American Institute of Mathematical Sciences

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February  2007, 1(1): 77-93. doi: 10.3934/ipi.2007.1.77

Approximation errors in nonstationary inverse problems

Janne M.J. Huttunen 1, and  J. P. Kaipio 2,

1. 

Department of Physics, University of Kuopio, P.O. Box 1627, 70211 Kuopio, Finland
2. 

Department of Physics, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland

Received  September 2006 Published  January 2007

Inverse problems are known to be very intolerant to both data errors and errors in the forward model. With several inverse problems the adequately accurate forward model can turn out to be computationally excessively complex. The Bayesian framework for inverse problems has recently been shown to enable the adoption of highly approximate forward models. This approach is based on the modelling of the associated approximation errors that are incorporated in the construction of the computational model. In this paper we investigate the extension of the approximation error theory to nonstationary inverse problems. We develop the basic framework for linear nonstationary inverse problems that allows one to use both highly reduced states and extended time steps. As an example we study the one dimensional heat equation.
Keywords: Model reduction, State-space models, Kalman filtering..
Mathematics Subject Classification: Primary: 93B30, 65P99; Secondary: 93B1.
Citation: Janne M.J. Huttunen, J. P. Kaipio. Approximation errors in nonstationary inverse problems. Inverse Problems & Imaging, 2007, 1 (1) : 77-93. doi: 10.3934/ipi.2007.1.77
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