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The paper is devoted to the study of regularized versions of multiobjective optimization problems described by directionally Lipschitzian functions. Such regularizations appear in proximal-type algorithms of multiobjective optimization,…

Optimization and Control · Mathematics 2025-11-21 G. C. Bento , J. X. Cruz Neto , J. O. Lopes , B. S. Mordukhovich , P. R. Silva Filho

Recovering high quality surfaces from noisy triangulated surfaces is a fundamental important problem in geometry processing. Sharp features including edges and corners can not be well preserved in most existing denoising methods except the…

Computational Geometry · Computer Science 2021-01-07 Zheng Liu , Rongjie Lai , Huayan Zhang , Chunlin Wu

We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…

Optimization and Control · Mathematics 2020-12-02 Julien Fageot , Matthieu Simeoni

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

This paper addresses explainability of the operator-regularization approach under the use of monotone Lipschitz-gradient (MoL-Grad) denoiser -- an operator that can be expressed as the Lipschitz continuous gradient of a differentiable…

Optimization and Control · Mathematics 2025-09-26 Masahiro Yukawa , Isao Yamada

For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…

Numerical Analysis · Mathematics 2015-05-20 Qinian Jin , Ulrich Tautenhahn

Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix has become an emerging alternative to the traditional sparse regularization, due to its ability to alleviate the basis mismatch between the true support in the…

Numerical Analysis · Mathematics 2020-12-15 Jian-Feng Cai , Jae Kyu Choi , Jingyang Li , Ke Wei

In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady non-linear Leray-Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes.…

Numerical Analysis · Mathematics 2018-05-29 Daniele A. Di Pietro , Jérôme Droniou

$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many…

Image and Video Processing · Electrical Eng. & Systems 2018-05-07 Yilei Shi , Xiao Xiang Zhu , Wotao Yin , Richard Bamler

We consider a new family of regularizers, termed {\it weighted sorted $\ell_1$ norms} (WSL1), which generalizes the recently introduced {\it octagonal shrinkage and clustering algorithm for regression} (OSCAR) and also contains the $\ell_1$…

Computer Vision and Pattern Recognition · Computer Science 2014-04-14 Xiangrong Zeng , Mário A. T. Figueiredo

In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ a…

Numerical Analysis · Mathematics 2022-07-20 Xiaobing Feng , Akash Ashirbad Panda , Andreas Prohl

The lack of smoothness is a common feature of weak solutions of nonlinear hyperbolic equations and is a crucial issue in their approximation. This has motivated several efforts to define appropriate indicators, based on the values of the…

Numerical Analysis · Mathematics 2020-03-18 Maurizio Falcone , Giulio Paolucci , Silvia Tozza

Classical first-order optimization methods for imaging inverse problems scale poorly with image resolution. Wavelet based multilevel strategies can accelerate convergence under strong blur, but their fixed coarse-to-fine schedules lose…

Signal Processing · Electrical Eng. & Systems 2026-03-03 Edgar Desainte-Maréville , Marion Foare , Paulo Gonçalves , Nelly Pustelnik , Elisa Riccietti

The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem's domain X the sum…

Optimization and Control · Mathematics 2015-10-05 Bruce Cox , Anatoli Juditsky , Arkadi Nemirovski

In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anisotropic extension of the classical isotropic Total Variation (TV) regularizer. The proposed regularizer comes…

Image and Video Processing · Electrical Eng. & Systems 2019-08-05 Luca Calatroni , Alessandro Lanza , Monica Pragliola , Fiorella Sgallari

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…

Statistics Theory · Mathematics 2012-04-03 Klaus Frick , Philipp Marnitz , Axel Munk

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

This paper considers the constrained total variation (TV) denoising problem for complex-valued images. We extend the definition of TV seminorms for real-valued images to dealing with complex-valued ones. In particular, we introduce two…

Image and Video Processing · Electrical Eng. & Systems 2021-09-14 Yunhui Gao , Liangcai Cao

Hybrid High-Order methods for elliptic diffusion problems have been originally formulated for loads in the Lebesgue space $L^2(\Omega)$. In this paper we devise and analyze a variant thereof, which is defined for any load in the dual…

Numerical Analysis · Mathematics 2019-05-01 Alexandre Ern , Pietro Zanotti

We devise and analyze two hybrid high-order (HHO) methods for the numerical approximation of the biharmonic problem. The methods support polyhedral meshes, rely on the primal formulation of the problem, and deliver $O(h^{k+1})$ $H^2$-error…

Numerical Analysis · Mathematics 2022-04-11 Zhaonan Dong , Alexandre Ern