Robust joint sparse recovery on data with outliers

We propose a method to solve the multiple measurement vector (MMV) sparse signal recovery problem in a robust manner when data contains outlier points which do not fit the shared sparsity structure otherwise contained in the data. This scenario occurs frequently in the applications of MMV models due to only partially known source dynamics. The algorithm we propose is a modification of MMV-based sparse bayesian learning (M-SBL) by incorporating the idea of least trimmed squares (LTS), which has previously been developed for robust linear regression. Experiments show a significant performance improvement over the conventional M-SBL under different outlier ratios and amplitudes.