Workshop on Statistical Inverse Problems

Statistical Inverse Problems
University of Göttingen
Germany
March 23-25, 2006

Organizing Committee
Frank Bauer, Nicolai Bissantz, Thorsten Hohage, Axel Munk

Overview

Aims and Scope
Talks
Posters
Sponsors
Abstracts

Aims and Scope
Inverse Problems is an area of growing interest both for statisticians and numerical analysts since such problems arise naturally in many applications e.g. inin medical imaging, economy, finance, physics, chemistry, biology and industrial research.So far a large part of the research on inverse problems in statisticsand numerics has followed different paths. Whereas a lot of progress has beenachieved on nonlinear deterministic inverse problems over thelast decade, the literature on nonlinear statistical inverse problemsis scarce. In contrast, a variety of sophisticated adaptive techniques forparameter and model selection have been developed in statistics,which do not have a counterpart in deterministic theory.Many questions of fundamental theoretical and practical importancearise in both fields: identifiability,consistency, computation of estimators, and optimality in various forms.Therefore, this workshop intends to establish and strengthen links between research in the statistical and the deterministic inverse problemscommunities.

The workshop covered the following topics:

Methods and Techniques:

Algorithmic Aspects of Inverse Problems
Bayesian Approaches
Minimax Theory
Convergence Analysis
Iterative Methods for Non-Linear Inverse Problems

Fields of Application:

Econometrics
Image Reconstruction
Deconvolution
Medical Applications
Technical/Physical/Industrial Applications

Talks download

A. Munk	University of Göttingen	Introductionary talk
M. Bertero	University of Genova	The Large Binocular Telescope: A Laboratory for developing Image Reconstruction in Astronomy
L. Cavalier	Université de Provence	Risk hull method for inverse problems
J. Florens	University of Toulouse I	Instrumental regression in partially linear models
N. Hengartner	Los Alamos National Laboraties	Passive detection and imaging of nuclear material using cosmic ray muons
J. Horowitz	Northwestern University	Nonparametric instrumental variables estimation of a quantile
G. Jongbloed	University of Amsterdam	Asymptotic distribution of the MLE in a class of deconvolution models
J. Kaipio	University of Kuopio	Recent results in the modelling of approximation errors in inverse problems
P. Kim	University of Guelph	Sharp Adaptation for Statistical Inverse Problems on Manifolds
J. Loubes	University Paris Sud	A class of stochastic inverse problems: curves warping
B. Mair	University of Florida	Joint Emission and Motion Estimation for a Cardiac Cycle in Gated Emission Tomography
E. Mammen	University of Mannheim	Kernel density estimation for the coefficients in randomcoefficient regression with applications to demand analysis
S. Pereverzev	Johann Radon Institute for Computational and Applied Mathematics	Regularization Algorithms in Learning Theory
M. Reiss	Ruprecht-Karls-Universität Heidelberg	Calibration of financial Levy models as inverse problem
F. Ruymgaart	Texas Tech University	Fréchet differentiation of functions of operators with application in functional data analysis
E. Somersalo	Helsinki University of Technology	Applications of Bayesian hypermodels
P. Stark	University of California	Measuring resolution in nonlinear and constrained inverse problems
F. Balabdaoui	University of Göttingen	Estimation of a convex density: Back to Hampel birds problem
F. Bauer	University of Göttingen	Inverse Problems: Strategies to counter noise which exhibits bad behavior
M. Pricop	University of Göttingen	Rates of convergence of Tikhonov regularization for nonlinear inverse problems with stochastic noise
N. Bissantz	University of Göttingen	Convergence rates of general regularization methods for statistical inverse problems
L. Boysen	University of Göttingen	Jump reconstruction in certain inverse problems

Posters download

D. Calvetti	Case University	Large scale statistical parameter estimation in complex systems with an application to metabolic models
H. Heese	University of Göttingen	An inverse problem in superconductivity
A. Hofinger	Johann Radon Institute for Computational and Applied Mathematics	A new Framework for Assesing Uncertainty in Ill-Posed Problems
O. Ivanyshyn	University of Göttingen	Nonlinear Integral Equations in Inverse Obstacle Scattering
A. Kharytonov	Kiel University	Particle Spectra by the Application of Regularization Methods
M. Langovoy	University of Göttingen	Efficient tests for the deconvolution hypothesis
F. Lenzen	University of Innsbruck	Non-convex regularization
M. Lesosky	University of Guelph	Statistical Inverse Problems on the Euclidean Motion Group
T. Levitina	Technische Universität Braunschweig	Sampling with Finite Fourier and Hankel Transform Eigenfunctions
C. Marteau	Universite de Provence	Regularization of inverse problems with noisy operator
Y.M. Marzouk	Sandia National Laboratories	Stochastic spectral methods for Bayesian inference in inverse problems
M. Meise	Universität Duisburg-Essen	On Deconvoluting Densities
S.S. Pereverzyev	Fraunhofer-Institut für Techno- und Wirtschaftsmathematik	Regularized Fixed-Point Iteration for Nonlinear Inverse Problems
M.L. Rapun	Universidad Complutense de Madrid	Detecting corrosion using thermal waves
P. Serranho	University of Göttingen	A hybrid method for inverse scattering for shape and impedance
H. Weinert/ T. Mildenberger	University of Dortmund	Data approximation and inverse problems
V. Zalipaev	University of Loughborough	The evolution-observation scheme in Blagovestchenskii's approach to the 1D inversion

Sponsors
We want to thank all sponsors which make this event possible. In particular these are the "Deutsche Forschungsgemeinschaft" (DFG) and the "Deutsche Akademische Austauschdienst" (DAAD).