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Sparse optimization problem with s-difference regularization
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DOI：10.1016/j.sigpro.2019.107369.png)
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Abstract
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In this paper, a s-difference type regularization for sparse recovery problem is proposed, which is the difference of the penalty function R(x) and its corresponding s-truncated function R(x(s)). First, we show the equivalent conditions between the l(0) constrained problem and the unconstrained s-difference penalty regularized problem. Next, we choose the forward-backward splitting (FBS) method to approximately solve the non-convex regularization function and further derive some closed-form solutions for the proximal mapping of the s-difference regularization with some commonly used R(x), which makes the FBS easy and fast. We also show that any cluster point of the sequence generated by the proposed algorithm converges to a stationary point. Numerical experiments demonstrate the efficiency of the proposed s-difference regularization in comparison with some other existing penalty functions. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Sparse optimization
Forward-Backward splitting
Proximal operator
Difference of convex
Truncated function
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