Fast recovery algorithm for complex sparse signal with arbitrary sparse structure and its inverse synthetic aperture radar imaging

Abstract

In order to improve both reconstruction performance and speed for multiple measurement vectors(MMV)model with arbitrary sparse structure in compressed sensing(CS),we propose an improved linearized Bregman iteration for MMV(ILBIMMV)algorithm in this paper.Firstly,an MMV model with arbitrary sparse structure is given.At the same time,the characteristics of the model are analyzed theoretically.To effectively reconstruct the MMV model with two dimensions(2D),the linearized Bregman iteration(LBI)is extended.Secondly,the reconstruction speed is improved by accelerating the algorithm′s convergence,which is achieved by optimizing the condition numbers of sensing matrices.In addition,the preconditioning is used to optimize the condition number.The convergence and the computational complexity of the proposed algorithm are theoretically analyzed,and the theoretic analysis is proved by the corresponding simulation results.Finally,the simulation results show that the MMV model with arbitrary sparse structure can be accurately recovered by the proposed algorithm.Meanwhile,the proposed algorithm has evident advantages in reconstruction speed.The effectiveness of the ILBIMMV algorithm is also verified by the inverse synthetic aperture radar(ISAR)imaging results based on real data with different signal to noise ratios.