Diversity measure minimization based method for computing sparse solutions to linear inverse problems with multiple measurement vectors

The problem of computing sparse solutions to linear inverse problems arises in a large number of signal processing application areas. We address the problem of finding sparse solutions to linear inverse problems when there are multiple measurement vectors (MMV) and the solutions are assumed to have a common, but unknown, sparsity profile. This is an important extension to the single measurement sparse solution problem that has been extensively studied in the past. Of particular interest are methods based on minimizing diversity measures. A measure appropriate for the multiple measurement problem is developed, and an algorithm is derived based on its minimization. The algorithm developed, M-FOCUSS, generalizes the focal underdetermined system solver (FOCUSS) algorithm developed for the single measurement case. The convergence of the algorithm is established and a simulation study is conducted to evaluate its effectiveness. The results clearly show the ability of M-FOCUSS to utilize multiple measurement vectors for accurate identification of the sparsity structure and sparse solution computation.