Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 198, Issue 2, Pages 493-504Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2005.09.027
Keywords
inverse problems; Bayesian statistics; discretization; modelling error
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The article discusses the discretization of linear inverse problems. When an inverse problem is formulated in terms of infinitedimensional 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. (c) 2005 Elsevier B.V. All rights reserved.
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