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Statistical and Computational Inverse Problems pp 223–309Cite as

Case Studies

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7.10 Notes and Comments

  1. K.E. Andersen, S.P. Brooks and M.B. Hansen. Bayesian inversion of geoelectrical resistivity data. J. R. Stat. Soc. Ser. B, Stat. Methodol., 65:619–642, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  2. A.C. Atkinson and A.N. Donev. Optimum Experimental Design. Oxford University Press, 1992.

    Google Scholar 

  3. J. Barzilai and J.M. Borwein. Two-point step-size gradient methods. IMA J. Numer. Anal., 8:141–148, 1988.

    MathSciNet  MATH  Google Scholar 

  4. M. Cheney and D. Isaacson. Distinguishability in impedance imaging. IEEE Trans. Biomed. Eng., 39:852–860, 1992.

    Article  Google Scholar 

  5. A.V. Fiacco and G.P. McCormick. Nonlinear Programming. SIAM, 1990.

    Google Scholar 

  6. M. Fink. Time-reversal of ultrasonic fields—part i: Basic principles. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 39:555–567, 1992.

    Article  Google Scholar 

  7. C. Fox and G. Nicholls. Sampling conductivity images via MCMC. In Proc. Leeds Annual Stat. Research Workshop 1997, pp. 91–100, 1997.

    Google Scholar 

  8. G.H. Golub and C.F. van Loan. Matrix Computations. The Johns Hopkins University Press, 1989.

    Google Scholar 

  9. P.J. Green. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82:711–732, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Hämäläinen, H. Haario and M.S. Lehtinen. Inferences about sources of neuromagnetic fields using Bayesian parameter estimation. Technical Report Report TKK-F-A620, Helsinki University of Technology, 1987.

    Google Scholar 

  11. J. Heino and E. Somersalo. Modelling error approach for optical anisotropies for solving the inverse problem in optical tomography. Preprint (2004).

    Google Scholar 

  12. J. Heino and E. Somersalo. Estimation of optical absorption in anisotropic background. Inverse Problems, 18:559–573, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Isaacson. Distinguishability of conductivities by electric current computed tomography. IEEE Trans. Med. Imaging, 5:91–95, 1986.

    Article  Google Scholar 

  14. J.P. Kaipio and E. Somersalo. Estimating anomalies from indirect observations. J. Comput. Phys., 181:398–406, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  15. J.P. Kaipio, A. Seppänen, E. Somersalo and H. Haario. Posterior covariance related optimal current patterns in electrical impedance tomography. Inv. Probl., 20:919–936, 2004.

    Article  MATH  Google Scholar 

  16. V. Kolehmainen, S.R. Arridge, W.R.B. Lionheart, M. Vauhkonen, and J.P. Kaipio. Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data. Inv. Probl., 15:1375–1391, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  17. V. Kolehmainen, S.R. Arridge, M. Vauhkonen and J.P. Kaipio. Simultaneous reconstruction of internal tissue region boundaries and coefficients in optical diffusion tomography. Phys. Med. Biol., 15:1375–1391, 2000.

    MathSciNet  Google Scholar 

  18. V. Kolehmainen, S. Prince, S.R. Arridge, and J.P. Kaipio. State-estimation approach to the nonstationary optical tomography problem. J. Opt. Soc. Am. A, 20(5):876–889, 2003.

    Google Scholar 

  19. V. Kolehmainen, S. Siltanen, S. Järvenpää, J.P. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E Somersalo. Statistical inversion for X-ray tomography with few radiographs II: Application to dental radiology. Phys Med Biol, 48:1465–1490, 2003.

    Article  Google Scholar 

  20. V. Kolehmainen, M. Vauhkonen, J.P. Kaipio, and S.R. Arridge. Recovery of piecewise constant coefficients in optical diffusion tomography. Opt. Express, 7(13):468–480, 2000.

    Article  Google Scholar 

  21. V. Kolehmainen, A. Voutilainen, and J.P. Kaipio. Estimation of non-stationary region boundaries in EIT: state estimation approach. Inv Probl., 17:1937–1956, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  22. K. Matsuura and U. Okabe. Selective minimum-norm solution of the biomagnetic inverse problem. IEEE Trans. Biomed. Eng., 42:608–615, 1995.

