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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

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 study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there…

Optimization and Control · Mathematics 2021-12-22 Thomas Debarre , Quentin Denoyelle , Michael Unser , Julien Fageot

Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…

Numerical Analysis · Mathematics 2025-11-13 Liang Luo , Lei Zhang

We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These…

Optimization and Control · Mathematics 2014-12-12 Andreas Weinmann , Laurent Demaret , Martin Storath

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…

Computer Vision and Pattern Recognition · Computer Science 2019-08-20 Tim Meinhardt , Michael Moeller , Caner Hazirbas , Daniel Cremers

Recent hardware advancements in AI Accelerators and GPUs allow to efficiently compute sparse matrix multiplications, especially when 2 out of 4 consecutive weights are set to zero. However, this so-called 2:4 sparsity usually comes at a…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

Optimization and Control · Mathematics 2024-12-10 Howard Heaton

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…

Computer Vision and Pattern Recognition · Computer Science 2019-04-08 Wenqi Lu , Jinming Duan , David Orive-Miguel , Lionel Herve , Iain B Styles

Proximal operators are of particular interest in optimization problems dealing with non-smooth objectives because in many practical cases they lead to optimization algorithms whose updates can be computed in closed form or very efficiently.…

Machine Learning · Computer Science 2019-10-10 Benjamín Béjar , Ivan Dokmanić , René Vidal

Inverse problems in image processing are typically cast as optimization tasks, consisting of data-fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two…

Image and Video Processing · Electrical Eng. & Systems 2020-10-30 Regev Cohen , Michael Elad , Peyman Milanfar

Sparse representation learning has recently gained a great success in signal and image processing, thanks to recent advances in dictionary learning. To this end, the $\ell_0$-norm is often used to control the sparsity level. Nevertheless,…

Computer Vision and Pattern Recognition · Computer Science 2017-09-19 Yuan Liu , Stéphane Canu , Paul Honeine , Su Ruan

This paper presents a scalable approximate Bayesian method for image restoration using total variation (TV) priors. In contrast to most optimization methods based on maximum a posteriori estimation, we use the expectation propagation (EP)…

Computer Vision and Pattern Recognition · Computer Science 2022-09-21 Dan Yao , Stephen McLaughlin , Yoann Altmann

The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In this paper, in order to alleviate the staircase effect,…

Numerical Analysis · Mathematics 2015-05-20 Gang Liu , Ting-Zhu Huang , Jun Liu , Xiao-Guang Lv

We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the operators underlying…

Image and Video Processing · Electrical Eng. & Systems 2020-06-11 Michael T. McCann , Saiprasad Ravishankar

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

Optimization and Control · Mathematics 2019-03-26 Jérôme Bolte , Zheng Chen , Edouard Pauwels

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

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

Coded ptychography has emerged as a powerful technique for high-throughput, high-resolution lensless imaging. However, the trade-off between acquisition speed and image quality remains a significant challenge. To address this, we introduce…

Image and Video Processing · Electrical Eng. & Systems 2024-09-04 Ninghe Liu , Qianhao Zhao , Guoan Zheng

Sparsity is a highly desired feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models (due to the smaller number of relevant features), and robustness. For linear models, it is…

Machine Learning · Computer Science 2024-04-01 Augustina C. Amakor , Konstantin Sonntag , Sebastian Peitz