Localization of More Sources Than Sensors via Jointly-Sparse Bayesian Learning

We analyze the jointly-sparse signal recovery problem in the regime where the number of sources k is larger than the number of measurements M. We show that the support set of sources can still be recovered with sparse Bayesian learning (M-SBL) even if k ≥ M. We provide sufficient conditions on the dictionary and sources which theoretically guarantee support set recovery in the noiseless case of M-SBL. We validate our sufficient conditions with experiments and also demonstrate that M-SBL outperforms M-CoSaMP, the algorithm recently used to localize more sources than sensors. Finally, we experimentally show robustness of the approach in the presence of noise.