000 04008nam a22005175i 4500
001 978-3-540-71227-5
003 DE-He213
005 20190213151851.0
007 cr nn 008mamaa
008 111207s2007 gw | s |||| 0|eng d
020 _a9783540712275
_9978-3-540-71227-5
024 7 _a10.1007/978-3-540-71227-5
_2doi
050 4 _aQA184-205
072 7 _aPBF
_2bicssc
072 7 _aMAT002050
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512.5
_223
100 1 _aSchuster, Thomas.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Method of Approximate Inverse: Theory and Applications
_h[electronic resource] /
_cby Thomas Schuster.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2007.
300 _aXIV, 202 p. 35 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1906
505 0 _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.
520 _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.
650 0 _aMatrix theory.
650 0 _aDifferential equations, partial.
650 0 _aIntegral equations.
650 0 _aNumerical analysis.
650 1 4 _aLinear and Multilinear Algebras, Matrix Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M11094
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aIntegral Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12090
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540836032
776 0 8 _iPrinted edition:
_z9783540712268
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1906
856 4 0 _uhttps://doi.org/10.1007/978-3-540-71227-5
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c12157
_d12157