A Simple Recovery Framework for Signals with Time-Varying Sparse Support

Sparse recovery methods have been developed to solve multiple measurement vector (MMV) problems. These methods seek to reconstruct a collection of sparse signals from a small number of linear measurements, exploiting not only the sparsity but also certain correlations between the signals. Typically, the assumption is that the collection of signals shares a common joint support, allowing the problem to be solved more efficiently (or with fewer measurements) than solving many individual, single measurement vector (SMV) subproblems. Here, we relax this stringent assumption so that the signals may exhibit a changing support, a behavior that is much more prominent in applications. We propose a simple windowed framework that can utilize any traditional MMV method as a subroutine, and exhibits improved recovery when the MMV method incorporates prior information on signal support. In doing so, our framework enjoys natural extensions of existing theory and performance of such MMV methods. We demonstrate the value of this approach by using different MMV methods as subroutines within the proposed framework and applying it to both synthetic and real-world data.