Sparse Reconstruction by Separable Approximation

Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution and reconstruction, and compressed sensing (CS) are a few well-known areas in which problems of this type appear. One standard approach is to minimize an objective function that includes a quadratic ( lscr 2 ) error term added to a sparsity-inducing (usually lscr 1 ) regularizater. We present an algorithmic framework for the more general problem of minimizing the sum of a smooth convex function and a nonsmooth, possibly nonconvex regularizer. We propose…