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A FAST ALGORITHM FOR SPARSE RECONSTRUCTION BASED ON SHRINKAGE, SUBSPACE OPTIMIZATION, AND CONTINUATION
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AI
DOI：10.1137/090747695.png)
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摘要
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We propose a fast algorithm for solving the l(1)-regularized minimization problem min(x is an element of Rn) mu parallel to x parallel to(1) + parallel to Ax - b parallel to(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 shrinkage method 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 l(1)-norm parallel to x parallel to(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 mu. This code exhibits state-of-the-art performance in terms of both its speed and its ability to recover sparse signals.
Keyword:
l(1)-minimization
basis pursuit
compressive sensing
subspace optimization
active set
continuation
shrinkage
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
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