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A stable Bayesian layer stripping algorithm for electrical impedance tomography.

MACSI at the department of Mathematics and Statistics at the University of Limerick invites you to a seminar

Date: Friday, June 7, 2019, Room A2-002 @ 16.00

Speaker: Prof. Erkki Somersalo, Case Western Reserve University, U.S.A.

Title: A stable Bayesian layer stripping algorithm for electrical impedance tomography.

Abstract: In electrical impedance tomography (EIT) the goal is to estimate an unknown conductivity distribution inside a body based on current-voltage measurements on the boundary of the body. Mathematically, the problem is tantamount to recovering a coefficient function of an elliptic PDE from the knowledge of complete Cauchy data at the boundary. Layer stripping method is based on the idea that the Dirichlet-to-Neumann map of the elliptic PDE can in principle be propagated into the body using an operator-valued backwards Riccati equation, while simultaneously estimating the unknown coefficient around the inwards moving artificial boundary. The ill-posedness of the inverse problem manifests itself as instability of the approach: among other things, the backwards Riccati equation may blow up in finite time. In this talk, the layer stripping algorithm is revisited in a Bayesian framework, and using novel ideas from particle filtering and sequential Monte Carlo methods, a stable computational scheme is proposed and tested numerically.

Further Information: If you have any questions regarding this seminar, please direct them to Romina Gaburro (061 2131930, email romina.gaburro@ul.ie  or Clifford Nolan (061 202766), clifford.nolan@ul.ie).

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.

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