Learned Discretization Schemes for the Second-Order Total Generalized Variation

Lea BogenspergerAntonin ChambolleAlexander EfflandThomas Pock

Mar 2023

摘要

The total generalized variation extends the total variation by incorporatinghigher-order smoothness. Thus, it can also suffer from similar discretizationissues related to isotropy. Inspired by the success of novel discretizationschemes of the total variation, there has been recent work to improve thesecond-order total generalized variation discretization, based on the samedesign idea. In this work, we propose to extend this to a generaldiscretization scheme based on interpolation filters, for which we provevariational consistency. We then describe how to learn these interpolationfilters to optimize the discretization for various imaging applications. Weillustrate the performance of the method on a synthetic data set as well as fornatural image denoising.

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