Robust Recovery of Temporally Smooth Signals From Under-Determined Multiple Measurements

In this paper, we consider the problem of recovering jointly sparse vectors from underdetermined measurements that are corrupted by both additive noise and outliers. This can be viewed as the robust extension of the Multiple Measurement Vector (MMV) problem. To solve this problem, we propose two general approaches. As a benchmark, the first approach preprocesses the input for outlier removal and then employs state-of-the-art technologies for signal recovery. The second approach, as the main contribution of this paper, is based on formulation of an innovative regularized fitting problem. By solving the regularized fitting problem, we jointly remove outliers and recover the sparse vectors. Furthermore, by exploiting temporal smoothness among the sparse vectors, we improve noise robustness of the proposed approach and avoid the problem of over-fitting. Extensive numerical results are provided to illustrate the excellent performance of the proposed approach.