Statistical inverse problems: Discretization, model reduction and inverse crimes

The article discusses the discretization of linear inverse problems. When an inverse problem is formulated in terms of infinite-dimensional function spaces and then discretized for computational purposes, a discretization error appears. Since inverse problems are typically ill-posed, neglecting this...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 198; no. 2; pp. 493 - 504
Main Authors: Kaipio, Jari, Somersalo, Erkki
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 15.01.2007
Elsevier
Subjects:
Bayesian statistics
Discretization
Exact sciences and technology
Inverse problems
Mathematics
Modelling error
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in probability and statistics
Sciences and techniques of general use
Inverse problems
Discretization
Bayesian statistics
Modelling error
Bayes estimation
Numerical analysis
Function space
Error estimation
Applied mathematics
Statistical model
Ill posed problem
Inverse problem
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:The article discusses the discretization of linear inverse problems. When an inverse problem is formulated in terms of infinite-dimensional function spaces and then discretized for computational purposes, a discretization error appears. Since inverse problems are typically ill-posed, neglecting this error may have serious consequences to the quality of the reconstruction. The Bayesian paradigm provides tools to estimate the statistics of the discretization error that is made part of the measurement and modelling errors of the estimation problem. This approach also provides tools to reduce the dimensionality of inverse problems in a controlled manner. The ideas are demonstrated with a computed example.
Bibliography:SourceType-Scholarly Journals-2
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.09.027