    Article  Google Scholar 

  23. R.L. Parker. Geophysical Inverse Theory. Princeton University Press, 1994.

    Google Scholar 

  24. S. Prince, V. Kolehmainen, J.P. Kaipio, M.A. Franceschini, D. Boas and S.R. Arridge. Time-series estimation of biological factors in optical diffusion tomography. Phys. Med. Biol., 48:1491–1504, 2003.

    Article  Google Scholar 

  25. T. Quinto. Singularities of the x-ray transform and limited data tomography in r2 and r3. SIAM J. Math. Anal., 24:1215–1225, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  26. D.M. Schmidt, J.S. George and C.C. Wood. Bayesian inference applied to the electromagnetic inverse problem. Human Brain Mapping, 7:195–212, 1999.

    Article  Google Scholar 

  27. A. Seppänen, L. Heikkinen, T. Savolainen, E. Somersalo and J.P. Kaipio. An experimental evaluation of state estimation with fluid dynamical models in process tomography. In 3rd World Congress on Industrial Process Tomography, Banff, Canada, pp. 541–546, 2003.

    Google Scholar 

  28. A. Seppänen, M. Vauhkonen, E. Somersalo and J.P. Kaipio. State space models in process tomography — approximation of state noise covariance. Inv. Probl. Eng., 9:561–585, 2001.

    Google Scholar 

  29. A. Seppänen, M. Vauhkonen, P.J. Vauhkonen, E. Somersalo and J.P. Kaipio. Fluid dynamical models and state estimation in process tomography: Effect due to inaccuracies in flow fields. J. Elect. Imaging, 10(3):630–640, 2001.

    Article  Google Scholar 

  30. A. Seppänen, M. Vauhkonen, P.J. Vauhkonen, E. Somersalo and J.P. Kaipio. State estimation with fluid dynamical evolution models in process tomography — an application to impedance tomography. Inv. Probl., 17:467–484, 2001.

    Article  MATH  Google Scholar 

  31. S. Siltanen, V. Kolehmainen, S. Järvenpää, J.P. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä and E Somersalo. Statistical inversion for X-ray tomography with few radiographs I: General theory. Phys. Med. Biol., 48: 1437–1463, 2003.

    Article  Google Scholar 

  32. K. Uutela, M. Hämäläinen and E. Somersalo. Visualization og magnetoencephalographic data using minimum current estimates. NeuroImage, 10:173–180, 1999.

    Article  Google Scholar 

  33. M. Vauhkonen, P.A. Karjalainen and J.P. Kaipio. A Kalman filter approach applied to the tracking of fast movements of organ boundaries. In Proc 20th Ann Int Conf IEEE Eng Med Biol Soc, pages 1048–1051, Hong Kong, China, October 1998.

    Google Scholar 

  34. M. Vauhkonen, P.A. Karjalainen and J.P. Kaipio. A Kalman filter approach to track fast impedance changes in electrical impedance tomography. IEEE Trans. Biomed. Eng., 45:486–493, 1998.

    Article  Google Scholar 

  35. P.J. Vauhkonen, M. Vauhkonen, T. Mäkinen, P.A. Karjalainen and J.P. Kaipio. Dynamic electrical impedance tomography: phantom studies. Inv. Prob. Eng., 8:495–510, 2000.

    Google Scholar 

  36. T. Vilhunen, L.M. Heikkinen, T. Savolainen, P.J. Vauhkonen, R. Lappalainen, J.P. Kaipio and M. Vauhkonen. Detection of faults in resistive coatings with an impedance-tomography-related approach. Measur. Sci. Technol., 13:865–872, 2002.

    Article  Google Scholar 

  37. A. Yagola and K. Dorofeev. Sourcewise representation and a posteriori error estimates for ill-posed problems. Fields Institute Comm., 25:543–550, 2000.

    MathSciNet  Google Scholar 

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(2005). Case Studies. In: Statistical and Computational Inverse Problems. Applied Mathematical Sciences, vol 160. Springer, New York, NY. https://doi.org/10.1007/0-387-27132-5_7

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