Total Variation Denoising in $l^1$ Anisotropy

DOI10.1137/16M1103610zbMath1451.94011arXiv1611.03261MaRDI QIDQ4689638

Michał Łasica, Salvador Moll, Piotr Bogusław Mucha

Publication date: 17 October 2018

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

Full work available at URL: https://arxiv.org/abs/1611.03261

zbMATH Keywords

regularityanisotropydenoisingrectanglestotal variation flowtetrisRudin-Osher-Fatemi modelrectilinear polygonspiecewise constant solutions

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Smoothness and regularity of solutions to PDEs (35B65) Regularity of solutions in optimal control (49N60) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Solutions to PDEs in closed form (35C05) Singular parabolic equations (35K67)

Related Items (13)

An augmented Lagrangian model for signal segmentation ⋮ A local estimate for vectorial total variation minimization in one dimension ⋮ Local estimates for vectorial Rudin–Osher–Fatemi type problems in one dimension ⋮ Invariant $\varphi$-Minimal Sets and Total Variation Denoising on Graphs ⋮ Weak solutions for the Stokes system for compressible non‐Newtonian fluids with unbounded divergence ⋮ Anisotropic Chan-Vese segmentation ⋮ Anisotropic tempered diffusion equations ⋮ A new numerical scheme for discrete constrained total variation flows and its convergence ⋮ Numerical computations of split Bregman method for fourth order total variation flow ⋮ A duality based approach to the minimizing total variation flow in the space \(H^{-s}\) ⋮ Regular 1-harmonic flow ⋮ Solution paths of variational regularization methods for inverse problems ⋮ Existence of W^{1,1} solutions to a class of variational problems with linear growth on convex domains

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• Regularity for solutions of the total variation denoising problem
• Anisotropic total variation filtering
• Anisotropic total variation regularized \(L^1\) approximation and denoising/deblurring of 2D bar codes
• The total variation flow in \(\mathbb R^N\)
• On the gradient flow of a one-homogeneous functional
• Total variation flow and sign fast diffusion in one dimension
• On total variation minimization and surface evolution using parametric maximum flows
• A characterization of convex calibrable sets in \(\mathbb R^N\) with respect to anisotropic norms
• Restoration of images with rotated shapes
• Pairings between measures and bounded functions and compensated compactness
• Regularization by functions of bounded variation and applications to image enhancement
• The anisotropic total variation flow
• A notion of total variation depending on a metric with discontinuous coefficients
• Almost classical solutions to the total variation flow
• Two cases of squares evolving by anisotropic diffusion
• Multi-Label Markov Random Fields as an Efficient and Effective Tool for Image Segmentation, Total Variations and Regularization
• Spectral Decompositions Using One-Homogeneous Functionals
• Inpainting by Flexible Haar-Wavelet Shrinkage
• The Split Bregman Method for L1-Regularized Problems
• The Discontinuity Set of Solutions of the TV Denoising Problem and Some Extensions
• On approximation in total variation penalization for image reconstruction and inverse problems
• Structural Properties of Solutions to Total Variation Regularization Problems
• Decomposition of images by the anisotropic Rudin-Osher-Fatemi model
• Continuity results for TV-minimizers
• Nonlinear Differential Equations of Monotone Types in Banach Spaces
• On a crystalline variational problem. II: \(BV\) regularity and structure of minimizers on facets
• On a crystalline variational problem. I: First variation and global \(L^\infty\) regularity

This page was built for publication: Total Variation Denoising in $l^1$ Anisotropy