Analysis and extensions of the FOCUSS algorithm

The FOCUSS (focal underdetermined system solution) algorithm is reexamined with a view to better understand, extend, and generalize the method. We address general issues that enhance its wider applicability and indicate its relevance to magnetoencephalography (MEG) whenever appropriate. Computing strategies are developed to enhance the attractiveness of FOCUSS. The multiple measurement vector problem is considered, uniqueness results developed, and the FOCUSS algorithm extended to compute the sparse solutions. An affine scaling transformation (AST) framework is developed to generalize the principles underlying FOCUSS. It allows for a systematic tradeoff between sparsity and the quality of approximation, and naturally provides the capability for dealing with noise. Computer simulations are provided to support the theory.