000 | 03771nam a22006015i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/b138659 _2doi |
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050 | 4 | _aQA273.A1-274.9 | |
050 | 4 | _aQA274-274.9 | |
072 | 7 |
_aPBT _2bicssc |
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072 | 7 |
_aPBWL _2bicssc |
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072 | 7 |
_aMAT029000 _2bisacsh |
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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. |
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300 |
_aXVI, 340 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aApplied Mathematical Sciences, _x0066-5452 ; _v160 |
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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 |