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Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography (Hardcover)
Loot Price: R2,421
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Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography (Hardcover)
Series: Contemporary Mathematics And Its Applications: Monographs, Expositions And Lecture Notes, 6
Expected to ship within 10 - 15 working days
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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.
General
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