Better than ℓ0 recovery via blind identification

In this work, we propose a novel approach to multiple measurement vector (MMV) compressed sensing. We show that by exploiting the statistical properties of the sources, we can do better than previously derived lower bounds in this context. We show that in the MMV case, we can identify the active sources with fewer sensors than sources. We first develop a general framework for recovering the sparsity profile of the sources by combining ideas from compressed sensing with blind identification methods. We do this by comparing the large known sensing matrix to the smaller matrix estimated by a blind identification method. Finally, we demonstrate the performance of this technique with a variety of data and blind identification methods, and show that under certain assumptions, it is possible to identify the active sources with only 2 sensors, regardless of the number of sources.