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A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…

Analysis of PDEs · Mathematics 2019-03-29 Pan Liu , Carola-Bibiane Schönlieb

A generalized additive model (GAM, Hastie and Tibshirani (1987)) is a nonparametric model by the sum of univariate functions with respect to each explanatory variable, i.e., $f({\mathbf x}) = \sum f_j(x_j)$, where $x_j\in\mathbb{R}$ is…

Machine Learning · Statistics 2018-02-19 Shin Matsushima

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

Recently, we have witnessed the success of total variation (TV) for many imaging applications. However, traditional TV is defined on the original pixel domain, which limits its potential. In this work, we suggest a new TV regularization…

Computer Vision and Pattern Recognition · Computer Science 2025-01-03 Yisi Luo , Xile Zhao , Kai Ye , Deyu Meng

We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional…

Computer Vision and Pattern Recognition · Computer Science 2025-03-07 Thanh Trung Vu , Andreas Kofler , Kostas Papafitsoros

Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating…

Computational Geometry · Computer Science 2021-06-09 Zheng Liu , YanLei Li , Weina Wang , Ligang Liu , Renjie Chen

Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…

Optimization and Control · Mathematics 2010-01-13 Yunhai Xiao , Junfeng Yang

Total variation (TV) denoising is a nonparametric smoothing method that has good properties for preserving sharp edges and contours in objects with spatial structures like natural images. The estimate is sparse in the sense that TV…

Methodology · Statistics 2016-05-06 Sylvain Sardy , Hatef Monajemi

We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general…

Optimization and Control · Mathematics 2020-02-13 Juan Carlos De Los Reyes , Carola-Bibiane Schönlieb , Tuomo Valkonen

This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary…

Image and Video Processing · Electrical Eng. & Systems 2024-04-29 Elena Morotti , Davide Evangelista , Andrea Sebastiani , Elena Loli Piccolomini

For image denoising problems, the structure tensor total variation (STV)-based models show good performances when compared with other competing regularization approaches. However, the STV regularizer does not couple the local information of…

Optimization and Control · Mathematics 2024-04-05 Xiuhan Sheng , Lijuan Yang , Jingya Chang

An optimization framework is presented for minimizing the energy functional developed around a generalized equation governing physical systems such as fluid dynamics, particle transport, phase transition, and other related systems. The…

Fluid Dynamics · Physics 2024-04-25 Varsha Gupta

Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…

Numerical Analysis · Mathematics 2018-06-15 Chunlin Wu , Zhifang Liu , Shuang Wen

Sampling high-dimensional images is challenging due to limited availability of sensors; scanning is usually necessary in these cases. To mitigate this challenge, snapshot compressive imaging (SCI) was proposed to capture the…

Image and Video Processing · Electrical Eng. & Systems 2020-05-19 Xin Yuan

In inverse problems, prior information and a priori-based regularization techniques play important roles. In this paper, we focus on image restoration problems, especially on restoring images whose texture mainly follow one direction. In…

Numerical Analysis · Mathematics 2017-08-23 Rasmus Dalgas Kongskov , Yiqiu Dong , Kim Knudsen

This paper proposes a novel regularization method, named Spatio-Spectral Structure Tensor Total Variation (S3TTV), for denoising and destriping of hyperspectral (HS) images. HS images are inevitably contaminated by various types of noise,…

Signal Processing · Electrical Eng. & Systems 2025-07-08 Shingo Takemoto , Kazuki Naganuma , Shunsuke Ono

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

In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…

Numerical Analysis · Mathematics 2021-02-23 A. H. Bentbib , A. El Hachimi , K. Jbilou , A. Ratnani

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

Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known…

Optimization and Control · Mathematics 2017-06-29 Adrien Faivre , Clément Dombry