TY - BOOK ID - 6978278 TI - Analytic tomography PY - 2006 VL - 106 SN - 0521793475 9780521793476 9780511530012 9781107438620 9781461941477 1461941474 0511530013 1107438624 1139882872 1107383897 1107387418 0511837720 1107390338 1107398746 1107395127 PB - Cambridge: Cambridge university press, DB - UniCat KW - Radon transforms KW - Geometric tomography KW - Geometric tomography. KW - Radon transforms. KW - Tomography (Mathematics) KW - Tomography, Geometric KW - Convex geometry KW - Integral transforms KW - Tomography KW - Transforms, Radon KW - Integral geometry UR - https://www.unicat.be/uniCat?func=search&query=sysid:6978278 AB - 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. ER -