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Total variation (TV) denoising is a nonparametric smoothing method that has good properties for preserving sharp edges and contours in objects with spatial structures like natural images. The estimate is sparse in the sense that TV…

Methodology · Statistics 2016-05-06 Sylvain Sardy , Hatef Monajemi

This work combines three paradigms of image processing: i) the total variation approach to denoising, ii) the superior structure of hexagonal lattices, and iii) fast and exact graph cut optimization techniques. Although isotropic in theory,…

Optimization and Control · Mathematics 2012-04-18 Clemens Kirisits

We propose an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms: the misfit between the imaging…

Numerical Analysis · Mathematics 2026-04-21 Junqing Chen , Haibo Liu

A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…

Analysis of PDEs · Mathematics 2019-03-29 Pan Liu , Carola-Bibiane Schönlieb

Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging…

Optimization and Control · Mathematics 2025-05-21 Felipe Guerra , Tuomo Valkonen

Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of…

Optimization and Control · Mathematics 2015-05-14 José M. Bioucas-Dias , Mário A. T. Figueiredo

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based on multiscale…

Optimization and Control · Mathematics 2012-10-10 Mário A. T. Figueiredo , José M. Bioucas-Dias

The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…

Optimization and Control · Mathematics 2015-11-18 Canyi Lu , Huan Li , Zhouchen Lin , Shuicheng Yan

In this paper, we denoise a given noisy image by minimizing a smoothness promoting function over a set of local similarity measures which compare the mean of the given image and some candidate image on a large collection of subboxes. The…

Optimization and Control · Mathematics 2024-06-24 Christian Kanzow , Fabius Krämer , Patrick Mehlitz , Gerd Wachsmuth , Frank Werner

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

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

This article proposes a novel regularization method, named Geometric Spatio-Spectral Total Variation (GeoSSTV), for hyperspectral (HS) image denoising and destriping. HS images are inevitably affected by various types of noise due to the…

Signal Processing · Electrical Eng. & Systems 2025-10-02 Shingo Takemoto , Shunsuke Ono

The alternating direction method of multipliers (ADMM) has recently sparked interest as a flexible and efficient optimization tool for imaging inverse problems, namely deconvolution and reconstruction under non-smooth convex regularization.…

Optimization and Control · Mathematics 2015-06-11 Mariana S. C. Almeida , Mário A. T. Figueiredo

In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…

Computer Vision and Pattern Recognition · Computer Science 2021-10-07 Joseph Bartlett , Jinming Duan

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

In this paper, we propose a novel symmetric alternating minimization algorithm to solve a broad class of total variation (TV) regularization problems. Unlike the usual $z^k\to x^k$ Gauss-Seidel cycle, the proposed algorithm performs the…

Data Structures and Algorithms · Computer Science 2020-06-08 Yuan Lei , Jiaxin Xie

In this paper we present a novel iterative procedure for multichannel image and data reconstruction using Bregman distances. With the motivation that multiple channels sharing a common subgradient with respect to a suitable regularization…

Numerical Analysis · Mathematics 2014-12-18 Michael Moeller , Eva-Maria Brinkmann , Martin Burger , Tamara Seybold

Since sparse unmixing has emerged as a promising approach to hyperspectral unmixing, some spatial-contextual information in the hyperspectral images has been exploited to improve the performance of the unmixing recently. The total variation…

Numerical Analysis · Computer Science 2020-07-14 Longfei Ren , Chengjing Wang , Peipei Tang , Zheng Ma

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved…

Image and Video Processing · Electrical Eng. & Systems 2025-08-26 Edward P. Chandler , Shirin Shoushtari , Brendt Wohlberg , Ulugbek S. Kamilov

The quadratic penalty alternating minimization (AM) method is widely used for solving the convex $\ell_1$ total variation (TV) image deblurring problem. However, quadratic penalty AM for solving the nonconvex nonsmooth $\ell_p$, $0 < p < 1$…

Optimization and Control · Mathematics 2023-09-12 Tarmizi Adam , Alexander Malyshev , Mohd Fikree Hassan , Nur Syarafina Mohamed , Md Sah Hj Salam