English
Related papers

Related papers: Total variation regularization with reduced basis …

200 papers

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…

Image and Video Processing · Electrical Eng. & Systems 2024-09-11 Bowen Tong , Junwu Wang , Dong Liu

The regularized D-bar method is a popular method for solving Electrical Impedance Tomography (EIT) problems due to its efficiency and simplicity. It utilizes the low-pass truncated scattering data in the non-linear Fourier domain to solve…

Numerical Analysis · Mathematics 2025-02-10 Xiang Cao , Qiaoqiao Ding , Xiaoqun Zhang

We propose a new joint image reconstruction method by recovering edge directly from observed data. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an $l_1$ minimization problem…

Numerical Analysis · Mathematics 2017-12-11 Yunmei Chen , Ruogu Fang , Xiaojing Ye

This article considers the inverse problem of Magnet resonance electrical impedance tomography (MREIT) in two dimensions. A rigorous mathematical framework for this inverse problem as well as the existing Harmonic $B_z$ Algorithm as a…

Numerical Analysis · Mathematics 2018-04-17 Dominik Garmatter , Bastian Harrach

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

Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…

Medical Physics · Physics 2024-12-11 Alexander Meaney , Mikael A. K. Brix , Miika T. Nieminen , Samuli Siltanen

We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…

Optimization and Control · Mathematics 2019-04-02 Lukas F. Lang , Sebastian Neumayer , Ozan Öktem , Carola-Bibiane Schönlieb

We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous…

Optimization and Control · Mathematics 2019-02-20 Bolaji James Adesokan , Bjørn Jensen , Bangti Jin , Kim Knudsen

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…

In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…

Numerical Analysis · Mathematics 2019-05-16 Bangti Jin , Yifeng Xu , Jun Zou

Many modern iterative solvers for large-scale tomographic reconstruction incur two major computational costs per iteration: expensive forward/adjoint projections to update the data fidelity term and costly proximal computations for the…

Optimization and Control · Mathematics 2026-02-11 Evangelos Papoutsellis , Zeljko Kereta , Kostas Papafitsoros

We present a powerful and easy-to-implement algorithm for solving constrained optimization problems that involve $L_1$/total-variation regularization terms, and both equality and inequality constraints. We discuss the relationship of our…

Optimization and Control · Mathematics 2015-05-22 Musa Maharramov , Stewart A. Levin

This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…

Numerical Analysis · Mathematics 2025-07-22 Kai Li , Kwancheol Shin , Zhi Zhou

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…

Computer Vision and Pattern Recognition · Computer Science 2019-04-08 Wenqi Lu , Jinming Duan , David Orive-Miguel , Lionel Herve , Iain B Styles

Electron tomography is a powerful tool for understanding the morphology of materials in three dimensions, but conventional reconstruction algorithms typically suffer from missing-wedge artifacts and data misalignment imposed by experimental…

Image and Video Processing · Electrical Eng. & Systems 2025-12-10 Cedric Lim , Corneel Casert , Arthur R. C. McCray , Serin Lee , Andrew Barnum , Jennifer Dionne , Colin Ophus

We propose an unsupervised approach for learning end-to-end reconstruction operators for ill-posed inverse problems. The proposed method combines the classical variational framework with iterative unrolling, which essentially seeks to…

Computer Vision and Pattern Recognition · Computer Science 2021-06-08 Subhadip Mukherjee , Marcello Carioni , Ozan Öktem , Carola-Bibiane Schönlieb

An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…

Optimization and Control · Mathematics 2022-09-27 Paul R. Arbic , Vladislav Bukshtynov

In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…

Numerical Analysis · Mathematics 2016-04-11 D. M. Pelt , K. J. Batenburg

Electron tomography (ET) has become a standard technique for 3D characterization of materials at the nano-scale. Traditional reconstruction algorithms such as weighted back projection suffer from disruptive artifacts with insufficient…

Computer Vision and Pattern Recognition · Computer Science 2019-04-05 Yi Jiang , Elliot Padgett , Robert Hovden , David A. Muller

Tomographic image reconstruction is relevant for many medical imaging modalities including X-ray, ultrasound (US) computed tomography (CT) and photoacoustics, for which the access to full angular range tomographic projections might be not…

Image and Video Processing · Electrical Eng. & Systems 2019-06-14 Valery Vishnevskiy , Richard Rau , Orcun Goksel