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In this paper we are concerned with the approximation of functions by single hidden layer neural networks with ReLU activation functions on the unit circle. In particular, we are interested in the case when the number of data-points exceeds…

Analysis of PDEs · Mathematics 2021-04-02 Benny Avelin , Vesa Julin

Low-rank Deconvolution (LRD) has appeared as a new multi-dimensional representation model that enjoys important efficiency and flexibility properties. In this work we ask ourselves if this analytical model can compete against Deep Learning…

Computer Vision and Pattern Recognition · Computer Science 2024-06-18 David Reixach , Josep Ramon Morros

We consider whether minimizers for total variation regularization of linear inverse problems belong to $L^\infty$ even if the measured data does not. We present a simple proof of boundedness of the minimizer for fixed regularization…

Optimization and Control · Mathematics 2023-06-28 Kristian Bredies , José A. Iglesias , Gwenael Mercier

This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…

Numerical Analysis · Mathematics 2025-07-08 Yohann De Castro , Vincent Duval , Romain Petit

In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…

Numerical Analysis · Mathematics 2022-09-14 Alireza Hosseini

We study \emph{TV regularization}, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for $\ell_p$-norm TV. The most important among these is $\ell_1$-norm…

Machine Learning · Statistics 2018-01-03 Álvaro Barbero , Suvrit Sra

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator and on…

Machine Learning · Computer Science 2022-06-30 Michael Unser

In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide…

Numerical Analysis · Mathematics 2018-04-30 Martin Storath , Andreas Weinmann

In this paper, we propose an active contour model with a local variance force (LVF) term that can be applied to multi-phase image segmentation problems. With the LVF, the proposed model is very effective in the segmentation of images with…

Computer Vision and Pattern Recognition · Computer Science 2022-03-18 Chaoyu Liu , Zhonghua Qiao , Qian Zhang

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

We consider the task of image reconstruction while simultaneously decomposing the reconstructed image into components with different features. A commonly used tool for this is a variational approach with an infimal convolution of…

Numerical Analysis · Mathematics 2025-04-16 Tobias Wolf , Derek Driggs , Kostas Papafitsoros , Elena Resmerita , Carola-Bibiane Schönlieb

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

The L1-norm of the gradient-magnitude images (GMI), which is the well-known total variation (TV) model, is widely used as regularization in the few views CT reconstruction. As the L1-norm TV regularization is tending to uniformly penalize…

Information Theory · Computer Science 2019-05-01 Yuli Sun , Jinxu Tao

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

BV functions cannot be approximated well by piecewise constant functions, but this work will show that a good approximation is still possible with (countably) piecewise affine functions. In particular, this approximation is area-strictly…

Analysis of PDEs · Mathematics 2015-07-23 Jan Kristensen , Filip Rindler

We propose a new superresolution imaging technique for interferometry using sparse modeling, utilizing two regularization terms: the $\ell_1$-norm and a new function named Total Squared Variation (TSV) of the brightness distribution. TSV is…

Instrumentation and Methods for Astrophysics · Physics 2018-06-06 Kazuki Kuramochi , Kazunori Akiyama , Shiro Ikeda , Fumie Tazaki , Vincent L. Fish , Hung-Yi Pu , Keiichi Asada , Mareki Honma

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

We prove regularity results for the unique minimizer of the total variation functional, currently used in image processing analysis since the work by L. Rudin, S. Osher and E. Fatemi. In particular we show that if the source term $f$ is…

Analysis of PDEs · Mathematics 2019-09-05 Alessio Porretta

We prove a partial regularity result for local minimizers of quasiconvex variational integrals with general growth. The main tool is an improved A-harmonic approximation, which should be interesting also for classical growth.

Analysis of PDEs · Mathematics 2012-05-14 Lars Diening , Daniel Lengeler , Bianca Stroffolini , Anna Verde

We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding…

Machine Learning · Computer Science 2019-05-28 K S Sesh Kumar , Francis Bach , Thomas Pock