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Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…

Computer Vision and Pattern Recognition · Computer Science 2026-04-22 Heng Zhang , Reza Parvaz , Rui Yang

The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…

Numerical Analysis · Mathematics 2024-01-19 Abdeslem Hafid Bentbib , Khalide Jbilou , Ridwane Tahiri

We propose two new variational models aimed to outperform the popular total variation (TV) model for image restoration with L$_2$ and L$_1$ fidelity terms. In particular, we introduce a space-variant generalization of the TV regularizer,…

Image and Video Processing · Electrical Eng. & Systems 2019-06-28 Alessandro Lanza , Serena Morigi , Monica Pragliola , Fiorella Sgallari

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

We consider $L^1$-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is non-convex for circle-valued data. In this paper,…

Numerical Analysis · Mathematics 2017-05-16 Martin Storath , Andreas Weinmann , Michael Unser

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

Machine Learning · Computer Science 2020-06-16 Mao Li , Yingyi Ma , Xinhua Zhang

We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…

Numerical Analysis · Mathematics 2025-12-05 Martin Burger , Ole Løseth Elvetun , Bjørn Fredrik Nielsen

In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via…

Numerical Analysis · Mathematics 2026-05-13 Helmut Gfrerer , Simon Hubmer , Stefan Kindermann , Jaakko Kultima , Ronny Ramlau , Tanja Tarvainen

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

Non-smooth regularization is widely used in image reconstruction to eliminate the noise while preserving subtle image structures. In this work, we investigate the use of proximal Newton (PN) method to solve an optimization problem with a…

Signal Processing · Electrical Eng. & Systems 2019-12-05 Tao Ge , Umberto Villa , Ulugbek S. Kamilov , Joseph A. O'Sullivan

Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…

Optimization and Control · Mathematics 2010-01-13 Yunhai Xiao , Junfeng Yang

Total Variation (TV) is an effective and popular prior model in the field of regularization-based image processing. This paper focuses on total variation for removing impulse noise in image restoration. This type of noise frequently arises…

Numerical Analysis · Computer Science 2018-12-31 Ganzhao Yuan , Bernard Ghanem

A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…

Analysis of PDEs · Mathematics 2019-03-19 Pan Liu

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

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

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

The variable projection (VarPro) method is an efficient method to solve separable nonlinear least squares problems. In this paper, we propose a modified VarPro for large-scale separable nonlinear inverse problems that promotes…

Numerical Analysis · Mathematics 2021-06-01 Malena Espanol , Mirjeta Pasha

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor…

Computer Vision and Pattern Recognition · Computer Science 2014-12-11 Giovanni Chierchia , Nelly Pustelnik , Beatrice Pesquet-Popescu , Jean-Christophe Pesquet

Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV…

Signal Processing · Electrical Eng. & Systems 2019-04-08 Sanjay Viswanath , Muthuvel Arigovindan

Over the last decades, the total variation (TV) evolved to one of the most broadly-used regularisation functionals for inverse problems, in particular for imaging applications. When first introduced as a regulariser, higher-order…

Optimization and Control · Mathematics 2020-12-30 Kristian Bredies , Martin Holler