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Vision Transformer (ViT) architectures represent images as collections of high-dimensional vectorized tokens, each corresponding to a rectangular non-overlapping patch. This representation trades spatial granularity for embedding…

Computer Vision and Pattern Recognition · Computer Science 2024-05-08 Dong Lao , Yangchao Wu , Tian Yu Liu , Alex Wong , Stefano Soatto

In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse…

Numerical Analysis · Mathematics 2021-12-06 Cécilia Tarpau , Javier Cebeiro , Geneviève Rollet , Mai K. Nguyen , Laurent Dumas

Relativistic impulse approximation (RIA) has been widely used in atomic, condensed matter, nuclear, and elementary particle physics. In former treatments of RIA formulation, differential cross sections for Compton scattering processes were…

In most of the successful versions of covariant density functional theory in nuclei, the Fock terms are not included explicitly, which leads to local functionals and forms the basis of their widespread applicability at present. However, it…

Nuclear Theory · Physics 2012-09-04 Haozhao Liang , Pengwei Zhao , Peter Ring , Xavier Roca-Maza , Jie Meng

Region-of-Interest (ROI) tomography aims at reconstructing a region of interest $C$ inside a body using only x-ray projections intersecting $C$ with the goal to reduce overall radiation exposure when only a small specific region of the body…

Mathematical Physics · Physics 2016-03-23 Robert Azencott , Bernhard G. Bodmann , Tasadduk Chowdhury , Demetrio Labate , Anando Sen , Daniel Vera

Quantum optimization for computed tomography (CT) reconstruction is constrained by the number of binary variables required for image representation, making direct whole-image quantum reconstruction difficult for large or structurally…

Quantum Physics · Physics 2026-05-29 Hyunju Lee , Jeonghwa Lee , Kyungtaek Jun

We extend the Geometric Refinement Transform (GRT) by introducing centroidal Voronoi tessellations (CVTs) into the refinement process, enhancing symmetry, reconstruction accuracy, and numerical stability. By applying Lloyds algorithm at…

Numerical Analysis · Mathematics 2025-03-28 Zachary Mullaghy

We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…

Optimization and Control · Mathematics 2024-07-19 Vasileios Charisopoulos , Rebecca Willett

The conical Radon transform, which assigns to a given function $f$ on $\mathbb R^3$ its integrals over conical surfaces, arises in several imaging techniques, e.g. in astronomy and homeland security, especially when the so-called Compton…

Mathematical Physics · Physics 2018-03-28 Sunghwan Moon

Measurement-critical ultrasound tasks often depend on a small anatomical region, making global reconstruction metrics an unreliable proxy for clinical fidelity. We propose an ROI-aware representation learning framework and instantiate it…

Computer Vision and Pattern Recognition · Computer Science 2026-04-28 Ines Abbes , Mahmood Alzubaidi , Mowafa Househ , Khalid Alyafei , Marco Agus , Samir Brahim Belhaouari

In this paper we study reconstruction of a function $f$ from its discrete Radon transform data in $\mathbb R^3$ when $f$ has jump discontinuities. Consider a conventional parametrization of the Radon data in terms of the affine and angular…

Numerical Analysis · Mathematics 2019-03-21 Alexander Katsevich

We study a particular broken ray transform on the Euclidean unit square and establish injectivity and stability for $C_{0}^{2}$ perturbations of the constant unit weight. Given an open subset $E$ of the boundary, we measure the attenuation…

Analysis of PDEs · Mathematics 2013-06-13 Mark Hubenthal

Generalized Abel equations have been employed in the recent literature to invert Radon transforms which arise in a number of important imaging applications, including Compton Scatter Tomography (CST), Ultrasound Reflection Tomography (URT),…

Functional Analysis · Mathematics 2023-06-16 James W. Webber

Spectral photon-counting X-ray CT (sCT) opens up new possibilities for the quantitative measurement of materials in an object, compared to conventional energy-integrating CT or dual energy CT. However, achieving reliable and accurate…

Image and Video Processing · Electrical Eng. & Systems 2020-07-15 Bingqing Xie , Pei Niu , Ting Su , Valérie Kaftandjian , Loic Boussel , Philippe Douek Feng Yang , Philippe Duvauchelle , Yuemin Zhu

Here we introduce a new reconstruction technique for two-dimensional Bragg Scattering Tomography (BST), based on the Radon transform models of [arXiv preprint, arXiv:2004.10961 (2020)]. Our method uses a combination of ideas from multibang…

Numerical Analysis · Mathematics 2021-01-26 James W. Webber , Eric L. Miller

In this paper we propose a new approach to the central limit theorem (CLT), based on functions of bounded F\'echet variation for the continuously differentiable linear statistics of random matrix ensembles which relies on: a weaker form of…

Probability · Mathematics 2022-01-12 Mario Diaz , James A. Mingo

In this work, we present a method for synthetic CT (sCT) generation from zero-echo-time (ZTE) MRI aimed at structural and quantitative accuracies of the image, with a particular focus on the accurate bone density value prediction. We…

In this article, we consider a generalized Radon transform that comes up in ultrasound reflection tomography. In our model, the ultrasound emitter and receiver move at a constant distance apart along a circle. We analyze the microlocal…

Analysis of PDEs · Mathematics 2011-10-20 Gaik Ambartsoumian , Venky P. Krishnan , Eric Todd Quinto

Spectral computed tomography (CT) can reconstruct spectral images from different energy bins using photon counting detectors (PCDs). However, due to the limited photons and counting rate in the corresponding spectral fraction, the…

Medical Physics · Physics 2020-10-28 Xiang Chen , Wenjun Xia , Yan Liu , Hu Chen , Jiliu Zhou , Yi Zhang

We propose a new acquisition geometry for electron density reconstruction in three dimensional X-ray Compton imaging using a monochromatic source. This leads us to a new three dimensional inverse problem where we aim to reconstruct a real…

Functional Analysis · Mathematics 2018-07-04 James Webber , William Lionheart