Generalized Radon Transforms And Imaging By Scattered Particles Broken Rays Cones And Stars In Tomography is popular PDF and ePub book, written by Gaik Ambartsoumian in 2023-03-14, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Generalized Radon Transforms And Imaging By Scattered Particles Broken Rays Cones And Stars In Tomography can be Read Online from any device for your convenience.
Generalized Radon Transforms And Imaging By Scattered Particles Broken Rays Cones And Stars In Tomography Book PDF Summary
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.
Detail Book of Generalized Radon Transforms And Imaging By Scattered Particles Broken Rays Cones And Stars In Tomography PDF
- Author : Gaik Ambartsoumian
- Release : 14 March 2023
- Publisher : World Scientific
- ISBN : 9789811242458
- Genre : Mathematics
- Total Page : 248 pages
- Language : English
- PDF File Size : 17,8 Mb
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