000 01544nam a22002297a 4500
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008 171212b xxu||||| |||| 00| 0 eng d
020 _a9780521793476
040 _cIITK
041 _aeng
082 _a515.723
_bM342a
100 _aMarkoe, Andrew
245 _a Analytic tomography
_cAndrew Markoe
260 _a New York
_bCambridge University Press
_c2006
300 _aviii, 400p
440 _aEncyclopedia of mathematics and its applications
490 _aedited by Gian-Carlo Rota: 106v
505 _aThis 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.
650 _aRadon transforms
650 _aTomography
942 _cBK
999 _c556874
_d556874