Search Results

Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography

Download or Read eBook Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography PDF written by Gaik Ambartsoumian and published by World Scientific. This book was released on 2023-03-14 with total page 248 pages. Available in PDF, EPUB and Kindle.
Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography
Author :
Publisher : World Scientific
Total Pages : 248
Release :
ISBN-10 : 9789811242458
ISBN-13 : 9811242453
Rating : 4/5 (58 Downloads)

Book Synopsis Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography by : Gaik Ambartsoumian

Book excerpt: A generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models of various imaging modalities. The GRTs integrating along smooth curves and surfaces (lines, planes, circles, spheres, amongst others) have been studied at great lengths for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. Recently, an interesting new class of GRTs emerged at the forefront of research in integral geometry. The two common features of these transforms are the presence of a 'vertex' in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).This book covers the relevant imaging modalities, their mathematical models, and the related GRTs. The discussion of the latter comprises a thorough exploration of their known mathematical properties, including injectivity, inversion, range description and microlocal analysis. The mathematical background required for reading most of the book is at the level of an advanced undergraduate student, which should make its content attractive for a large audience of specialists interested in imaging. Mathematicians may appreciate certain parts of the theory that are particularly elegant with connections to functional analysis, PDEs and algebraic geometry.


Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography Related Books

Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography
Language: en
Pages: 248
Authors: Gaik Ambartsoumian
Categories: Mathematics
Type: BOOK - Published: 2023-03-14 - Publisher: World Scientific

DOWNLOAD EBOOK

A generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models
Microlocal Analysis and Inverse Problems in Tomography and Geometry
Language: en
Pages: 252
Authors: Eric Todd Quinto
Categories: Mathematics
Type: BOOK - Published: 2024-09-23 - Publisher: Walter de Gruyter GmbH & Co KG

DOWNLOAD EBOOK

Microlocal Analysis has proven to be a powerful tool for analyzing and solving inverse problems; including answering questions about stability, uniqueness, reco
Mathematics Of Multilevel Systems: Data, Scaling, Images, Signals, And Fractals
Language: en
Pages: 270
Authors: Palle Jorgensen
Categories: Mathematics
Type: BOOK - Published: 2023-05-30 - Publisher: World Scientific

DOWNLOAD EBOOK

This book presents the mathematics of wavelet theory and its applications in a broader sense, comprising entropy encoding, lifting scheme, matrix factorization,
Frontiers In Entropy Across The Disciplines - Panorama Of Entropy: Theory, Computation, And Applications
Language: en
Pages: 757
Authors: M Zuhair Nashed
Categories: Science
Type: BOOK - Published: 2022-08-30 - Publisher: World Scientific

DOWNLOAD EBOOK

Frontiers in Entropy Across the Disciplines presents a panorama of entropy emphasizing mathematical theory, physical and scientific significance, computational
Operator Theory And Analysis Of Infinite Networks
Language: en
Pages: 449
Authors: Palle Jorgensen
Categories: Mathematics
Type: BOOK - Published: 2023-03-21 - Publisher: World Scientific

DOWNLOAD EBOOK

This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical proce
Scroll to top