Statistical and Computational Inverse Problems (eBook)

Jari Kaipio, E. Somersalo (Autoren)

eBook Download: PDF

2006 | 2005
XVI, 340 Seiten
Springer New York (Verlag)
978-0-387-27132-3 (ISBN)

Infos

This 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.

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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.

Inhalt

Inverse Problems and Interpretation of Measurements.- Classical Regularization Methods.- Statistical Inversion Theory.- Nonstationary Inverse Problems.- Classical Methods Revisited.- Model Problems.- Case Studies.

Produkt-Details

• Erscheint lt. Verlag: 30.3.2006
• Reihe/Serie: Applied Mathematical Sciences
• Reihe/Serie: Applied Mathematical Sciences
• Zusatzinfo: XVI, 340 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Schlagworte: biomedical engineering • Complexity • Construction • Markov • measure • Mechanics • Model • Modeling • Optimization • Probability Distribution • Random Variable
• ISBN-10: 0-387-27132-5 / 0387271325
• ISBN-13: 978-0-387-27132-3 / 9780387271323