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An Iterative Threshold Algorithm of Log-sum Regularization for Sparse Problem
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  • xin zhou ,
  • Xiaowen Liu ,
  • Gong Zhang ,
  • Luliang Jia ,
  • Xu Wang ,
  • Zhiyuan Zhao
xin zhou
the College of Information and Communication

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Xiaowen Liu
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Gong Zhang
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Luliang Jia
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Zhiyuan Zhao
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Abstract

The log-sum regularization has been always drawing widespread attention in the field of sparse problem. However, it brings about a non-convex, non-smooth, and non-Lipschitz optimization problem that is difficult to tackle. To overcome the problem, an iterative threshold algorithm of log-sum regularization is proposed in this paper. Firstly, by deducing the derivative mathematical expression of log-sum function, a property theorem about solution for log-sum regularization is established. Secondly, based on the above theorem, the optimal setting rules of the compromising parameters are elaborated, and the iterative log-sum threshold algorithm is proposed. Thirdly, under the situation that the compromising parameters of log-sum regularization are relatively small, it can be proven that the proposed algorithm converges to a local minimizer of log-sum regularization. Finally, a series of simulations are implemented to examine performance of the algorithm, and the results exhibit that the proposed algorithm outperforms the state-of-the-art algorithms in terms of iterations and precision.
Sep 2023Published in IEEE Transactions on Circuits and Systems for Video Technology volume 33 issue 9 on pages 4728-4740. 10.1109/TCSVT.2023.3247944