Statistical and Computational Inverse Problems [electronic resource] / by Jari P. Kaipio, Erkki Somersalo.
By: Kaipio, Jari P [author.].
Contributor(s): Somersalo, Erkki [author.]  SpringerLink (Online service).
Material type: TextSeries: Applied Mathematical Sciences: 160Publisher: New York, NY : Springer New York, 2005Description: XVI, 340 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387271323.Subject(s): Distribution (Probability theory  Global analysis (Mathematics)  Computer science  Mathematics  Engineering  Biomedical engineering  Probability Theory and Stochastic Processes  Analysis  Computational Mathematics and Numerical Analysis  Theoretical, Mathematical and Computational Physics  Complexity  Biomedical EngineeringAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 519.2 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

EBOOKS 
ISI Library, Kolkata

Available  EB903 
Inverse Problems and Interpretation of Measurements  Classical Regularization Methods  Statistical Inversion Theory  Nonstationary Inverse Problems  Classical Methods Revisited  Model Problems  Case Studies.
The 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 Carlomethods as well as optimization methods are employed to explore the probability distributions. The results and techniques are clarified with classroom examples that are often nontrivial 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 Besides the simple examples, the book contains previously unpublished research material, where the statistical approach is developed further to treat such problems as discretization errors, and statistical model reduction.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.
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Statistical and computational inverse problems by Kaipio Jari 
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