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Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in…

Analysis of PDEs · Mathematics 2022-07-18 Jian-Feng Cai , Jae Kyu Choi , Ke Wei

We consider the problem of reconstructing missing data on a smooth manifold from incomplete and nonuniform samples. While classical methods for manifold approximation typically assume quasi-uniform data, their performance deteriorates…

Numerical Analysis · Mathematics 2026-04-15 David Levin

Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying…

Computer Vision and Pattern Recognition · Computer Science 2019-01-14 Sebastian Lunz , Ozan Öktem , Carola-Bibiane Schönlieb

Total variation regularization based on the l1 norm is ubiquitous in image reconstruction. However, the resulting reconstructions are not always as sparse in the edge domain as desired. Iteratively reweighted methods provide some…

Image and Video Processing · Electrical Eng. & Systems 2022-04-01 Victor Churchill , Rick Archibald , Anne Gelb

Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…

Numerical Analysis · Mathematics 2016-03-25 V Grimm , R I McLachlan , D McLaren , G R W Quispel , C-B Schönlieb

We consider linear inverse problems that are formulated in the continuous domain. The object of recovery is a function that is assumed to minimize a convex objective functional. The solutions are constrained by imposing a continuous-domain…

Information Theory · Computer Science 2018-08-15 Harshit Gupta , Julien Fageot , Michael Unser

In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with $L^{2}$ data fitting term. We examine some properties of this model and we calculate exact solutions using simple…

Optimization and Control · Mathematics 2013-09-24 Konstantinos Papafitsoros , Kristian Bredies

The total variation (TV) model and its related variants have already been proposed for image processing in previous literature. In this paper a novel total variation model based on kernel functions is proposed. In this novel model, we first…

Computer Vision and Pattern Recognition · Computer Science 2017-11-21 Zhizheng Liang , Lei Zhang , Jin Liu , Yong Zhou

Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for…

Statistics Theory · Mathematics 2026-05-08 Miguel del Álamo , Housen Li , Axel Munk

Owing to its significant success, the prior imposed on gradient maps has consistently been a subject of great interest in the field of image processing. Total variation (TV), one of the most representative regularizers, is known for its…

Computer Vision and Pattern Recognition · Computer Science 2023-09-14 Shuang Xu , Yifan Wang , Zixiang Zhao , Jiangjun Peng , Xiangyong Cao , Deyu Meng , Yulun Zhang , Radu Timofte , Luc Van Gool

Multi-modality (or multi-channel) imaging is becoming increasingly important and more widely available, e.g. hyperspectral imaging in remote sensing, spectral CT in material sciences as well as multi-contrast MRI and PET-MR in medicine.…

Image and Video Processing · Electrical Eng. & Systems 2020-12-25 Leon Bungert , Matthias J. Ehrhardt

Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning…

Numerical Analysis · Mathematics 2023-09-15 Simon Göppel , Jürgen Frikel , Markus Haltmeier

The problem of restoring images corrupted by Poisson noise is common in many application fields and, because of its intrinsic ill posedness, it requires regularization techniques for its solution. The effectiveness of such techniques…

Numerical Analysis · Mathematics 2021-04-30 Daniela di Serafino , Germana Landi , Marco Viola

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…

Optimization and Control · Mathematics 2014-12-16 Martin Burger , Alex Sawatzky , Gabriele Steidl

It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to…

Optimization and Control · Mathematics 2022-06-08 Laurent Condat

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Optimization and Control · Mathematics 2014-12-09 Samuel Vaiter , Gabriel Peyré , Jalal M. Fadili

Video super-resolution (VSR) aims to reconstruct a sequence of high-resolution (HR) images from their corresponding low-resolution (LR) versions. Traditionally, solving a VSR problem has been based on iterative algorithms that can exploit…

Image and Video Processing · Electrical Eng. & Systems 2021-02-24 Benjamin Naoto Chiche , Arnaud Woiselle , Joana Frontera-Pons , Jean-Luc Starck

In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…

Optimization and Control · Mathematics 2020-02-19 Sebastian Banert , Axel Ringh , Jonas Adler , Johan Karlsson , Ozan Öktem

Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space…

Analysis of PDEs · Mathematics 2019-07-02 Remco Duits , Etienne St-Onge , Jim Portegies , Bart Smets

Total generalization variation (TGV) is a very powerful and important regularization for various inverse problems and computer vision tasks. In this paper, we proposed a semismooth Newton based augmented Lagrangian method to solve this…

Optimization and Control · Mathematics 2022-01-28 Hongpeng Sun