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Bayesian Learning of Material Density Function by Multiple Sequential Inversions of 2-D Images in Electron Microscopy

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posted on 2015-02-04, 09:51 authored by Dalia Chakrabarty, S. Paul
We discuss a novel inverse problem in which the data is generated by the sequential contractive projections of the convolution of two unknown functions, both of which we aim to learn. The method is illustrated using an application that relates to the multiple inversions of image data recorded with a Scanning Electron Microscope, with the aim of learning the density of a given material sample and the microscopy correction function. Given the severe logistical difficulties in this application of taking multiple images at different viewing angles, a novel imaging experiment is undertaken, resulting in expansion of information. In lieu of training data, it is noted that the highly discontinuous material density function cannot be modelled using a Gaussian Process (GP) as the parametrisation of the required non-stationary covariance function of such a GP cannot be achieved without training data. Consequently, we resort to estimating values of the unknown functions at chosen locations in their domain–locations at which an image data are available. Image data across a range of resolutions leads to multiscale models which we use to estimate material densities from the micro-metre to nano-metre length scales. We discuss applications of the method in non-destructive learning of material density using simulated metallurgical image data, as well as perform inhomogeneity detection in multi-component composite on nano metre scales, by inverting real image data of a brick of nano-particles.

History

Citation

Interdisciplinary Bayesian Statistics EBEB 2014, 2014

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Source

EBEB 2014 - XII Brazilian Meeting on Bayesian Statistics

Version

  • AM (Accepted Manuscript)

Published in

Interdisciplinary Bayesian Statistics EBEB 2014

Publisher

Springer

issn

2194-1009

isbn

978-3-319-12453-7;978-3-319-12454-4

Publisher version

http://www.springer.com/statistics/statistical+theory+and+methods/book/978-3-319-12453-7 http://link.springer.com/chapter/10.1007/978-3-319-12454-4_3

Editors

Polpo de Campos, A;Neto,;Ramos Rifo,;Stern,;Lauretto,

Book series

Springer Proceedings in Mathematics & Statistics;Vol. 118

Language

en

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