shrinkage – Optimization Online

A Fast Algorithm for Sparse Reconstruction based on Shrinkage, Subspace Optimization and Continuation

Published: 2009/03/11

Convex Optimization, Nonsmooth Optimization active set, basis pursuit, compressed sensing, continuation, l1-minimization, shrinkage, subspace optimization

We propose a fast algorithm for solving the l1-regularized least squares problem for recovering sparse solutions to an undetermined system of linear equations Ax = b. The algorithm is divided into two stages that are performed repeatedly. In the first stage a first-order iterative method called “shrinkage” yields an estimate of the subset of components … Read more

Coordinate and Subspace Optimization Methods for Linear Least Squares with Non-Quadratic Regularization

Published: 2006/05/04, Updated: 2006/05/08

Michael Elad

Michael Zibulevsky

Boaz Matalon

Statistics, Unconstrained Optimization basis pursuit, denoising, inverse problems, least squares, regularization, shrinkage

This work addresses the problem of regularized linear least squares (RLS) with non-quadratic separable regularization. Despite being frequently deployed in many applications, the RLS problem is often hard to solve using standard iterative methods. In a recent work [10], a new iterative method called Parallel Coordinate Descent (PCD) was devised. We provide herein a convergence … Read more