State estimation approach to nonstationary inverse problems: Discretization error and filtering problem

Inverse Problems

Volumn 22, Issue 1, 2006, Pages 365-379

  Pikkarainen, Hanna Katriina ^a  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; PROBLEM SOLVING; SIGNAL FILTERING AND PREDICTION; SPURIOUS SIGNAL NOISE; STATE ESTIMATION;

INFINITE-DIMENSIONAL STATE ESTIMATION SYSTEM; TIME DISCRETIZATION;

INVERSE PROBLEMS;

EID: 31844445344     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/22/1/020     Document Type: Article

References (18)

1. Baroudi D, Kaipio J and Somersalo E 1998 Dynamical electric wire tomography: a time series approach Inverse Problems 14 799-813
2. Huttunen J M J 2005 Private communication
3. Kaipio J and Somersalo E 1999 Nonstationary inverse problems and state estimation J. Inverse Ill-Posed Problems 7 273-82
4. Kaipio J P and Somersalo E 2004 Statistical and Computational Inverse Problems (Berlin: Springer)
5. Kalman R E 1960 A new approach to linear filtering and prediction problems Trans. ASME D 82 35-45
6. Lunardi A 1995 Analytic Semigroups and Optimal Regularity in Parabolic Problems (Basel: Birkhäuser)
7. Øksendal B 1998 Stochastic Differential Equations - An Introduction with Applications (Berlin: Springer)
8. Pikkarainen H K 2005 A Mathematical Model for Electrical Impedance Process Tomography (Helsinki University of Technology Institute of Mathematics Research Reports vol A486) (Espoo: Helsinki University of Technology) http://lib.tkk.fi/Diss/2005/isbn9512276720/
9. Da Prato G and Zabczyk J 1992 Stochastic Equations in Infinite Dimensions (Cambridge: Cambridge University Press)
10. Rao M M 1993 Conditional Measures and Applications (New York: Dekker)
11. Ruuskanen A R, Seppänen A, Duncan S, Somersalo E and Kaipio J P 2006 Using process tomography as a sensor for optimal control Appl. Numer. Math. 56 37-54
12. Seppänen A, Heikkinen L, Savolainen T, Somersalo E and Kaipio J P 2003 An experimental evaluation of state estimation with fluid dynamical models in process tomography Proc. 3rd World Congress on Industrial Process Tomography (Banff, Canada) pp 541-6
13. Seppänen, Vauhkonen M, Somersalo E and Kaipio J P 2001 State space models in process tomography-approximation of state noise covariance Inverse Problems Eng. 9 561-85
14. Seppänen A, Vauhkonen M, Vauhkonen P J, Somersalo E and Kaipio J P 2001 Fluid dynamical models and state estimation in process tomography: effect due to inaccuracies in flow fields J. Electr. Imaging 10 630-40
15. Seppänen A, Vauhkonen M, Vauhkonen P J, Somersalo E and Kaipio J P 2001 State estimation with fluid dynamical evolution models in process tomography - an application with impedance tomography Inverse Problems 17 467-84
16. Seppänen A 2005 State Estimation in Process Tomography (Kuopio University Publications C. Natural and Environmental Sciences vol C185) (Kuopio: University of Kuopio)
17. Vauhkonen M 1997 Electrical Impedances Tomography and Prior Information (Kuopio University Publications C. Natural and Environmental Sciences vol C62) (Kuopio: University of Kuopio) http://venda.uku.fi/~mvauhkon/phd_mvau.pdf
18. Voutilainen A 2001 Statistical Inversion Methods for the Reconstruction of Aerosol Size Distributions (Report Series in Aerosol Science no 52) (Helsinki: The Finnish Association for Aerosol Research) http://venda.uku.fi/ ~avoutila/phdthesisav.pdf