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Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation…

Optimization and Control · Mathematics 2022-05-09 Michael Hintermüller , Kostas Papafitsoros , Carlos N. Rautenberg , Hongpeng Sun

The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images, such as sharp edges and enables spectral, scale, and texture analysis.…

Computer Vision and Pattern Recognition · Computer Science 2024-04-23 Tamara G. Grossmann , Sören Dittmer , Yury Korolev , Carola-Bibiane Schönlieb

We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an…

Optimization and Control · Mathematics 2014-08-26 Zhiwei Qin , Donald Goldfarb , Shiqian Ma

1D Total Variation (TV) denoising, considering the data fidelity and the Total Variation (TV) regularization, proposes a good restored signal preserving shape edges. The main issue is how to choose the weight $\lambda$ balancing those two…

Signal Processing · Electrical Eng. & Systems 2020-12-18 Zhanhao Liu , Marion Perrodin , Thomas Chambrion , Radu Stoica

Numerous total variation (TV) regularizers, engaged in image restoration problem, encode the gradients by means of simple $[-1,1]$ FIR filter. Despite its low computational processing, this filter severely deviates signal's high frequency…

Optimization and Control · Mathematics 2015-06-17 Mahdi S. Hosseini , Konstantinos N. Plataniotis

The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…

Image and Video Processing · Electrical Eng. & Systems 2023-06-14 Congpei An , Hao-Ning Wu , Xiaoming Yuan

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

This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such problems we consider regularizers consisting of two terms that must be…

Numerical Analysis · Mathematics 2022-06-30 Ali Gholami , Silvia Gazzola

Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we…

Computer Vision and Pattern Recognition · Computer Science 2024-06-05 Elisha Dayag , Kevin Bui , Fredrick Park , Jack Xin

We study the problem of machine unlearning and identify a notion of algorithmic stability, Total Variation (TV) stability, which we argue, is suitable for the goal of exact unlearning. For convex risk minimization problems, we design…

Machine Learning · Computer Science 2021-03-01 Enayat Ullah , Tung Mai , Anup Rao , Ryan Rossi , Raman Arora

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

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

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

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

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Computer Vision and Pattern Recognition · Computer Science 2020-06-17 Erich Kobler , Alexander Effland , Karl Kunisch , Thomas Pock

Total variation regularization has proven to be a valuable tool in the context of optimal control of differential equations. This is particularly attributed to the observation that TV-penalties often favor piecewise constant minimizers with…

Optimization and Control · Mathematics 2025-10-03 Giacomo Cristinelli , José A. Iglesias , Daniel Walter

Although regularization methods based on derivatives are favored for their robustness and computational simplicity, research exploring higher-order derivatives remains limited. This scarcity can possibly be attributed to the appearance of…

Image and Video Processing · Electrical Eng. & Systems 2023-09-08 Manu Ghulyani , Muthuvel Arigovindan

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

The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the…

Computer Vision and Pattern Recognition · Computer Science 2016-11-17 Oleg Michailovich

We consider $L^1$-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is non-convex for circle-valued data. In this paper,…

Numerical Analysis · Mathematics 2017-05-16 Martin Storath , Andreas Weinmann , Michael Unser