It is now generally accepted that Euclidean-based metrics may not always adequately represent the subjective judgement of a human observer. As a result, many image processing methodologies have been recently extended to take advantage of alternative visual quality measures, the most prominent of which is the Structural Similarity Index Measure (SSIM). The superiority of the latter over Euclidean-based metrics have been demonstrated in several studies. However, being focused on specific applications, the findings of such studies often lack generality which, if otherwise acknowledged, could have provided a useful guidance for further development of SSIM-based image processing algorithms. Accordingly, instead of focusing on a particular image processing task, in this paper, we introduce a general framework that encompasses a wide range of imaging applications in which the SSIM can be employed as a fidelity measure. Subsequently, we show how the framework can be used to cast some standard as well as original imaging tasks into optimization problems, followed by a discussion of a number of novel numerical strategies for their solution.

现在已经普遍接受的是，基于欧几里得的度量可能并不总是足以代表人类观察者的主观判断。结果，最近已扩展了许多图像处理方法，以利用替代的视觉质量度量，其中最突出的是结构相似性指数度量（SSIM）。多项研究已经证明了后者优于基于欧几里得的度量标准。但是，由于专注于特定应用，因此此类研究的结果通常缺乏通用性，如果没有其他公认的话，它们可能为进一步开发基于SSIM的图像处理算法提供有用的指导。因此，在本文中，不是专注于特定的图像处理任务，我们介绍了一个通用框架，该框架涵盖了广泛的成像应用，在这些应用中，可以将SSIM用作保真度度量。随后，我们展示了如何使用该框架将某些标准以及原始成像任务转换为优化问题，然后讨论了许多新颖的数值解决方案。