Analytical aspects of spatially adapted total variation regularisation

DOI10.1016/j.jmaa.2017.05.025zbMath1416.94016arXiv1609.01074OpenAlexW2964185338WikidataQ57618110 ScholiaQ57618110MaRDI QIDQ2360032

Carlos N. Rautenberg, Michael Hintermüller, Konstantinos Papafitsoros

Publication date: 23 June 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01074

zbMATH Keywords

denoisingregularisationstructure of solutionsweighted total variationtotal variation minimisation

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)

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Cites Work

• Unnamed Item
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• Nonlinear total variation based noise removal algorithms
• A study of the one dimensional total generalised variation regularisation problem
• Some remarks on the staircasing phenomenon in total variation-based image denoising
• Infimal convolution regularisation functionals of BV and \(\mathrm{L}^p\) spaces. I: The finite \(p\) case
• A multi-scale vectorial \(L^{\tau }\)-TV framework for color image restoration
• Locally adaptive image denoising by a statistical multiresolution criterion
• Properties of \(L^{1}-TGV^{2}\) : The one-dimensional case
• Variational methods in imaging
• An introduction to \(\Gamma\)-convergence
• TV based image restoration with local constraints
• Automated regularization parameter selection in multi-scale total variation models for image restoration
• Statistical multiresolution Dantzig estimation in imaging: fundamental concepts and algorithmic framework
• A combined first and second order variational approach for image reconstruction
• Combined first and second order variational approaches for image processing
• The equivalence of the taut string algorithm and BV-regularization
• A TV based restoration model with local constraints
• Spatially dependent regularization parameter selection in total generalized variation models for image restoration
• Variational Analysis in Sobolev and BV Spaces
• Total Variation Regularization for Image Denoising, II. Examples
• Total Variation Regularization for Image Denoising, III. Examples.
• Total Variation Regularization for Image Denoising, I. Geometric Theory
• The Discontinuity Set of Solutions of the TV Denoising Problem and Some Extensions
• The TVL1 Model: A Geometric Point of View
• Expected absolute value estimators for a spatially adapted regularization parameter choice rule in L ¹ -TV-based image restoration
• Analysis of bounded variation penalty methods for ill-posed problems
• Edge-preserving and scale-dependent properties of total variation regularization
• Structural Properties of Solutions to Total Variation Regularization Problems
• The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising
• Aspects of Total Variation RegularizedL¹Function Approximation
• An Iterative Regularization Method for Total Variation-Based Image Restoration
• Total Generalized Variation