), then under the suitable constraint on min t ∈ T ⁡ | x t | , NR-A⁎OMP can recover the support of K -sparse signal x , where B is the number of child paths for each candidate in the algorithm. Compared with the existing results, we showed that the theoretical conclusion in the text is more relaxed. In the noiseless case, we also presented a condition which guaranteed that NR-A⁎OMP can not recover the support in K iterations by a counterexample. Besides, we also considered the theoretical analysis of NR-A⁎OMP when b is a Gaussian noise. [ABSTRACT FROM AUTHOR]