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Large-scale data analysis

Working Group 8.42

Overview

Large-scale measurement systems are becoming increasingly important in applications such as quantitative imaging, nanometrology, or environmental and climate monitoring. The sheer number of variables and measured data often challenges the evaluation of uncertainties and can even prohibit estimation and handling of covariance matrices. Least-squares fitting in nonlinear regression problems leads to non-convex, large-scale optimization tasks which are difficult to solve.  The calculation of results of a Bayesian inference is particularly challenging since state-of-the-art Markov chain Monte Carlo techniques do not scale well to high dimensions, and sampling from the posterior distribution may remain impossible. Suitable approximations to the posterior distribution, or to results derived thereof, are then needed.

Example of a large-scale regression problem: estimation of spatially distributed T1 relaxation times (in ms) in magnetic resonance (MR) fingerprinting for simulated data. Approximate uncertainties are compared with actual errors.

Research

The focus of PTB’s Working Group 8.42 is on the development of Bayesian methods for tasks of large-scale data analysis where the number of parameters is large or even huge. This comprises the development of approximate calculation procedures and the assignment of suitable prior distributions. Examples for the latter are Gaussian Markov Random field priors used to express smoothness in spatial models. Applications include quantitative magnetic imaging techniques such as MR fingerprinting or cardiac MR-perfusion imaging. Another route of research is the further development of compressed sensing or low-rank matrix approximation. Application of these techniques is intended to enable efficient experimental sampling, for example in near-field FTIR spectroscopy.

Software

Publications

S. Metzner, G. Wübbeler, S. Flassbeck, C. Gatefait, C. Kolbitsch;C. Elster
Physics in Medicine & Biology, 66(7),
075006,
2021.
G. Wübbeler;C. Elster
Metrologia, 58(1),
014002,
2021.
(online)
M. Marschall, A. Hornemann, G. Wübbeler, A. Hoehl, E. Rühl, B. Kästner;C. Elster
Opt. Express, 26(28),
38762--38772,
2020.
J. Lehnert, C. Kolbitsch, G. Wübbeler, A. Chiribiri, T. Schäffter;C. Elster
SIAM J. Imaging Sci., 12(4),
2035--2062,
2019.
S. Metzner, G. Wübbeler;C. Elster
AStA Adv Stat Anal, 103(3),
333--355,
2019.
J. Lehnert, G. Wübbeler, C. Kolbitsch, A. Chiribiri, L. Coquelin, G. Ebrard, N. Smith, T. Schäffter;C. Elster
Physics in Medicine & Biology, 63
215017,
2018.
B. Kästner, F. Schmähling, A. Hornemann, G. Ulrich, A. Hoehl, M. Kruskopf, K. Pierz, M. Raschke, G. Wübbeler;C. Elster
Optics Express, 14
18115--18124,
2018.
F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling;C. Elster
Color, Research and Application, 43(1),
6--16,
2017.
G. Wübbeler;C. Elster
SIAM J. Imaging Sci., 10(3),
979--1004,
2017.
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