2014/04/29 by Nuutti Hyvönen, Hyvönen, Nuutti, Aku Seppänen +3
Earth and Planetary Sciences · Engineering · #35Q60 #62F15 #65N21 #Electrical and Bioimpedance Tomography #FOS: Mathematics #Flow Measurement and Analysis #Geophysical and Geoelectrical Methods #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1404.7300
openalex publication_date 2014/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized) conductivity, i.e., the conditional density of the conductivity given the measurements, is as localized as possible. To make such an approach computationally feasible, the complete electrode forward model of impedance tomography is linearized around the prior expectation of the conductivity, allowing explicit representation for the (approximate) posterior covariance matrix. Two approaches are considered: minimizing the trace or the determinant of the posterior covariance. The introduced optimization algorithm is of the steepest descent type, with the needed gradients computed based on appropriate Fréchet derivatives of the complete electrode model. The functionality of the methodology is demonstrated via two-dimensional numerical experiments.