Support Recovery of Sparse Signals in the Presence of Multiple Measurement Vectors

This paper studies the performance limits in the support recovery of sparse signals based on multiple measurement vectors (MMV). An information-theoretic analytical framework inspired by the connection to the single-input multiple-output multiple-access channel communication is established to reveal the performance limits in the support recovery of sparse signals with fixed number of nonzero entries. Sharp sufficient and necessary conditions for asymptotically successful support recovery are derived in terms of the number of measurements per vector, the number of nonzero rows, the measurement noise level, and the number of measurement vectors. Through the interpretations of the results, the benefit of having MMV for sparse signal recovery is illustrated, thus providing a theoretical foundation to the performance improvement enabled by MMV as observed in many existing simulation results. In particular, it is shown that the structure (rank) of the matrix formed by the nonzero entries plays an important role in the performance limits of support recovery.