A gradient set matching pursuit algorithm with anti-base mismatch ability for sparse reconstruction under low SNR

Abstract

This paper is concerned with designing an effective algorithm for recovering mismatched sparse signals from noise underdetermined measurements. The sparse recovery problem is formulated as the gradient optimization model of the residual cost function in a multidimensional continuous parameter space. The mismatched atoms of the discrete dictionary matrix are recovered as the accurate target sparse coefficient by solving a gradient descent algorithm with a hyperparameters joint adaptive adjustment function. To estimate the target parameters of frequency agile radar, we propose a gradient set matching pursuit algorithm. The algorithm uses the prior knowledge of resolution of the two-dimensional ambiguity function to build a discrete dictionary and obtains the support set according to the orthogonal matching pursuit principle. We divide the gradient set space in the neighborhood of the support set and calculate the mean gradient as the judgment direction and iteration step of the initial optimization process to overcome the residual function distortion and gradient error caused by random noise. The iterative convergence process of the proposed algorithm in the support set vector space is more robust, and the problem of falling into local optimum is avoided. Compared with the conventional sparse recovery algorithm and gradient descent algorithm, the proposed algorithm boosts its reconstruction performance of target parameters in the scenario of low SNR and mismatch of multiple scattering points. Simulation results show the effectiveness of the proposed algorithm.