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This paper focuses on finite-time (FT) convergent distributed algorithms for solving time-varying (TV) distributed optimization (TVDO). The objective is to minimize the sum of local TV cost functions subject to the possible TV constraints…

Optimization and Control · Mathematics 2023-09-04 Xinli Shi , Guanghui Wen , Xinghuo Yu

In this paper, we consider using total variation minimization to recover signals whose gradients have a sparse support, from a small number of measurements. We establish the proof for the performance guarantee of total variation (TV)…

Information Theory · Computer Science 2013-10-14 Jian-Feng Cai , Weiyu Xu

Total variation (TV) regularization has proven effective for a range of computer vision tasks through its preferential weighting of sharp image edges. Existing TV-based methods, however, often suffer from the over-smoothing issue and…

Computer Vision and Pattern Recognition · Computer Science 2018-12-26 Dong Gong , Mingkui Tan , Qinfeng Shi , Anton van den Hengel , Yanning Zhang

Balancing spectral, spatial, and temporal resolutions is a key challenge in spectral imaging. The Dual-Camera Coded Aperture Snapshot Spectral Imaging (DC-CASSI) system alleviates this trade-off but suffers from severely ill-posed…

Computer Vision and Pattern Recognition · Computer Science 2026-04-24 Weiqiang Zhao , Tianzhu Liu , Yuzhe Gui , Wei Bian , Yanfeng Gu

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

Loss function are an essential part in modern data-driven approach, such as bi-level training scheme and machine learnings. In this paper we propose a loss function consisting of a $r$-order (an)-isotropic total variation semi-norms $TV^r$,…

Analysis of PDEs · Mathematics 2022-04-12 Pan Liu , Xin Yang Lu , Kunlun He

Over the last decade or so, reconstruction methods using $\ell_1$ regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The…

Numerical Analysis · Mathematics 2017-03-07 Toby Sanders , Anne Gelb , Rodrigo Platte , Ilke Arslan , Kai Landskron

In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings…

Machine Learning · Computer Science 2012-06-22 Tong Lin , Hanlin Xue , Ling Wang , Hongbin Zha

Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space…

Analysis of PDEs · Mathematics 2019-07-02 Remco Duits , Etienne St-Onge , Jim Portegies , Bart Smets

We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous…

Numerical Analysis · Mathematics 2026-05-20 Alexander Humer , Ivo Steinbrecher , Astrid Pechstein

The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…

Numerical Analysis · Mathematics 2019-12-03 Qiuxiang Zhong , Ke Yin , Yuping Duan

The aim of this article is to derive discontinuous finite elements vector spaces which can be put in a discrete de-Rham complex for which an harmonic gap property may be proven. First, discontinuous finite element spaces inspired by…

Numerical Analysis · Mathematics 2025-01-16 Vincent Perrier

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

Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular non-differentiable…

Optimization and Control · Mathematics 2017-02-21 Ivan Selesnick

Cartoon-texture image decomposition is a critical preprocessing problem bottlenecked by the numerical intractability of classical variational or optimization models and the tedious manual tuning of global regularization parameters.We…

Numerical Analysis · Mathematics 2026-01-09 Alessandro Lanza , Serena Morigi , Youwei Wen , Li Yang

In this paper, we propose a general approach for explicit a posteriori error representation for convex minimization problems using basic convex duality relations. Exploiting discrete orthogonality relations in the space of element-wise…

Numerical Analysis · Mathematics 2023-07-11 Sören Bartels , Alex Kaltenbach

We describe a method to discretize optimization problems arising in the regularization of linear inverse problem having compact forward operator defined on 3-D valed measures, compactly supported on a fixed set. The criterion is a quadratic…

Optimization and Control · Mathematics 2025-05-05 L Baratchart , D P Hardin , C Villalobos-Guillén

In this paper, we propose a regularization technique for noisy-image super-resolution and image denoising. Total variation (TV) regularization is adopted in many image processing applications to preserve the local smoothness. However, TV…

Image and Video Processing · Electrical Eng. & Systems 2022-02-23 Kaicong Sun , Sven Simon

Computer vision methods that explicitly detect object parts and reason on them are a step towards inherently interpretable models. Existing approaches that perform part discovery driven by a fine-grained classification task make very…

Computer Vision and Pattern Recognition · Computer Science 2024-07-23 Ananthu Aniraj , Cassio F. Dantas , Dino Ienco , Diego Marcos

A fundamental concept in solving inverse problems is the use of regularizers, which yield more physical and less-oscillatory solutions. Total variation (TV) has been widely used as an edge-preserving regularizer. However, objects are often…

Image and Video Processing · Electrical Eng. & Systems 2018-11-29 Shai Biton , Guy Gilboa