Adaptive importance sampling with prior information in dynamic process imaging

Abstract

AbstractThe estimation of cross‐sectional material distributions from non‐stationary sparse tomographic measurement data is a demanding class of ill‐posed inverse problems. In this context, electrical capacitance tomography (ECT) is a well‐established modality that aims at monitoring and controlling dynamic industrial processes arising e.g. in pneumatic conveying or heterogeneous flow fields. By measuring the capacitances between certain electrodes that are arranged around the periphery, the permittivity distribution inside closed objects can be spatially resolved. In this paper, the main focus is on the robust estimation of time‐dependent material distributions given uncertain measurements. The underlying inverse problem is formulated in a Bayesian inferential framework, by specifying a prior parameter distribution, and characterizing the statistics of the measurement noise, to give a posterior distribution conditioned on measured data. Transitions between different material phases are described by means of a Fourier contour model of second order implying a geometric regularization. Sequential importance filtering – particle filtering – is applied to solve the non‐stationary ECT problem. A tracking experiment is presented in order to show the robustness of the Bayesian filtering approach to solve the non‐stationary inverse problem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)