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The use of discrete gradient methods for total variation type regularization problems in image processing

Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing tasks. We promote the use of discrete gradient methods in image processing by exhibiting experiments with nonlinear total variation (TV) deblurring, denoising, and inpainting.