000 03771nam a22006015i 4500
001 978-0-387-27132-3
003 DE-He213
005 20161121230924.0
007 cr nn 008mamaa
008 100301s2005 xxu| s |||| 0|eng d
020 _a9780387271323
_9978-0-387-27132-3
024 7 _a10.1007/b138659
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aKaipio, Jari P.
_eauthor.
245 1 0 _aStatistical and Computational Inverse Problems
_h[electronic resource] /
_cby Jari P. Kaipio, Erkki Somersalo.
264 1 _aNew York, NY :
_bSpringer New York,
_c2005.
300 _aXVI, 340 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v160
505 0 _aInverse Problems and Interpretation of Measurements -- Classical Regularization Methods -- Statistical Inversion Theory -- Nonstationary Inverse Problems -- Classical Methods Revisited -- Model Problems -- Case Studies.
520 _aThe book develops the statistical approach to inverse problems with an emphasis on modeling and computations. The framework is the Bayesian paradigm, where all variables are modeled as random variables, the randomness reflecting the degree of belief of their values, and the solution of the inverse problem is expressed in terms of probability densities. The book discusses in detail the construction of prior models, the measurement noise modeling and Bayesian estimation. Markov Chain Monte Carlo-methods as well as optimization methods are employed to explore the probability distributions. The results and techniques are clarified with classroom examples that are often non-trivial but easy to follow. Besides the simple examples, the book contains previously unpublished research material, where the statistical approach is developed further to treat such problems as discretization errors, and statistical model reduction. Furthermore, the techniques are then applied to a number of real world applications such as limited angle tomography, image deblurring, electrical impedance tomography and biomagnetic inverse problems. The book is intended to researchers and advanced students in applied mathematics, computational physics and engineering. The first part of the book can be used as a text book on advanced inverse problems courses. The authors Jari Kaipio and Erkki Somersalo are Professors in the Applied Physics Department of the University of Kuopio, Finland and the Mathematics Department at the Helsinki University of Technology, Finland, respectively.
650 0 _aMathematics.
650 0 _aMathematical analysis.
650 0 _aAnalysis (Mathematics).
650 0 _aComputer mathematics.
650 0 _aProbabilities.
650 0 _aPhysics.
650 0 _aComplexity, Computational.
650 0 _aBiomedical engineering.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aAnalysis.
650 2 4 _aComputational Mathematics and Numerical Analysis.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
650 2 4 _aComplexity.
650 2 4 _aBiomedical Engineering.
700 1 _aSomersalo, Erkki.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387220734
830 0 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v160
856 4 0 _uhttp://dx.doi.org/10.1007/b138659
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c505973
_d505973