As an important, challenging, and difficult problem in image processing, multiplicative noise removal (MNR) has attracted great attention. To this end, many variational methods have been effectively proposed in the past few decades. Among these variational methods, total variation (TV) and its higher-order extensions are very effective, where the former can preserve sharp edges but cause some undesirable staircase effects and the latter can better reduce the staircase effects but sometimes smooth the image details. To overcome the drawbacks while taking full use of their merits, the authors propose a novel hybrid higher-order TV regularisation model for MNR, in which the novelty of the proposed model consists of combining the image prior information of first-order and second-order derivatives to propose a novel higher-order regulariser, named as hybrid higher-order TV (HHTV). More specifically, a more preferable equivalent formulation of HHTV is derived. Then, they use the derived equivalent formulation to design an efficient alternating iterative algorithm to solve the proposed model. Finally, the experimental results demonstrate that the proposed HHTV method outperforms several state-of-the-art methods in terms of image quality and convergence speed.

中文翻译：

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混合高阶总方差模型用于乘性噪声去除

作为图像处理中的重要，具有挑战性和困难的问题，乘法噪声消除（MNR）引起了极大的关注。为此，在过去的几十年中已经有效地提出了许多变型方法。在这些变分方法中，总变分（TV）及其高阶扩展非常有效，前者可以保留锐利的边缘，但会引起一些不希望的阶梯效应，而后者可以更好地减小阶梯效应，但有时会平滑图像细节。为了克服缺点，同时充分利用其优点，作者提出了一种新颖的MNR混合高阶电视正则化模型，该模型的新颖性在于将一阶和二阶图像先验信息相结合。衍生出一种新颖的高阶正则化器，被称为混合高阶电视（HHTV）。更具体地，得到HHTV的更优选的等效制剂。然后，他们使用导出的等效公式设计一种有效的交替迭代算法来求解所提出的模型。最后，实验结果表明，在图像质量和收敛速度方面，所提出的HHTV方法优于几种最新方法。