# 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).