Available online at www.sciencedirect.com ScienceDirect Comput. Methods Appl. Mech. Engrg. 373 (2021) 113489 www.elsevier.com/locate/cma Optimal Bayesian experimental design for electrical impedance tomography in medical imaging Ahmad Karimi a ,∗ , Leila Taghizadeh a , Clemens Heitzinger a,b a Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8–10, 1040 Vienna, Austria b School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA Received 13 May 2020; received in revised form 19 September 2020; accepted 5 October 2020 Available online xxxx Abstract Optimal design of electronic devices such as sensors is essential since it results in more accurate output at the shortest possible time. In this work, we develop optimal Bayesian inversion for electrical impedance tomography (EIT) technology in order to improve the quality of medical images generated by EIT and to put this promising imaging technology into practice. We optimize Bayesian experimental design by maximizing the expected information gain in the Bayesian inversion process in order to design optimal experiments and obtain the most informative data about the unknown parameters. We present optimal experimental designs including optimal frequency and optimal electrode configuration, all of which result in the most accurate estimation of the unknown quantities to date and high-resolution EIT medical images, which are crucial for diagnostic purposes. Numerical results show the efficiency of the proposed optimal Bayesian inversion method for the EIT inverse problem. c ⃝ 2020 Elsevier B.V. All rights reserved. Keywords: Bayesian experimental design; Expected information gain; Stochastic optimization; Electrical impedance tomography; Medical imaging 1. Introduction Bayesian analysis in inverse modeling aims to compute expectations of so-called quantities of interest (QoI), constrained by forward PDE models, using probabilistic methods under a prior probability on uncertain PDE inputs, and taking the availability of possibly massive, noisy and redundant data into account. Prominent examples are climate and weather forecasts, subsurface flow, nanotechnology, life sciences and biomedical data. Bayesian inference tools have been so far applied successfully to many inverse problems in various applications (see for example [1–3]). Electrical impedance tomography (EIT) [4–8] is an imaging technology which reconstructs electrical properties of the interior of a body using surface electrode measurements. The electrical and physical properties of a human body produce great information about the body interior for the identification and characterization of inclusions, for instance cancerous tissues. This phenomenon is exploited in EIT, where the electrical properties such as conductivity information is used to build images of the interior. This technology has attracted lots of attention since it possesses ∗ Corresponding author. E-mail addresses: ahmad.karimi@tuwien.ac.at (A. Karimi), leila.taghizadeh@tuwien.ac.at (L. Taghizadeh), clemens.heitzinger@tuwien.ac.at (C. Heitzinger). https://doi.org/10.1016/j.cma.2020.113489 0045-7825/ c ⃝ 2020 Elsevier B.V. All rights reserved.