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Related papers: Adaptive Rates for Total Variation Image Denoising

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This paper deals with the so-called staircasing phenomenon, which frequently arises in total variation based denoising models in image analysis. We prove in particular that staircasing always occurs at global extrema of the datum and at all…

Numerical Analysis · Mathematics 2014-02-04 Khalid Jalalzai

We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV) regularization, in image denoising problems. We describe…

Numerical Analysis · Mathematics 2022-09-27 Lukas Baumgärtner , Ronny Bergmann , Roland Herzog , Stephan Schmidt , José Vidal-Núñez

Denoising is of utmost importance for the visualization and processing of images featuring low signal-to-noise ratio. Total variation methods are among the most popular techniques to perform this task improving the signal-to-noise ratio…

Signal Processing · Electrical Eng. & Systems 2022-01-24 Gonzalo D. Maso Talou , Pablo J. Blanco

We present some results of geometric convergence of level sets for solutions of total variation denoising as the regularization parameter tends to zero. The common feature among them is that they make use of explicit constructions of…

Optimization and Control · Mathematics 2021-03-24 José A. Iglesias , Gwenael Mercier

A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…

Optimization and Control · Mathematics 2018-12-10 Antonin Chambolle , Martin Holler Thomas Pock

In this paper we propose a method to determine explicitly the solution of the total variation denoising problem with an $L^p$ fidelity term, where $p>1$, for piecewise constant initial data in dimension one.

Optimization and Control · Mathematics 2017-09-12 Riccardo Cristoferi

In this paper, we propose an adaptive finite difference scheme in order to numerically solve total variation type problems for image processing tasks. The automatic generation of the grid relies on indicators derived from a local estimation…

Numerical Analysis · Mathematics 2024-10-18 Thomas Jacumin , Andreas Langer

The study of the regularity of the minimizer of the weighted anisotropic total variation with a general fidelity term is at the heart of this paper. We generalized some recent results on the inclusion of the discontinuities of the minimizer…

Optimization and Control · Mathematics 2014-02-04 Khalid Jalalzai

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Computer Vision and Pattern Recognition · Computer Science 2020-06-17 Erich Kobler , Alexander Effland , Karl Kunisch , Thomas Pock

This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field,…

Optimization and Control · Mathematics 2015-03-09 Eva-Maria Brinkmann , Martin Burger , Joana Grah

In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the $r$-order (an)-isotropic total variation seminorms $TV^r$, with $r\in \mathbb R^+$, defined via the…

Analysis of PDEs · Mathematics 2019-01-17 Pan Liu , Xin Yang Lu

We revisit total variation denoising and study an augmented model where we assume that an estimate of the image gradient is available. We show that this increases the image reconstruction quality and derive that the resulting model…

Optimization and Control · Mathematics 2018-04-05 Birgit Komander , Dirk A. Lorenz , Lena Vestweber

We propose a new type of regularization functional for images called oscillation total generalized variation (TGV) which can represent structured textures with oscillatory character in a specified direction and scale. The infimal…

Numerical Analysis · Mathematics 2018-09-17 Yiming Gao , Kristian Bredies

We propose a PDE-constrained optimization approach for the determination of noise distribution in total variation (TV) image denoising. An optimization problem for the determination of the weights correspondent to different types of noise…

Optimization and Control · Mathematics 2012-07-17 Juan-Carlos De los Reyes , Carola-Bibiane Schönlieb

Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well…

Computer Vision and Pattern Recognition · Computer Science 2013-10-22 Jun Liu , Ting-Zhu Huang , Ivan W. Selesnick , Xiao-Guang Lv , Po-Yu Chen

We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the…

Computer Vision and Pattern Recognition · Computer Science 2016-04-26 Vladimir Kolmogorov , Thomas Pock , Michal Rolinek

Even after over two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly to move from scalar to vector-valued…

Computer Vision and Pattern Recognition · Computer Science 2016-06-21 Joan Duran , Michael Moeller , Catalina Sbert , Daniel Cremers

This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, an…

Computer Vision and Pattern Recognition · Computer Science 2015-03-20 Deanna Needell , Rachel Ward

We tackle the problem of reflectance estimation from a set of multi-view images, assuming known geometry. The approach we put forward turns the input images into reflectance maps, through a robust variational method. The variational model…

Computer Vision and Pattern Recognition · Computer Science 2018-01-24 Jean Mélou , Yvain Quéau , Jean-Denis Durou , Fabien Castan , Daniel Cremers

We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a…

Analysis of PDEs · Mathematics 2017-11-06 Michał Łasica , Salvador Moll , Piotr B. Mucha