Joint Sparse Recovery Method for Compressed Sensing with Structured Dictionary Mismatch

In traditional compressed sensing theory, the dictionary matrix is given a priori, whereas in real applications this matrix suffers from random noise and fluctuations. In this paper we consider a signal model where each column in the dictionary matrix is affected by a structured noise. This formulation is common in problems such as radar signal processing and direction-of-arrival (DOA) estimation. We propose to use joint sparse signal recovery in this compressed sensing problem with dictionary mismatch and also give an analytical performance bound on this joint sparse recovery. We show that, under mild conditions, the reconstruction error of the original sparse signal is bounded by both the sparsity and the noise level in the measurement model. Moreover, we implement a fast first-order method to speed up the computing process. Detecting off-grid targets with compressed sensing MIMO radar is solved in this paper by using the proposed joint sparse recovery method. Numerical examples demonstrate the good performance of the proposed algorithm, and also show that the joint-sparse recovery method converges faster and gives a better reconstruction result than existing methods. By implementing the joint sparse recovery method, the accuracy and efficiency of DOA estimation with MIMO radar is improved.