A Robust Sparse Signal Recovery Method for Perturbed Compressed Sensing Based on Max-min Residual Regularization

Compressive sensing (CS) is a new signal acquisition framework for sparse and compressible signals with a sampling rate much below the Nyquist rate. In this work, we consider the problem of perturbed compressive sensing (CS) with uncertainty in the measurement matrix as well as in the measurements. In order to eliminate the effects of measurement matrix uncertainty, this paper proposed a robust reconstruction method based on max-min residual regularization. We also deduced the solver of the optimization model with the sub-gradient algorithm. Simulation and numerical results shown that the proposed recovery method performs better than the traditional reconstruction methods.