Approximation errors in nonstationary inverse problems

Inverse Problems and Imaging

Volumn 1, Issue 1, 2007, Pages 77-93

  Huttunen, Janne M J ^a   Kaipio, Jari P ^a  

^a UNIVERSITY OF EASTERN FINLAND   (Finland)

Author keywords

Kalman filtering; Model reduction; State space models

Indexed keywords

EID: 38849099711     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2007.1.77     Document Type: Article

References (17)

1. B.D.O. Anderson and J.B. Moore. “Optimal Filtering,” Prentice-Hall, inc, 1979.
2. A.C. Antoulas. “Approximation of Large-Scale Dynamical Systems,” Advances in Design and Control 6. Society for Industrial and Applied Mathematic, 2005.
3. S.R. Arridge, J.P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen. Approximation errors and model reduction with an application in optical diffusion tomography. Inverse Problems, 22(1):175–196, 2006.
4. P.J. Brockwell and R.A. Davis. “Time Series: Theory and Methods,” Springer-Verlag, 1991.
5. A. Doucet, N. de Freitas, and N. Gordon. “Sequential Monte Carlo Methods in Practice,” Statistics for Engineering and Information Science. Springer-Verlag, NY, 2001.
6. J. Heino. Approaches for modelling and reconstruction in optical tomography in the presence of anisotropies, Doctoral dissertation, Helsinki University of Technology, 2005.
7. R.A. Horn and C.R. Johnson. “Matrix Analysis,” Cambridge University Press, 1985.
8. J.P. Kaipio and E. Somersalo. Nonstationary inverse problems and state estimation, Journal of Inverse and Ill-Posed Problems, 7:273–282, 1999.
9. J.P. Kaipio and E. Somersalo. “Statistical and Computational Inverse Problems,” Applied Mathematical Sciences 160, Springer-Verlag, 2004.
10. J.P. Kaipio and E. Somersalo. Statistical inverse problems: Discretization, model reduction, and inverse crimes, J. Comput. Appl. Math., 198:493–504, 2007.
11. R.E. Kalman. A new approach to linear filtering and prediction problems, J. Basic Eng. Trans. ASME, Ser. D, 82:35–45, 1960.
12. B. Øksendal. “Stochastic Differential Equations,” Springer-Verlag, 1998.
13. H.K. Pikkarainen. A mathematical model for electrical impedance process tomography, Doctoral dissertation, Helsinki University of Technology, 2005.
14. H.K. Pikkarainen. State estimation approach to nonstationary inverse problems: discretization error and filtering problem, Inverse Problems, 22:365–379, 2006.
15. A.R. Ruuskanen, A. Seppnen, S. Duncan, E. Somersalo, and J.P. Kaipio. Using process tomography as a sensor for optimal control. Applied Numerical Mathematics, 56:37–54, 2006.
16. A. Seppnen, M. Vauhkonen, P.J. Vauhkonen, E. Somersalo, and J.P. Kaipio. State estimation with fluid dynamical evolution models in process tomography – an application with impedance tomography, Inverse Problems, 17:467–484, 2001.
17. M. West and J. Harrison. “Bayesian Forecasting and Dynamic Models,” Springer Series in Statistics. Springer-Verlag, NY, second edition, 1999.