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Applied Mathematical Sciences Ser.: Statistical and Computational Inverse Problems by Jari Kaipio and Erkki Somersalo (2004, Hardcover)
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Rm background in mathem- ics. rst four chapters can be used as the material for a ?. rst course on inverse problems with a focus on computational and statistical aspects.
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About this product
Product Identifiers
PublisherSpringer New York
ISBN-100387220739
ISBN-139780387220734
eBay Product ID (ePID)30773901
Product Key Features
Number of PagesXvi, 340 Pages
Publication NameStatistical and Computational Inverse Problems
LanguageEnglish
SubjectDifferential Equations / General, Probability & Statistics / General, Numerical Analysis, Mathematical Analysis
Publication Year2004
TypeTextbook
AuthorJari Kaipio, Erkki Somersalo
Subject AreaMathematics
SeriesApplied Mathematical Sciences Ser.
FormatHardcover
Dimensions
Item Weight52.9 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2004-049181
ReviewsFrom the reviews: "The book is devoted to the development of the statistical approach to inverse problems ... . The content is written clearly and without citations in the main text. Every chapter has a section called 'Notes and comments' where the citations and further reading, as well as brief comments on more advanced topics, are provided. The book is aimed at postgraduate students ... . The book also will be of interest for many researchers and scientists working in the area of image processing." (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1068, 2005) "Inverse problems are usually ill-posed in the sense that a solution need not exist, need not be unique, and depends in a discontinuous way on the data ... . there have been two quite separate communities dealing with such problems, one basing their methods mainly on functional analysis, the other one on statistics. ... several attempts have been made to bridge the gap between these two groups. The book under review ... is a further, quite successful attempt in this direction." (Heinz W. Engel, SIAM Review, Vol. 48 (1), 2006), From the reviews:"The book is devoted to the development of the statistical approach to inverse problems … . The content is written clearly and without citations in the main text. Every chapter has a section called 'Notes and comments' where the citations and further reading, as well as brief comments on more advanced topics, are provided. The book is aimed at postgraduate students … . The book also will be of interest for many researchers and scientists working in the area of image processing." (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1068, 2005)"Inverse problems are usually ill-posed in the sense that a solution need not exist, need not be unique, and depends in a discontinuous way on the data … . there have been two quite separate communities dealing with such problems, one basing their methods mainly on functional analysis, the other one on statistics. … several attempts have been made to bridge the gap between these two groups. The book under review … is a further, quite successful attempt in this direction." (Heinz W. Engel, SIAM Review, Vol. 48 (1), 2006), From the reviews: "The book is devoted to the development of the statistical approach to inverse problems a? . The content is written clearly and without citations in the main text. Every chapter has a section called a?Notes and commentsa? where the citations and further reading, as well as brief comments on more advanced topics, are provided. The book is aimed at postgraduate students a? . The book also will be of interest for many researchers and scientists working in the area of image processing." (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1068, 2005) "Inverse problems are usually ill-posed in the sense that a solution need not exist, need not be unique, and depends in a discontinuous way on the data a? . there have been two quite separate communities dealing with such problems, one basing their methods mainly on functional analysis, the other one on statistics. a? several attempts have been made to bridge the gap between these two groups. The book under review a? is a further, quite successful attempt in this direction." (Heinz W. Engel, SIAM Review, Vol. 48 (1), 2006)
Dewey Edition22
Series Volume Number160
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal515/.357
Table Of ContentInverse Problems and Interpretation of Measurements.- Classical Regularization Methods.- Statistical Inversion Theory.- Nonstationary Inverse Problems.- Classical Methods Revisited.- Model Problems.- Case Studies.
SynopsisThis book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering., This book is aimed at postgraduate students in applied mathematics as well as at engineering and physics students with a ?rm background in mathem- ics. The ?rst four chapters can be used as the material for a ?rst course on inverse problems with a focus on computational and statistical aspects. On the other hand, Chapters 3 and 4, which discuss statistical and nonstati- ary inversion methods, can be used by students already having knowldege of classical inversion methods. There is rich literature, including numerous textbooks, on the classical aspects of inverse problems. From the numerical point of view, these books concentrate on problems in which the measurement errors are either very small or in which the error properties are known exactly. In real-world pr- lems, however, the errors are seldom very small and their properties in the deterministic sensearenot wellknown.For example,inclassicalliteraturethe errornorm is usuallyassumed to be a known realnumber. In reality,the error norm is a random variable whose mean might be known., This book is aimed at postgraduate students in applied mathematics as well as at engineering and physics students with a ?rm background in mathem- ics. The ?rst four chapters can be used as the material for a ?rst course on inverse problems with a focus on computational and statistical aspects. On the other hand, Chapters 3 and 4, which discuss statistical and nonstati- ary inversion methods, can be used by students already having knowldege of classical inversion methods. There is rich literature, including numerous textbooks, on the classical aspects of inverse problems. From the numerical point of view, these books concentrate on problems in which the measurement errors are either very small or in which the error properties are known exactly. In real-world pr- lems, however, the errors are seldom very small and their properties in the deterministic sensearenot wellknown.For example, inclassicalliteraturethe errornorm is usuallyassumed to be a known realnumber. In reality, the error norm is a random variable whose mean might be know, This book develops the statistical approach to inverse problems with an emphasis on modeling and computations. It details 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 examples and applied to a number of real world applications.
LC Classification NumberQA273.A1-274.9
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