Optimization of Structural Similarity in Mathematical Imaging
This work provides a foundational approach for developing SSIM-based image processing algorithms, which is incremental in extending SSIM from specific applications to a broader framework.
The paper introduces a general optimization framework for using the Structural Similarity Index Measure (SSIM) across various imaging applications, addressing the lack of generality in prior studies and proposing novel numerical strategies for solving these problems.
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.