TY - BOOK ID - 5343489 TI - Statistical and computational inverse problems AU - Kaipio, Jari AU - Somersalo, Erkki PY - 2005 VL - 160 SN - 0387220739 1441919643 9786610263127 1280263121 0387271325 9780387220734 PB - New York (N.Y.): Springer, DB - UniCat KW - Inverse problems (Differential equations) KW - Problèmes inversés (Equations différentielles) KW - Numerical solutions. KW - Solutions numériques KW - Inverse problems (Differential equations) -- Numerical solutions. KW - Mathematics - General KW - Mathematical Theory KW - Calculus KW - Mathematics KW - Physical Sciences & Mathematics KW - Numerical solutions KW - Inverse problems (Differential equations). KW - Problèmes inversés (Equations différentielles) KW - Solutions numériques KW - EPUB-LIV-FT LIVMATHE SPRINGER-B KW - Mathematics. KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Computer mathematics. KW - Probabilities. KW - Physics. KW - Complexity, Computational. KW - Biomedical engineering. KW - Probability Theory and Stochastic Processes. KW - Analysis. KW - Computational Mathematics and Numerical Analysis. KW - Theoretical, Mathematical and Computational Physics. KW - Complexity. KW - Biomedical Engineering. KW - Clinical engineering KW - Medical engineering KW - Bioengineering KW - Biophysics KW - Engineering KW - Medicine KW - Complexity, Computational KW - Electronic data processing KW - Machine theory KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Computer mathematics KW - Discrete mathematics KW - 517.1 Mathematical analysis KW - Mathematical analysis KW - Math KW - Science KW - Numerical analysis KW - Differential equations KW - Distribution (Probability theory. KW - Global analysis (Mathematics). KW - Computer science KW - Engineering. KW - Biomedical Engineering and Bioengineering. KW - Construction KW - Industrial arts KW - Technology KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Mathematical physics. KW - Computational complexity. KW - Physical mathematics KW - Physics KW - Inverse problems (Differential equations) - Numerical solutions. UR - https://www.unicat.be/uniCat?func=search&query=sysid:5343489 AB - 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 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. ER -