In this paper we propose a new method of solving optimization problems involving the structural similarity image quality measure with L~1-regularization. The regularization term ||x||_1 is approximated by a sequence of smooth functions ||x||_1~ε by means of C_0~∞ functions known as mollifiers. Because the functions ||x||_1~ε epi-converge to ||x||_1, the sequence of minimizers of the smooth objective functions converges to a mini-mizer of the non-smooth problem. This approach permits the use of gradient-based methods to solve the minimization problems as opposed to methods based on subdifferentials.
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机译：在本文中，我们提出了一种解决优化问题的新方法，该方法涉及具有L〜1正则化的结构相似图像质量度量。正则项|| x || _1通过一系列平滑函数|| x || _1〜ε通过C_0〜∞函数（称为mollifiers）来近似。因为函数|| x || _1〜ε外收敛到|| x || _1，所以平滑目标函数的极小值序列收敛到非平滑问题的极小值。与基于次微分的方法相反，该方法允许使用基于梯度的方法来解决最小化问题。
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