Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography
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A01=Gaik Ambartsoumian
Artifacts
Author_Gaik Ambartsoumian
Boltzmann Equation
Broken Line
Broken Ray
Category=PBKL
Compton
Cone Transform
Conical Transform
Divergent Beam
eq_isMigrated=1
eq_nobargain
Gamma-ray
Generalized Radon Transform
Image Reconstruction
Imaging
Integral Geometry
Inversion
Lebesgue Differentiation
Microlocal Analysis
Numerical Implementation
Optical Tomography
Particle Scattering
Phantom
Photon
Radiative Transport
Radon Transform
Range Description
Scattering
Single Scattering
Stability
Star Transform
Tomography
V-line
Vector Tomography
X-ray
Product details
- ISBN 9789811242434
- Publication Date: 14 Apr 2023
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
