Nonparametric Simultaneous Sparse Recovery: an Application to Source Localization

We consider multichannel sparse recovery problem where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors. Many popular greedy or convex algorithms perform poorly under non-Gaussian heavy-tailed noise conditions or in the face of outliers. In this paper, we propose the usage of mixed $\ell_{p,q}$ norms on data fidelity (residual matrix) term and the conventional $\ell_{0,2}$-norm constraint on the signal matrix to promote row-sparsity. We devise a greedy pursuit algorithm based on simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Simulation studies highlight the effectiveness of the proposed approaches to cope with different noise environments (i.i.d., row i.i.d, etc) and outliers. Usefulness of the methods are illustrated in source localization application with sensor arrays.