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Related papers: Modified Radon transform inversion using moments

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The spherical Radon transform (SRT) is an integral transform that maps a function to its integrals over concentric spherical shells centered at specified sensor locations. It has several imaging applications, including synthetic aperture…

Image and Video Processing · Electrical Eng. & Systems 2024-02-27 Luke Lozenski , Refik Mert Cam , Mark A. Anastasio , Umberto Villa

Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute…

Computer Vision and Pattern Recognition · Computer Science 2020-09-07 Mathé Zeegers , Felix Lucka , Kees Joost Batenburg

We study the inversion of the conical Radon which integrates a function in three-dimensional space from integrals over circular cones. The conical Radon recently got significant attention due to its relevance in various imaging applications…

Numerical Analysis · Mathematics 2020-02-26 Markus Haltmeier , Sunghwan Moon

A reconstruction technique based on Radon transforms is used to obtain 3D electron momentum density rho(p) using nine recently measured high-resolution Compton profiles (CPs) from a Cu_{0.9}Al_{0.1} disordered alloy single crystal. The…

The method of moments is widely used for the reduction of kinetic equations into fluid models. It consists in extracting the moments of the kinetic equation with respect to a velocity variable, but the resulting system is a priori…

Computational Physics · Physics 2023-04-05 Michael R. A. Abdelmalik , Zhenning Cai , Teddy Pichard

We introduce a new CT image reconstruction algorithm that is less affected by various artifacts. The new reconstruction algorithm is a method of minimizing the difference between synchrotron X-ray tomography data and sinograms generated…

Medical Physics · Physics 2021-11-22 Byung Chun Kim , Hyunju Lee , Kyungtaek Jun

The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…

Functional Analysis · Mathematics 2007-05-23 E. Ournycheva , B. Rubin

The Radon transform is a linear integral transform that mimics the data formation process in medical imaging modalities like X-ray Computerized Tomography and Positron Emission Tomography. The Hough transform is a pattern recognition…

Numerical Analysis · Mathematics 2016-05-31 Riccardo Aramini , Fabrice Delbary , Mauro C. Beltrametti , Michele Piana , Anna Maria Massone

Magnetic resonance imaging (MRI) is a potent diagnostic tool, but suffers from long examination times. To accelerate the process, modern MRI machines typically utilize multiple coils that acquire sub-sampled data in parallel. Data-driven…

Image and Video Processing · Electrical Eng. & Systems 2023-10-24 Moritz Erlacher , Martin Zach

The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…

Mathematical Physics · Physics 2009-11-13 Yuan Xu

Tomography is a central tool in medical applications, allowing doctors to investigate patients' interior features. The Radon transform (in two dimensions) is commonly used to model the measurement process in parallel-beam CT. Suitable…

Numerical Analysis · Mathematics 2026-02-27 Richard Huber

In this paper, we consider the conical Radon transform on all cones with horizontal central axis whose vertices are on a straight line. We derive an explicit inversion formula for such transform. The inversion makes use of the vertical…

Classical Analysis and ODEs · Mathematics 2019-08-23 Duy N. Nguyen , Linh V. Nguyen

The hyperbolic Radon transform is a commonly used tool in seismic processing, for instance in seismic velocity analysis, data interpolation and for multiple removal. A direct implementation by summation of traces with different moveouts is…

Numerical Analysis · Mathematics 2017-05-24 Viktor V. Nikitin , Fredrik Andersson , Marcus Carlsson , Anton A. Duchkov

The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates…

Numerical Analysis · Mathematics 2026-02-02 Matthias Beckmann , Robert Beinert , Jonas Bresch

Radon transform and its inverse operation are important techniques in medical imaging tasks. Recently, there has been renewed interest in Radon transform for applications such as content-based medical image retrieval. However, all studies…

Computer Vision and Pattern Recognition · Computer Science 2017-10-12 Morteza Babaie , H. R. Tizhoosh , Amin Khatami , M. E. Shiri

Magnetic particle imaging is a promising medical imaging technique. Applying changing magnetic fields to tracer material injected into the object under investigation results in a change in magnetization. Measurement of related induced…

Image and Video Processing · Electrical Eng. & Systems 2023-06-21 Stephanie Blanke , Christina Brandt

Magnetic particle imaging is a relatively new tracer-based medical imaging technique exploiting the non-linear magnetization response of magnetic nanoparticles to changing magnetic fields. If the data are generated by using a field-free…

Image and Video Processing · Electrical Eng. & Systems 2022-11-23 Stephanie Blanke , Christina Brandt

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

We propose a novel direct sampling method (DSM) for the effective and stable inversion of the Radon transform. The DSM is based on a generalization of the important almost orthogonality property in classical DSMs to fractional order Sobolev…

Numerical Analysis · Mathematics 2020-10-22 Yat Tin Chow , Fuqun Han , Jun Zou

We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms.…

Differential Geometry · Mathematics 2009-08-21 Bruce Solomon