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Related papers: Adaptive Rates for Total Variation Image Denoising

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In this paper we study the structure of solutions of the one dimensional weighted total variation regularisation problem, motivated by its application in signal recovery tasks. We study in depth the relationship between the weight function…

Optimization and Control · Mathematics 2016-09-06 Michael Hintermüller , Konstantinos Papafitsoros , Carlos N. Rautenberg

The rise of machine learning in image processing has created a gap between trainable data-driven and classical model-driven approaches: While learning-based models often show superior performance, classical ones are often more transparent.…

Image and Video Processing · Electrical Eng. & Systems 2020-04-15 Tobias Alt , Joachim Weickert

This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based…

Computer Vision and Pattern Recognition · Computer Science 2012-04-16 Ayan Chakrabarti , Todd Zickler

In inverse problems, prior information and a priori-based regularization techniques play important roles. In this paper, we focus on image restoration problems, especially on restoring images whose texture mainly follow one direction. In…

Numerical Analysis · Mathematics 2017-08-23 Rasmus Dalgas Kongskov , Yiqiu Dong , Kim Knudsen

In a recent paper by A. Chambolle et al. [Geometric properties of solutions to the total variation denoising problem. Inverse Problems 33, 2017] it was proven that if the subgradient of the total variation at the noise free data is not…

Optimization and Control · Mathematics 2021-06-09 José A. Iglesias , Gwenael Mercier , Otmar Scherzer

An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element…

Numerical Analysis · Mathematics 2020-06-24 Ronny Bergmann , Marc Herrmann , Roland Herzog , Stephan Schmidt , José Vidal Núñez

The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii)…

Computer Vision and Pattern Recognition · Computer Science 2016-04-01 Vania V. Estrela , Hermes Aguiar Magalhaes , Osamu Saotome

Nonlocal equations effectively preserve textures but exhibit weak regularization effects in image denoising, whereas local equations offer strong denoising capabilities yet fail to protect textures. To integrate the advantages of both…

Analysis of PDEs · Mathematics 2025-10-31 Yi Ran , Zhichang Guo , Kehan Shi , Qirui Zhou , Jingfeng Shao , Martin Burger , Boying Wu

Total variation (TV) regularization is a classical tool for image denoising, but its convex $\ell_1$ formulation often leads to staircase artifacts and loss of contrast. To address these issues, we introduce the Transformed $\ell_1$ (TL1)…

Image and Video Processing · Electrical Eng. & Systems 2025-11-20 Nabiha Choudhury , Jianqing Jia , Yifei Lou

We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the…

Machine Learning · Statistics 2016-12-12 Charles-Alban Deledalle , Nicolas Papadakis , Joseph Salmon , Samuel Vaiter

We show how total variation regularization of images in arbitrary dimensions can be approximately performed by applying appropriate shrinkage to some Haar wavelets coefficients. The approach works directly on the wavelet coefficients and is…

Numerical Analysis · Mathematics 2024-11-04 Tomas Sauer , A. Michael Stock

The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…

Numerical Analysis · Mathematics 2015-12-01 Martin Burger , Jan Modersitzki , Sebastian Suhr

In this paper, we present a fast and effective method for solving the Poisson-modified total variation model proposed in [9]. The existence and uniqueness of the model are again proved using different method. A semi-implicit difference…

Optimization and Control · Mathematics 2017-04-05 Wei Wang , Chuanjiang He

Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…

Numerical Analysis · Mathematics 2018-06-15 Chunlin Wu , Zhifang Liu , Shuang Wen

Image denoising is a typical ill-posed problem due to complex degradation. Leading methods based on normalizing flows have tried to solve this problem with an invertible transformation instead of a deterministic mapping. However, the…

Computer Vision and Pattern Recognition · Computer Science 2023-02-01 Wenchao Du , Hu Chen , Yi Zhang , H. Yang

Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise,…

Computer Vision and Pattern Recognition · Computer Science 2018-06-05 Jérémy Anger , Mauricio Delbracio , Gabriele Facciolo

To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order…

Computer Vision and Pattern Recognition · Computer Science 2015-09-15 Jianping Zhang , Ke Chen

Sparse representation of images under certain transform domain has been playing a fundamental role in image restoration tasks. One such representative method is the widely used wavelet tight frame systems. Instead of adopting fixed filters…

Computer Vision and Pattern Recognition · Computer Science 2016-03-02 Dai-Qiang Chen

In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. Each image is uniquely associated with a solution to these wave equations, allowing for its reconstruction with…

Computer Vision and Pattern Recognition · Computer Science 2024-10-17 Yinpeng Chen , Dongdong Chen , Xiyang Dai , Mengchen Liu , Yinan Feng , Youzuo Lin , Lu Yuan , Zicheng Liu

Visual representations are defined in terms of minimal sufficient statistics of visual data, for a class of tasks, that are also invariant to nuisance variability. Minimal sufficiency guarantees that we can store a representation in lieu of…

Computer Vision and Pattern Recognition · Computer Science 2016-06-29 Stefano Soatto , Alessandro Chiuso