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Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous…

Numerical Analysis · Mathematics 2025-01-23 Toluwani Okunola , Mirjeta Pasha , Misha Kilmer , Melina Freitag

Iterative neural networks (INN) are rapidly gaining attention for solving inverse problems in imaging, image processing, and computer vision. INNs combine regression NNs and an iterative model-based image reconstruction (MBIR) algorithm,…

Image and Video Processing · Electrical Eng. & Systems 2023-08-31 Il Yong Chun , Zhengyu Huang , Hongki Lim , Jeffrey A. Fessler

We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide an application of a projection algorithm, utilized and…

Numerical Analysis · Mathematics 2021-03-11 Andrea Aspri , Leon Frischauf , Yury Korolev , Otmar Scherzer

In recent years Landweber(-Kaczmarz) method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex…

Numerical Analysis · Mathematics 2016-08-24 Qinian Jin

Magnetic resonance imaging (MRI) exam protocols consist of multiple contrast-weighted images of the same anatomy to emphasize different tissue properties. Due to the long acquisition times required to collect fully sampled k-space…

Image and Video Processing · Electrical Eng. & Systems 2023-06-08 Brett Levac , Ajil Jalal , Kannan Ramchandran , Jonathan I. Tamir

In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic…

Image and Video Processing · Electrical Eng. & Systems 2025-12-01 Junqi Tang , Guixian Xu , Jinglai Li

An inverse iterative algorithm for microwave imaging based on moment method solution is presented here. The iterative scheme has been developed on constrained optimization technique and is certain to converge. Different mesh size for the…

Computer Vision and Pattern Recognition · Computer Science 2010-10-05 Anjan Kumar Kundu , Bijoy Bandopadhyay , Sugata Sanyal

Building on the well-known total-variation (TV), this paper develops a general regularization technique based on nonlinear isotropic diffusion (NID) for inverse problems with piecewise smooth solutions. The novelty of our approach is to be…

Numerical Analysis · Mathematics 2021-08-25 Bernadette N. Hahn , Gael Rigaud , Richard Schmähl

Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…

Computer Vision and Pattern Recognition · Computer Science 2019-06-05 Davis Gilton , Greg Ongie , Rebecca Willett

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

Purpose: To develop a synergistic image reconstruction framework that exploits multicontrast (MC), multicoil, and compressed sensing (CS) redundancies in magnetic resonance imaging (MRI). Approach: CS, MC acquisition, and parallel imaging…

Image and Video Processing · Electrical Eng. & Systems 2022-02-22 Erfan Ebrahim Esfahani

Context. The numerical modeling of the generation and transfer of polarized radiation is a key task in solar and stellar physics research and has led to a relevant class of discrete problems that can be reframed as linear systems. In order…

Solar and Stellar Astrophysics · Physics 2021-12-08 Gioele Janett , Pietro Benedusi , Luca Belluzzi , Rolf Krause

The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…

Optimization and Control · Mathematics 2019-11-07 Utkan Candogan , Yong Sheng Soh , Venkat Chandrasekaran

Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…

Computer Vision and Pattern Recognition · Computer Science 2018-07-04 Yu Sun , Zhihao Xia , Ulugbek S. Kamilov

The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…

Numerical Analysis · Mathematics 2024-08-07 Xuan Liu , Zhigang Jia , Xiaoqing Jin

The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation…

Numerical Analysis · Mathematics 2017-11-22 Markus Haltmeier , Richard Kowar , Linh V. Nguyen

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

Geophysics · Physics 2012-05-29 Nick Polydorides , Alireza Aghasi , Eric L. Miller

The main disadvantage of Magnetic Resonance Imaging (MRI) are its long scan times and, in consequence, its sensitivity to motion. Exploiting the complementary information from multiple receive coils, parallel imaging is able to recover…

Numerical Analysis · Computer Science 2017-03-07 Martin Uecker

We investigate generalized versions of the Iteratively Regularized Landweber Method, initially introduced in [Appl. Math. Optim., 38(1):45-68, 1998], to address linear and nonlinear ill-posed problems. Our approach is inspired by the…

Numerical Analysis · Mathematics 2023-12-07 Andrea Aspri , Otmar Scherzer

We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…

Numerical Analysis · Mathematics 2020-12-25 Leon Bungert , Martin Burger , Yury Korolev , Carola-Bibiane Schoenlieb