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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

Second MaPhySto Workshop on

Inverse Problems

Inverse Problems from a Statistical Perspective

28-31 March 2001, Aalborg University, Denmark

This workshop was the second in a series organized by MaPhySto. The workshop brought together researchers with varied backgrounds, and common interest in inverse problems seen from a statistical perspective. There were a series of lectures by leading scientists having an active interest in the themes of the workshop.

The Workshop was organized by Martin B. Hansen (MaPhySto, Aalborg), Jens Ledet Jensen (MaPhySto, Aarhus), and Steffen Lilholt Lauritzen (MaPhySto, Aalborg).


The term inverse problems is used to denote a wide area of problems from both pure and applied mathematics, where one must recover information about a quantity or a phenomenon under study from measurements which are indirect and possibly noisy as well. This corresponds to the situations confronting engineers, scientists and industrial mathematicians on a daily basis. Informally, a direct problem corresponds to calculating the effect of some given cause, whereas the inverse problem corresponds to deriving the cause given some of its effects.
A practical example comes from the scattering of sound waves as occurs in ultrasonic imaging. The direct problem is to calculate the scattered waves given the scattering medium. On the other hand, the inverse problem consists in determining the structure of the scattering medium, given the wave source and measurements of the scattered waves. As noise and uncertainty is inevitable in most applications the focus of the workshop will be on statistical aspects of inverse problems.


Wednesday 28 March

09.30-10.15 Registration/Coffee
10.15-10.30 Martin B. Hansen: Welcome
10.30-11.30 Finbarr O'Sullivan, Cork: Quantitative Analysis of Data from PET Imaging Studies
11.30-11.45 Break
11.45-12.45 Philip B. Stark, Berkeley: Inverse Problems in Helioseismology
12.45-14.00 Lunch
14.00-15.00 Viktor Benes, Prague: On stereological unfolding problems
15.00-15.15 Coffee
15.15-16.15 Markus Kiderlen, Karlsruhe: Discrete Inversion of The Spherical Cosine Transform in Stereology

Thursday 29 March

09.00-10.00 Geoff Nicholls, Auckland: Bayesian Inversion of Boundary Value Data
10.00-10.30 Coffee
10.30-11.30 Henning Omre, Trondheim: Bayesian Inversion in Reservoir Characterization with Complex Forward Models
11.30-11.45 Break
11.45-12.45 Klaus Mosegaard, Copenhagen: Geophysical Applications of MCMC: Bayesian Calculations and MC-Optimization with Slow Forward Algorithms
12.45-14.00 Lunch
14.00-15.00 Odd Kolbjørnsen, Trondheim: Bayesian Inversion of Piecewise Affine Inverse Problems
15.00-15.15 Coffee
15.15-15.45 Marcela Hlawiczkova: On the precision of the rose of directions estimation

Friday 30 March

09.00-10.00 Grace Wahba, Madison: Combining Observations with Models: Penalized Likelihood and Related Methods in Numerical Weather Prediction
10.00-10.30 Coffee
10.30-11.30 Douglas W. Nychka, Boulder: Posterior Distributions for Numerical Weather Forecasts
11.30-11.45 Break
11.45-12.45 Robin Morris, NASA Ames: 3D Surface Reconstruction as Bayesian Inference
12.45-14.00 Lunch
14.00-15.00 M.D. Ruiz-Medina and J.M. Angulo, Granada: Inverse Estimation of Random Fields: Regularization and Approximation
15.00-15.15 Coffee
15.15-16.15 Anne Vanhems, Toulouse: Nonparametric 
Study of Differential Equations and Inverse Problems
16.15-16.30 Break
16.30-17.30 Round Table Discussion
19.00 Conference Dinner

Saturday 31 March

09.00-10.00 Robert S. Anderssen, Canberra: Recovering Molecular Information from the Mixing of Wheat-Flour Dough
10.00-10.30 Coffee
10.30-11.30 Frits Ruymgaart, Lubbock: Spectral Methods for Noisy Integral Equations
11.30-11.45 Break
11.45-12.45 Per Christian Hansen, Lyngby: Inverse Acoustic Problems: Sound Source Reconstruction
12.45-14.00 Lunch

This document, http://www.maphysto.dk/events/2ndIP2001/index.html, was last modified Wednesday, 31-Jan-2001 12:05:00 MET. Questions or comments to the contents of this document should be directed to maphysto@maphysto.dk.