This book is a comprehensive study of the Radon transform, which
operates on a function by integrating it over hyperplanes. The book
begins with an elementary and graphical introduction to the Radon
transform, tomography and CT scanners, followed by a rigorous
development of the basic properties of the Radon transform. Next
the author introduces Grassmann manifolds in the study of the
k-plane transform (a version of the Radon transform) which
integrates over k-dimensional planes rather than hyperplanes. The
remaining chapters are concerned with more advanced topics, such as
the attenuated Radon transform and generalized Radon transforms
defined by duality of homogeneous spaces and double fibrations.
Questions of invertibility and the range of the Radon transform are
dealt with and inversion formulas are developed with particular
attention to functions on L2 spaces and some discussion of the case
of Lp spaces.
General
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