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We present an out-of-core variational approach for surface reconstruction from a set of aligned depth maps. Input depth maps are supposed to be reconstructed from regular photos or/and can be a representation of terrestrial LIDAR point…

Computer Vision and Pattern Recognition · Computer Science 2021-08-17 Nikolai Poliarnyi

Multi-energy CT based on compression sensing theory with sparse-view sampling can effectively reduce radiation dose and maintain the quality of the reconstructed image. However,when the projection data are noisy, the reconstructed image can…

Medical Physics · Physics 2019-12-04 Cheng Kai , Jiang Min , Jianqiao Yu , Sun Yi

We introduce a class of higher-order anisotropic total variation regularisers, which are defined for possibly inhomogeneous, smooth elliptic anisotropies, that extends the Total Generalized Variation (TGV) regulariser and its variants. We…

Numerical Analysis · Mathematics 2020-07-10 Simone Parisotto , Jan Lellmann , Simon Masnou , Carola-Bibiane Schönlieb

Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…

Numerical Analysis · Mathematics 2016-03-25 V Grimm , R I McLachlan , D McLaren , G R W Quispel , C-B Schönlieb

The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical…

Computer Vision and Pattern Recognition · Computer Science 2011-07-28 Aditya Chopra , Heng Lian

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

Many methods for processing scalar and vector valued images, volumes and other data in the context of inverse problems are based on variational formulations. Such formulations require appropriate regularization functionals that model…

Numerical Analysis · Mathematics 2019-09-20 Martin Holler , Andreas Weinmann

In this paper we analyse an infimal convolution type regularisation functional called $\mathrm{TVL}^{\infty}$, based on the total variation ($\mathrm{TV}$) and the $\mathrm{L}^{\infty}$ norm of the gradient. The functional belongs to a more…

The core of many approaches for the resolution of variational inverse problems arising in signal and image processing consists of promoting the sought solution to have a sparse representation in a well-suited space. A crucial task in this…

Numerical Analysis · Mathematics 2022-09-07 Gabriele Scrivanti , Emilie Chouzenoux , Jean-Christophe Pesquet

In this paper, we consider a backward problem for a time-space fractional diffusion process. For this problem, we propose to construct the initial data by minimizing data residual error in fourier space domain and variable total variation…

Numerical Analysis · Mathematics 2016-05-24 Junxiong Jia , Jigen Peng , Jinghuai Gao , Yujiao Li

Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging…

Image and Video Processing · Electrical Eng. & Systems 2021-05-26 Manu Ghulyani , Deepak G Skariah , Muthuvel Arigovindan

We present a semi-sparsity model for 3D triangular mesh denoising, which is motivated by the success of semi-sparsity regularization in image processing applications. We demonstrate that such a regularization model can be also applied for…

Graphics · Computer Science 2023-05-09 Junqing Huang , Haihui Wang , Michael Ruzhansky

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 study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a…

Numerical Analysis · Mathematics 2013-08-09 Konstantinos Papafitsoros , Carola-Bibiane Schönlieb

We introduce discretizations of infinite-dimensional optimization problems with total variation regularization and integrality constraints on the optimization variables. We advance the discretization of the dual formulation of the total…

Numerical Analysis · Mathematics 2024-11-18 Annika Schiemann , Paul Manns

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

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

The Bayesian inference is widely used in many scientific and engineering problems, especially in the linear inverse problems in infinite-dimensional setting where the unknowns are functions. In such problems, choosing an appropriate prior…

Statistics Theory · Mathematics 2021-12-13 Zejun Sun , Guang-Hui Zheng

This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…

Numerical Analysis · Mathematics 2023-01-02 Martin Averseng , Xavier Claeys , Ralf Hiptmair

We consider linear inverse problems that are formulated in the continuous domain. The object of recovery is a function that is assumed to minimize a convex objective functional. The solutions are constrained by imposing a continuous-domain…

Information Theory · Computer Science 2018-08-15 Harshit Gupta , Julien Fageot , Michael Unser