LEADER 04086nam 2200709 450 001 996466617403316 005 20210217233338.0 010 $a1-280-85346-8 010 $a9786610853465 010 $a3-540-71227-5 024 7 $a10.1007/978-3-540-71227-5 035 $a(CKB)1000000000282963 035 $a(SSID)ssj0000303140 035 $a(PQKBManifestationID)11232697 035 $a(PQKBTitleCode)TC0000303140 035 $a(PQKBWorkID)10275133 035 $a(PQKB)10935281 035 $a(DE-He213)978-3-540-71227-5 035 $a(MiAaPQ)EBC3036628 035 $a(MiAaPQ)EBC4435036 035 $a(MiAaPQ)EBC6351724 035 $a(Au-PeEL)EBL4435036 035 $a(CaONFJC)MIL85346 035 $a(OCoLC)191468003 035 $a(PPN)123726905 035 $a(EXLCZ)991000000000282963 100 $a20210217d2007 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe method of approximate inverse $etheory and applications /$fThomas Schuster 205 $a1st ed. 2007. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[2007] 210 4$dİ2007 215 $a1 online resource (XIV, 202 p. 35 illus.) 225 1 $aLecture notes in mathematics ;$v1906 300 $aRevised habilitation - Universita?t des Saarlandes, Saarbru?cken, 2004. 311 $a3-540-71226-7 320 $aIncludes bibliographical references (pages [189]-195). 327 $aInverse and Semi-discrete Problems -- Ill-posed problems and regularization methods -- Approximate inverse in L 2-spaces -- Approximate inverse in Hilbert spaces -- Approximate inverse in distribution spaces -- Conclusion and perspectives -- Application to 3D Doppler Tomography -- A semi-discrete setup for Doppler tomography -- Solving the semi-discrete problem -- Convergence and stability -- Approaches for defect correction -- Conclusion and perspectives -- Application to the spherical mean operator -- The spherical mean operator -- Design of a mollifier -- Computation of reconstruction kernels -- Numerical experiments -- Conclusion and perspectives -- Further Applications -- Approximate inverse and X-ray diffractometry -- A filtered backprojection algorithm -- Computation of reconstruction kernels in 3D computerized tomography -- Conclusion and perspectives. 330 $aInverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one. Besides medical imaging and non-destructive testing, inverse problems also play an increasing role in other disciplines such as industrial and financial mathematics. Hence, there is a need for stable and efficient solvers. The book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings such as L2-spaces, Hilbert spaces or spaces of distributions. The performance and functionality of the method is demonstrated on several examples from medical imaging and non-destructive testing such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography. The book addresses graduate students and researchers interested in the numerical analysis of inverse problems and regularization techniques or in efficient solvers for the applications mentioned above. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1906. 606 $aInverse problems (Differential equations) 606 $aTomography 615 0$aInverse problems (Differential equations) 615 0$aTomography. 676 $a515.357 686 $a31.76$2bcl 686 $aMAT 150f$2stub 686 $aMED 385f$2stub 686 $aPHY 013f$2stub 686 $aSI 850$2rvk 700 $aSchuster$b Thomas$f1971-$01162550 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466617403316 996 $aThe method of approximate inverse$92830753 997 $aUNISA