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 (ℓ2) error term added to a sparsity-inducing (usually ℓ1) regularizer. We present an algorithmic framework for the more general problem of minimizing the sum of a smooth convex function and a nonsmooth, possibly nonconvex, sparsity-inducing function. We propose iterative methods in which each step is an optimization subproblem involving a separable quadratic term (diagonal Hessian) plus the original sparsity-inducing term. Our approach is suitable for cases in which this subproblem can be solved much more rapidly than the original pr...

• Type: Conference
• Year: 2008
• Where: ICASSP
• Authors: Stephen J. Wright, Robert D. Nowak, Mário A. T. Figueiredo
• Keywords: ICASSP 2008, Separable Quadratic Term, Signal Processing, Smooth Convex Function, Sparse Approximate Solutions