000			03736nam a22005295i 4500
001			978-3-540-71227-5
003			DE-He213
005			20160624101834.0
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
082	0	4	_a512.5 _223
100	1		_aSchuster, Thomas. _eauthor.
245	1	4	_aThe Method of Approximate Inverse: Theory and Applications _h[electronic resource] / _cby Thomas Schuster.
260		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2007.
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	_aMathematics.
650		0	_aMatrix theory.
650		0	_aIntegral equations.
650		0	_aDifferential equations, partial.
650		0	_aNumerical analysis.
650	1	4	_aMathematics.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
650	2	4	_aPartial Differential Equations.
650	2	4	_aIntegral Equations.
650	2	4	_aNumerical Analysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540712268
786			_dSpringer
830		0	_aLecture Notes in Mathematics, _x0075-8434 ; _v1906
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-540-71227-5
942			_2EBK1857 _cEBK
999			_c31151 _d31151