Learning Consistent Discretizations of the Total Variation

DOI10.1137/20M1377199zbMath1477.49047OpenAlexW3167249630MaRDI QIDQ5860342

Antonin Chambolle, Thomas Pock

Publication date: 19 November 2021

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m1377199

zbMATH Keywords

discretizationtotal variationfinite elementslearningfinite differencesimage denoisingbilevel optimizationimage inpaintingprimal-dual algorithms

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Free boundary problems for PDEs (35R35) Finite difference methods for boundary value problems involving PDEs (65N06) Discrete approximations in optimal control (49M25) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87)

Related Items (11)

Optimality Conditions for Bilevel Imaging Learning Problems with Total Variation Regularization ⋮ Convergence of a Piggyback-Style Method for the Differentiation of Solutions of Standard Saddle-Point Problems ⋮ A primal-dual finite element method for scalar and vectorial total variation minimization ⋮ Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems ⋮ Linearly convergent bilevel optimization with single-step inner methods ⋮ Enhanced total variation minimization for stable image reconstruction ⋮ The total variation-Wasserstein problem: a new derivation of the Euler-Lagrange equations ⋮ On mathematical modeling in image reconstruction and beyond ⋮ Learning phase field mean curvature flows with neural networks ⋮ Efficient Boosted DC Algorithm for Nonconvex Image Restoration with Rician Noise ⋮ Bilevel Methods for Image Reconstruction

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