000 02436nam a22003738i 4500
001 CR9780511530012
003 UkCbUP
005 20200124160233.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090409s2006||||enk o ||1 0|eng|d
020 _a9780511530012 (ebook)
020 _z9780521793476 (hardback)
020 _z9781107438620 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA672
_b.M37 2006
082 0 0 _a515/.723
_222
100 1 _aMarkoe, Andrew,
_d1943-
_eauthor.
245 1 0 _aAnalytic tomography /
_cAndrew Markoe.
264 1 _aCambridge :
_bCambridge University Press,
_c2006.
300 _a1 online resource (viii, 400 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aEncyclopedia of mathematics and its applications ;
_vvolume 106
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 _aIntroduction -- Computerized tomography, x-rays, and the radon transform -- Radon transform -- The k-plane transform, Radon-John transform -- Range and differential equations -- Generalizations and variants of the radon transform
520 _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 0 _aRadon transforms.
650 0 _aGeometric tomography.
776 0 8 _iPrint version:
_z9780521793476
830 0 _aEncyclopedia of mathematics and its applications ;
_vv. 106.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511530012
999 _c517780
_d517778