Abstract In this paper, we study the image deblurring with impulsive noise problem. In order to find a high quality recovery solution, we propose a nonconvex optimization model that combines total variation regularization and nonconvex log penalty for data fitting. The new model can overcome the limitation of the L1-norm penalized data fitting term with total variation regularization model for high noise levels, and is easier to choose the scalar parameter in the data fitting term than the existing methods. For solving the nonconvex optimization problem, a difference of convex (DC) functions algorithm with adaptive proximal parameter is developed. Theoretically, using the Kurdyka-Łojasiewicz property, we establish that the sequence generated by the proposed algorithm converges to a critical point. The experiment results demonstrate the superiority of the new approach against the competing methods.

中文翻译：

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一种用于脉冲噪声图像去模糊的 TV-log 非凸方法

摘要 在本文中，我们研究了带有脉冲噪声的图像去模糊问题。为了找到高质量的恢复解决方案，我们提出了一种非凸优化模型，该模型结合了总变异正则化和非凸对数惩罚来进行数据拟合。新模型克服了全变分正则化模型对高噪声水平的L1范数惩罚数据拟合项的局限性，并且比现有方法更容易选择数据拟合项中的标量参数。为了解决非凸优化问题，开发了一种具有自适应近端参数的凸（DC）函数差分算法。从理论上讲，使用 Kurdyka-Łojasiewicz 属性，我们确定所提出算法生成的序列收敛到临界点。