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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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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),…
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…
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…
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…
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…
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…
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…