LEADER 04622nam 2200757 450 001 9910813739403321 005 20230607232331.0 010 $a3-11-094093-0 024 7 $a10.1515/9783110940930 035 $a(CKB)3390000000062278 035 $a(SSID)ssj0001560042 035 $a(PQKBManifestationID)16191284 035 $a(PQKBTitleCode)TC0001560042 035 $a(PQKBWorkID)14824388 035 $a(PQKB)11583112 035 $a(MiAaPQ)EBC3049437 035 $a(DE-B1597)57192 035 $a(OCoLC)1013949647 035 $a(OCoLC)900796381 035 $a(DE-B1597)9783110940930 035 $a(Au-PeEL)EBL3049437 035 $a(CaPaEBR)ebr11008785 035 $a(CaONFJC)MIL807303 035 $a(OCoLC)922950231 035 $a(EXLCZ)993390000000062278 100 $a20011231d2001 uy| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aComputer modelling in tomography and ill-posed problems /$fM.M. Lavrente?v, S.M. Zerkal and O.E. Trofimov 205 $aReprint 2014 210 1$aUtrecht ;$aBoston :$cVSP,$d2001. 215 $a1 online resource (136 pages) $cillustrations 225 1 $aInverse and ill-posed problems series 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-11-036412-3 311 $a90-6764-350-5 320 $aIncludes bibliographical references. 327 $aMachine 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. 330 $aComparatively weakly researched untraditional tomography problems are solved because of new achievements in calculation mathematics and the theory of ill-posed problems, the regularization process of solving ill-posed problems, and the increase of stability. Experiments show possibilities and applicability of algorithms of processing tomography data. This monograph is devoted to considering these problems in connection with series of ill-posed problems in tomography settings arising from practice.The book includes chapters to the following themes: Mathematical basis of the method of computerized tomography Cone-beam tomography reconstruction Inverse kinematic problem in the tomographic setting 410 0$aInverse and ill-posed problems series. 606 $aGeometric tomography 606 $aInverse problems (Differential equations) 610 $aAlgorithms. 610 $aCalculation Mathematics. 610 $aCone-beam. 610 $aIll-posed Problems. 610 $aInverse Kinematic Problem. 610 $aRegularization. 610 $aTomography. 615 0$aGeometric tomography. 615 0$aInverse problems (Differential equations) 676 $a516 686 $aST 640$2rvk 700 $aLavrent?ev$b M. M$g(Mikhail Mikhai?lovich),$01185700 702 $aZerkal$b S. M. 702 $aTrofimov$b O. E$g(Oleg Evgen?evich), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813739403321 996 $aComputer modelling in tomography and ill-posed problems$94088345 997 $aUNINA