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We develop an algorithm for reconstruction of elastic strain fields from their Longitudinal Ray Transform (LRT) in either two or three dimensions. In general, the LRT only determines the solenoidal part of a symmetric tensor field, but…

Numerical Analysis · Mathematics 2024-08-21 Chris Wensrich , Sean Holman , William Lionheart , Matias Courdurier , Anna Polyakova , Ivan Svetov , Ty Doubikin

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

Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…

Applications · Statistics 2022-04-06 Sanket R. Jantre , Zichao Wendy Di

This paper treats the inverse problem of retrieving the electrical conductivity of a material starting from boundary measurements in the framework of Electrical Resistance Tomography (ERT). In particular, the focus is on non-iterative…

Numerical Analysis · Mathematics 2026-05-15 Antonello Tamburrino , Vincenzo Mottola

The Jiangmen Underground Neutrino Observatory (JUNO) is designed to determine the neutrino mass ordering and measure neutrino oscillation parameters. A precise muon reconstruction is crucial to reduce one of the major backgrounds induced by…

Instrumentation and Detectors · Physics 2021-05-11 Yan Liu , Weidong Li , Tao Lin , Wenxing Fang , Simon C. Blyth , Jilei Xu , Miao He , Kun Zhang

We examine the problem of Bragg-edge elastic strain tomography from energy resolved neutron transmission imaging. A new approach is developed for two-dimensional plane-stress and plane-strain systems whereby elastic strain can be…

Numerical Analysis · Mathematics 2024-02-13 C. M. Wensrich , S. Holman , M. Courdurier , W. R. B. Lionheart , A. Polyalova , I. Svetov

Eigenstrain tomography combines diffraction-based strain measurement with elasticity theory to reconstruct full three-dimensional residual stress fields within solids. Notwithstanding a number of recent examples, the uniqueness of such…

Analysis of PDEs · Mathematics 2025-12-15 Christopher Wensrich , Sean Holman , William Lionheart , Matias Courdurier , Roxanne Jackson

In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal…

Numerical Analysis · Computer Science 2020-01-24 Tai-Xiang Jiang , Ting-Zhu Huang , Xi-Le Zhao , Liang-Jian Deng

Energy resolved neutron transmission techniques can provide high-resolution images of strain within polycrystalline samples allowing the study of residual strain and stress in engineered components. Strain is estimated from such data by…

Computational Engineering, Finance, and Science · Computer Science 2020-04-28 Johannes Hendriks , Nicholas O'Dell , Adrian Wills , Anton Tremsin , Christopher Wensrich , Takenao Shinohara

Neutron Computed Tomography (CT) is an increasingly utilised non-destructive analysis tool in material science, palaeontology, and cultural heritage. With the development of new neutron imaging facilities (such as DINGO, ANSTO, Australia)…

Instrumentation and Detectors · Physics 2019-09-04 Jeremy M. C. Brown , Ulf Garbe , Daniele Pelliccia

In Bragg Coherent Diffraction Imaging (BCDI), Phase Retrieval of highly strained crystals is often challenging with standard iterative algorithms. This computational obstacle limits the potential of the technique as it precludes the…

Spatial transcriptomics data analysis integrates cellular transcriptional activity with spatial coordinates to identify spatial domains, infer cell-type dynamics, and characterize gene expression patterns within tissues. Despite recent…

Quantitative Methods · Quantitative Biology 2026-03-25 Sean Cottrell , Guo-Wei Wei , Longxiu Huang

Spatially resolved strain measurements are crucial to understanding the properties of engineering materials. Although strain measurements utilizing techniques such as transmission electron microscopy and electron backscatter diffraction…

Materials Science · Physics 2025-09-10 Brinthan Kanesalingam , Darshan Chalise , Carsten Detlefs , Leora Dresselhaus-Marais

Deep learning-based Magnetic Resonance (MR) reconstruction methods have focused on generating high-quality images but often overlook the impact on downstream tasks (e.g., segmentation) that utilize the reconstructed images. Cascading…

Image and Video Processing · Electrical Eng. & Systems 2025-06-25 Hwihun Jeong , Se Young Chun , Jongho Lee

For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data.…

Machine Learning · Computer Science 2021-09-07 Xinhai Zhao , Yuyuan Yu , Guoxu Zhou , Qibin Zhao , Weijun Sun

We propose an improved tensor renormalization group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize the conventional TRG by introducing bond weights on the edges of the tensor network. We show that BTRG outperforms the…

Statistical Mechanics · Physics 2022-03-03 Daiki Adachi , Tsuyoshi Okubo , Synge Todo

Although strain-based models have been widely adopted in robotics, no comparison beyond the uniform bending test is commonly recognized to assess their performance. In addition, the increasing effort in prototyping continuum robots…

Robotics · Computer Science 2026-02-27 Annika Delucchi , Vincenzo Di Paola , Andreas Müller , and Matteo Zoppi

In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…

Numerical Analysis · Computer Science 2017-12-01 Damiana Lazzaro , Elena Loli Piccolomini , Fabiana Zama

A variety of modeling techniques have been developed in the past decade to reduce the computational expense and improve the accuracy of modeling. In this study, a new framework of modeling is suggested. Compared with other popular methods,…

Machine Learning · Computer Science 2018-09-06 Yu Li , Hu Wang , Kangjia Mo , Tao Zeng

In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…

Analysis of PDEs · Mathematics 2018-10-11 Bastian Harrach , Mach Nguyet Minh