On the perturbation of measurement matrix in non-convex compressed sensing

We study l(p) (0 < p < 1) minimization under both additive and multiplicative noise. Theorems are presented for completely perturbed l(p) (0 < p < 1) minimization. Theorems reveal that under suitable conditions the stability of l(p) minimization with certain values of 0 < p < 1 is limited by the noise level in the observation. The restricted isometry property condition and the worst case reconstruction error bound are given in terms of restricted isometry constant and relative perturbations. Simulation results are presented and compared to state-of-the-art methods. (C) 2013 Elsevier B.V. All rights reserved.