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The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…

Analysis of PDEs · Mathematics 2015-06-18 François Monard

Bragg coherent X-ray diffraction imaging (BCDI) allows the three-dimensional (3D) measurement of lattice strain along the scattering vector for specific microcrystals. If at least three linearly independent reflections are measured, the 3D…

A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced…

Analysis of PDEs · Mathematics 2017-12-08 Huaian Diao , Peijun Li , Xiaokai Yuan

X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered backprojection reconstruction method requires the complete knowledge of the…

Numerical Analysis · Mathematics 2016-02-24 Jae Kyu Choi , Bin Dong , Xiaoqun Zhang

We give an explicit plane-by-plane filtered back-projection reconstruction algorithm for the transverse ray transform of symmetric second rank tensor fields on Euclidean 3-space, using data from rotation about three orthogonal axes. We show…

Analysis of PDEs · Mathematics 2016-11-03 Naeem M. Desai , William R. B. Lionheart

A unique inversion of the exponential X-ray transform of some class of symmetric 2-tensor field in a two dimensional strictly convex set is considered. The approach to inversion is based on the Cauchy problem for a Beltrami-like equation…

Analysis of PDEs · Mathematics 2024-12-06 David Omogbhe

We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in $\mathbb{R}^d,$ $d\geq 2$. In this region, we consider a hyperplane $X$ with sufficiently…

Analysis of PDEs · Mathematics 2025-09-29 Roman Novikov , Vladimir Sivkin

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…

Numerical Analysis · Mathematics 2020-02-25 Trung Truong , Dinh-Liem Nguyen , Michael Klibanov

We report the results of a simulation and reconstruction of observations of a young stellar object (YSO) jet with the LINC-NIRVANA (LN) interferometric instrument, which will be mounted on the Large Binocular Telescope (LBT). This…

Instrumentation and Methods for Astrophysics · Physics 2015-06-11 Andrea La Camera , Simone Antoniucci , Mario Bertero , Patrizia Boccacci , Dario Lorenzetti , Brunella Nisini

Strain engineering is a powerful tool for tuning the electronic, magnetic, and topological properties of two-dimensional (2D) materials and thin films - particularly at high values of strain (>3%) where many electronic, magnetic, and…

Materials Science · Physics 2026-04-30 Yangchen He , Jessica Kienbaum , Wuzhang Fang , Hongrui Ma , Ying Wang , Ping Yuan , Daniel A. Rhodes

The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…

General Physics · Physics 2016-01-01 E. E. Libin , S. V. Chakhlov , D. Trinca

Broadband longitudinal-to-transverse mode conversion under normal incidence remains difficult to achieve, especially with structurally simple designs. Numerical simulations show that a single periodic row of inclined long-slits near a free…

Applied Physics · Physics 2025-11-26 Kaifei Feng , Weidong Wang , Yucheng Gao , Fengming Liu , Qiujiao Du , Wenshuai Zhang , Pai Peng

We present a direct method for limited angle tomographic reconstruction using convolutional networks. The key to our method is to first stretch every tilt view in the direction perpendicular to the tilt axis by the secant of the tilt angle.…

Image and Video Processing · Electrical Eng. & Systems 2023-06-21 Kyle Luther , Sebastian Seung

We consider hyperelastic problems and their numerical solution using a conforming finite element discretization and iterative linearization algorithms. For these problems, we present equilibrated, weakly symmetric, $H(\rm{div)}$-conforming…

Numerical Analysis · Mathematics 2017-10-19 Michele Botti , Rita Riedlbeck

A novel reconstruction method is introduced for the severely ill-posed inverse problem of limited-angle tomography. It is well known that, depending on the available measurement, angles specify a subset of the wavefront set of the unknown…

Image and Video Processing · Electrical Eng. & Systems 2023-10-26 Elli Karvonen , Matti Lassas , Pekka Pankka , Samuli Siltanen

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered…

Numerical Analysis · Mathematics 2018-04-17 Xiaoli Liu , Bo Zhang , Haiwen Zhang

Diffraction-based methods have become an invaluable tool for the detailed assessment of residual strain and stress within experimental mechanics. These methods typically measure a component of the average strain within a gauge volume. It is…

Applied Physics · Physics 2019-02-25 J. N. Hendriks , C. M. Wensrich , A. Wills , V Luzin , A. W. T Gregg

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

Numerical Analysis · Mathematics 2026-02-10 Daniel Hayes , Jing-Mei Qiu , Tianyi Shi

We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…

Complex Variables · Mathematics 2010-11-17 Nicholas Hoell , Guillaume Bal

A generalized cross-validation approach to estimate the reconstruction filter bandwidth in two-dimensional Filtered Backprojection is presented. The method writes the reconstruction equation in equivalent backprojected filtering form,…

Methodology · Statistics 2019-10-02 Ranjan Maitra