Denoising and inpainting of images using TV-type energies: theoretical and computational aspects

DOI10.1007/s10958-016-3153-yzbMath1381.94011OpenAlexW2552077903MaRDI QIDQ509542

Joachim Weickert, Michael Bildhauer, Fuchs, Martin

Publication date: 17 February 2017

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-016-3153-y

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Existence theories for free problems in two or more independent variables (49J10) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)

Related Items

On the solvability in Sobolev spaces and related regularity results for a variant of the TV-image recovery model: the vector-valued case ⋮ A remark on denoising of greyscale images using energy densities with varying growth rates ⋮ Convex regularization of multi-channel images based on variants of the TV-model ⋮ Iterative TV-regularization of grey-scale images ⋮ $C^{1,\alpha }$-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting ⋮ Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Applications to Contour Lines, Sparse Data, and Inpainting

Cites Work

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• Nonlinear total variation based noise removal algorithms
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• A variational framework for exemplar-based image inpainting
• Image inpainting with energies of linear growth. A collection of proposals
• Regularity for solutions of the total variation denoising problem
• Existence of generalized minimizers and dual solutions for a class of variational problems with linear growth related to image recovery
• Convex functionals and partial regularity
• Image recovery via total variation minimization and related problems
• A variational approach to the denoising of images based on different variants of the TV-regularization
• On some perturbations of the total variation image inpainting method. I: Regularity theory
• On some perturbations of the total variation image inpainting method. II: Relaxation and dual variational formulation
• On some perturbations of the total variation image inpainting method. III: Minimization among sets with finite perimeter
• Weak convergence of completely additive vector functions on a set
• Mathematical Models for Local Nontexture Inpaintings
• $C^{1,\alpha }$-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting
• Simple proofs of some results of Reshetnyak
• NONLOCAL VARIATIONAL MODELS FOR INPAINTING AND INTERPOLATION
• Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images
• Analysis of bounded variation penalty methods for ill-posed problems
• A Variational Method in Image Recovery
• Euler's Elastica and Curvature-Based Inpainting
• Digital inpainting based on the Mumford–Shah–Euler image model
• Fast Parallel Algorithms for a Broad Class of Nonlinear Variational Diffusion Approaches
• On the Dirichlet problem for variational integrals in BV
• Aspects of Total Variation RegularizedL¹Function Approximation
• Variable Exponent, Linear Growth Functionals in Image Restoration
• A study in the BV space of a denoising-deblurring variational problem
• Mathematical problems in image processing. Partial differential equations and the calculus of variations. Foreword by Olivier Faugeras