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2010

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

11 years 4 months ago
A Fast Algorithm for Sparse Reconstruction Based on Shrinkage, Subspace Optimization, and Continuation
We propose a fast algorithm for solving the ℓ1-regularized minimization problem minx∈Rn µ x 1 + Ax − b 2 2 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 of x likely to be nonzero in an optimal solution. Restricting the decision variables x to this subset and fixing their signs at their current values reduces the ℓ1-norm x 1 to a linear function of x. The resulting subspace problem, which involves the minimization of a smaller and smooth quadratic function, is solved in the second phase. Our code FPC AS embeds this basic two-stage algorithm in a continuation (homotopy) approach by assigning a decreasing sequence of values to µ. This code exhibits state-of-the-art performance both in terms of its speed and its ability to recover sparse signals. It...
Zaiwen Wen, Wotao Yin, Donald Goldfarb, Yin Zhang
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where SIAMSC
Authors Zaiwen Wen, Wotao Yin, Donald Goldfarb, Yin Zhang
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