04622nam 2200757 450 991081373940332120230607232331.03-11-094093-010.1515/9783110940930(CKB)3390000000062278(SSID)ssj0001560042(PQKBManifestationID)16191284(PQKBTitleCode)TC0001560042(PQKBWorkID)14824388(PQKB)11583112(MiAaPQ)EBC3049437(DE-B1597)57192(OCoLC)1013949647(OCoLC)900796381(DE-B1597)9783110940930(Au-PeEL)EBL3049437(CaPaEBR)ebr11008785(CaONFJC)MIL807303(OCoLC)922950231(EXLCZ)99339000000006227820011231d2001 uy| 0engurcnu||||||||txtccrComputer modelling in tomography and ill-posed problems /M.M. Lavrentèv, S.M. Zerkal and O.E. TrofimovReprint 2014Utrecht ;Boston :VSP,2001.1 online resource (136 pages) illustrationsInverse and ill-posed problems seriesBibliographic Level Mode of Issuance: Monograph3-11-036412-3 90-6764-350-5 Includes bibliographical references.Machine generated contents note: Chapter 1. Mathematical basis of the method of computerized -- tomography 11 -- 1.1. Basic notions of the theory of ill-posed problems11 -- 1.2. Problem of integral geometry16 -- 1.3. The Radon transform18 -- 1.4. Radon problem as an example of an ill-posed problem20 -- 1.5. The algorithm of inversion of the two-dimensional Radon -- transform based on the convolution with the generalized -- function l/z225 -- Chapter 2. Cone-beam tomography reconstruction 33 -- 2.1. Reducing the inversion formulas of cone-beam tomography recont -- struction to the form convenient for constructing numerical -- algorithm s33 -- 2.2. Elements of the theory of generalized functions in application to -- problems of inversion of the ray transformation45 -- 2.3. The relations between the Radon, Fourier, -- and ray transformations51 -- Chapter 3. Inverse kinematic problem -- in the tomographic setting 55 -- 3.1. Direct kinematic problem and numerical solution -- for three-dimensional regular media55 -- 3.2. Formulation of the inverse kinematic problem with the use of -- a tomography system of data gathering66 -- 3.3. Deduction of the basic inversion formula and the algorithm of -- solving the inverse kinematic problem in -- three-dimensional linearized formulation68 -- 3.4. Model experiment and numerical study of the algorithm79 -- 3.5. Solution of the inverse kinematic problem by the method of -- computerized tomography for media with opaque inclusions 98 -- Appendix: Reconstruction with the use -- of the standard model 112 -- Bibliography 119.Comparatively weakly researched untraditional tomography problems are solved because of new achievements in calculation mathematics and the theory of ill-posed problems, the regularization process of solving ill-posed problems, and the increase of stability. Experiments show possibilities and applicability of algorithms of processing tomography data. This monograph is devoted to considering these problems in connection with series of ill-posed problems in tomography settings arising from practice.The book includes chapters to the following themes: Mathematical basis of the method of computerized tomography Cone-beam tomography reconstruction Inverse kinematic problem in the tomographic settingInverse and ill-posed problems series.Geometric tomographyInverse problems (Differential equations)Algorithms.Calculation Mathematics.Cone-beam.Ill-posed Problems.Inverse Kinematic Problem.Regularization.Tomography.Geometric tomography.Inverse problems (Differential equations)516ST 640rvkLavrentʹev M. M(Mikhail Mikhaĭlovich),1185700Zerkal S. M.Trofimov O. E(Oleg Evgenʹevich),MiAaPQMiAaPQMiAaPQBOOK9910813739403321Computer modelling in tomography and ill-posed problems4088345UNINA