English
Related papers

Related papers: Higher-order total variation approaches and genera…

200 papers

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

While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or…

Computer Vision and Pattern Recognition · Computer Science 2011-02-22 Vincent Michel , Alexandre Gramfort , Gaël Varoquaux , Evelyn Eger , Bertrand Thirion

This paper presents an efficient algorithm to solve total variation (TV) regularizations of images contaminated by a both blur and noise. The unconstrained structure of the problem suggests that one can solve a constrained optimization…

Numerical Analysis · Computer Science 2018-02-13 A. Bentbib , M. El Guide , K. Jbilou

In this paper we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space valued data. These kind of data appear when dealing with nonlinear color spaces such as HSV, and they can be obtained by…

Numerical Analysis · Mathematics 2018-12-10 Ronny Bergmann , Andreas Weinmann

Total variation(TV) regularization is applied to X-Ray computed tomography(CT) in an effort to reduce metal artifacts. Tikhonov regularization with $L^2$ data fidelity term and total variation regularization is augmented in this novel model…

Numerical Analysis · Mathematics 2018-10-09 Clemens Schiffer

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 study the solutions of infinite dimensional linear inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary…

Optimization and Control · Mathematics 2017-11-03 Axel Flinth , Pierre Weiss

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

This article studies the denoising performance of total variation (TV) image regularization. More precisely, we study geometrical properties of the solution to the so-called Rudin-Osher-Fatemi total variation denoising method. The first…

Optimization and Control · Mathematics 2016-12-21 Antonin Chambolle , Vincent Duval , Gabriel Peyré , Clarice Poon

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian…

Optimization and Control · Mathematics 2014-02-20 Stamatios Lefkimmiatis , John Paul Ward , Michael Unser

Optimization within a layer of a deep-net has emerged as a new direction for deep-net layer design. However, there are two main challenges when applying these layers to computer vision tasks: (a) which optimization problem within a layer is…

Computer Vision and Pattern Recognition · Computer Science 2022-04-08 Raymond A. Yeh , Yuan-Ting Hu , Zhongzheng Ren , Alexander G. Schwing

In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide…

Numerical Analysis · Mathematics 2018-04-30 Martin Storath , Andreas Weinmann

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 this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational…

Optimization and Control · Mathematics 2025-01-15 Bin Fan

In this paper we introduce the notion of second-order total generalized variation (TGV) regularization for manifold-valued data in a discrete setting. We provide an axiomatic approach to formalize reasonable generalizations of TGV to the…

Numerical Analysis · Mathematics 2018-09-17 K. Bredies , M. Holler , M. Storath , A. Weinmann

The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image…

Computer Vision and Pattern Recognition · Computer Science 2024-10-04 Jing-En Huang , Jia-Wei Liao , Ku-Te Lin , Yu-Ju Tsai , Mei-Heng Yueh

In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The approach is based on the idea of variational inequalities,…

Optimization and Control · Mathematics 2011-07-14 Markus Grasmair

Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…

Medical Physics · Physics 2024-12-11 Alexander Meaney , Mikael A. K. Brix , Miika T. Nieminen , Samuli Siltanen

The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the…

Optimization and Control · Mathematics 2020-07-13 Michael Unser

In the past decade, sparsity-driven regularization has led to significant improvements in image reconstruction. Traditional regularizers, such as total variation (TV), rely on analytical models of sparsity. However, increasingly the field…

Computer Vision and Pattern Recognition · Computer Science 2018-10-31 Jiaming Liu , Yu Sun , Xiaojian Xu , Ulugbek S. Kamilov