Sparse inverse solution methods for signal and image processing applications

This paper addresses image and signal processing problems where the result most consistent with prior knowledge is the minimum order, or “maximally sparse” solution. These problems arise in such diverse areas as astronomical star image deblurring, neuromagnetic image reconstruction, seismic deconvolution, and thinned array beamformer design. An optimization theoretic formulation for sparse solutions is presented, and its relationship to the MUSIC algorithm is discussed. Two algorithms for sparse inverse problems are introduced, and examples of their application to beamforming array design and star image deblurring are presented