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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

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

Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best-known methods in image denoising. However,…

Analysis of PDEs · Mathematics 2025-02-11 Elisa Davoli , Rita Ferreira , Irene Fonseca , José A. Iglesias

We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…

Numerical Analysis · Mathematics 2022-08-16 Saeed Vatankhah , Rosemary A. Renaut , Vahid E. Ardestani

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

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

In this paper, we propose a variational approach for video denoising, based on a total directional variation (TDV) regulariser proposed in Parisotto et al. (2018), for image denoising and interpolation. In the TDV regulariser, the…

Numerical Analysis · Mathematics 2019-04-01 Simone Parisotto , Carola-Bibiane Schönlieb

We explore the use of the recently proposed "total nuclear variation" (TNV) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued…

Medical Physics · Physics 2015-06-23 David Rigie , Patrick La Riviere

Recovering clear images from blurry ones with an unknown blur kernel is a challenging problem. Deep image prior (DIP) proposes to use the deep network as a regularizer for a single image rather than as a supervised model, which achieves…

Computer Vision and Pattern Recognition · Computer Science 2023-11-13 Tingting Wu , Zhiyan Du , Zhi Li , Feng-Lei Fan , Tieyong Zeng

Total variation regularization has proven to be a valuable tool in the context of optimal control of differential equations. This is particularly attributed to the observation that TV-penalties often favor piecewise constant minimizers with…

Optimization and Control · Mathematics 2025-10-03 Giacomo Cristinelli , José A. Iglesias , Daniel Walter

We propose a second-order total generalized variation (TGV) regularization for the reconstruction of the initial condition in variational data assimilation problems. After showing the equivalence between TGV regularization and the Bayesian…

Optimization and Control · Mathematics 2018-04-13 J. C. De los Reyes , E. Loayza

We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or…

Numerical Analysis · Mathematics 2021-06-17 Daniela di Serafino , Germana Landi , Marco Viola

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

In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is…

Optimization and Control · Mathematics 2018-05-23 Michael Hintermüller , Martin Holler , Kostas Papafitsoros

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

Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total…

Image and Video Processing · Electrical Eng. & Systems 2025-06-04 Songlin Wei , Gene Cheung , Fei Chen , Ivan Selesnick

We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised…

Statistics Theory · Mathematics 2021-01-27 Francesco Ortelli , Sara van de Geer

Improving the quality of positron emission tomography (PET) images, affected by low resolution and high level of noise, is a challenging task in nuclear medicine and radiotherapy. This work proposes a restoration method, achieved after…

Computer Vision and Pattern Recognition · Computer Science 2015-06-17 Stéphanie Guérit , Laurent Jacques , Benoît Macq , John A. Lee

We propose an original method for vectorizing an image or zooming it at an arbitrary scale. The core of our method relies on the resolution of a geometric variational model and therefore offers theoretic guarantees. More precisely, it…

Image and Video Processing · Electrical Eng. & Systems 2020-08-03 Bertrand Kerautret , Jacques-Olivier Lachaud