Spatial-temporal modeling for electrical impedance imaging of a mixing process

Abstract

The use of electrical tomography techniques for process visualization and investigation is a well-known example of a nonlinear, ill-posed, and underdetermined inverse problem. Hence stable and reliable solution is not possible using measured data alone, but requires regularization through prior information. The rôle of a Bayesian approach is therefore of fundamental importance, and when coupled with Markov chain Monte Carlo (MCMC) sampling, it can provide valuable statistical information about solution behavior and reliability, which is in contrast to most current approaches which provide only a single image reconstruction with unquantified errors. For many applications of dynamic electrical impedance imaging, some degree of both spatial and temporal smoothness is expected. Often temporal smoothness is ignored and only spatial smoothing is used. In the current application, the addition of an aliquot to a mixing vessel, smoothness is not appropriate prior information. Instead an aliquot prior is proposed, parameterized in terms of location, size, and resistivity. This approach leads to data-driven and adaptive smoothing, in contrast to the more usual global smoothing of standard regularization methods. Of further interest is the inclusion of temporal prior information: it is known that the aliquot moves and disperses in a specific manner. With this added temporal information, imaging is improved as are derived process parameters.