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Learning Consistent Discretizations of the Total Variation
SIAM Journal on Imaging Sciences ( IF 2.1 ) Pub Date : 2021-06-16 , DOI: 10.1137/20m1377199
Antonin Chambolle , Thomas Pock

SIAM Journal on Imaging Sciences, Volume 14, Issue 2, Page 778-813, January 2021.
In this work, we study a general framework of discrete approximations of the total variation for image reconstruction problems. The framework, for which we can show consistency in the sense of $\Gamma$-convergence, unifies and extends several existing discretization schemes. In addition, we propose algorithms for learning discretizations of the total variation in order to achieve the best possible reconstruction quality for particular image reconstruction tasks. Interestingly, the learned discretizations significantly differ between the tasks, illustrating that there is no universal best discretization of the total variation.


中文翻译:

学习全变的一致离散化

SIAM Journal on Imaging Sciences,第 14 卷,第 2 期,第 778-813 页,2021
年1 月。在这项工作中,我们研究了图像重建问题总变异的离散近似的一般框架。我们可以在 $\Gamma$-convergence 意义上展示一致性的框架统一并扩展了几个现有的离散化方案。此外,我们提出了用于学习总变化离散化的算法,以便为特定的图像重建任务实现最佳的重建质量。有趣的是,学习到的离散化在任务之间存在显着差异,这说明总变异没有通用的最佳离散化。
更新日期:2021-06-17
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