Deriving algorithms for computing sparse solutions to linear inverse problems

A novel methodology is employed to develop algorithms for computing sparse solutions to linear inverse problems, starting from suitably defined diversity measures whose minimization promotes sparsity. These measures include p-norm-like (l((p less than or equal to 1))) diversity measures, and the Gaussian and Shannon Entropies. The algorithm development methodology uses a factored representation of Me gradient, and involves successive relaxation of the Lagrangian necessary condition. The general nature of the methodology provides a systematic approach for deriving a recently developed class of algorithms called FOCUSS (FOCal Underdetermined System Solver), and a natural mechanism for extending them.