Separating Radar Signals From Impulsive Noise Using Atomic Norm Minimization

We consider the problem of corrupted radar super-resolution, a generalization of compressed radar super-resolution in which one aims to recover the continuous-valued delay-Doppler pairs of moving objects from a collection of corrupted and noisy measurements. The received signal in this type consists of contributions from objects, outlier and noise. While this problem is ill-posed in general, tractable recovery is possible when both the number of objects and corrupted measurements are limited. In this brief, we propose an atomic norm optimization in order to find the delay-Doppler pairs and the outlier signal. The objective function of our optimization problem encourages both sparsity in the continuous delay-Doppler domain and the sparsity of perturbations in the outlier signal. We show that the associated problem can be solved via semidefinite programming (SDP). Moreover, we provide a reasonably fast and efficient algorithm for solving this SDP based on the alternating method of multipliers (ADMM). Simulations results verify the superior performance of our proposed problem and the high accuracy and low computational complexity of our algorithm.