Spatial resolution analysis for real time applications in electrical capacitance tomography

Electrical capacitance tomography (ECT) has proven to be a suitable tool for monitoring tasks in various multiphase flows. Due to the nonlinearity of the forward model, accurate reconstruction results are mostly obtained by nonlinear/iterative methods like Gauß–Newton. The reconstruction time of this method grows rapidly with the number of degrees of freedom (DoF) of the problem. Due to the no uniform sensitivity, the achievable spatial resolution is not uniformly distributed. In this work we fit the size of the reconstruction elements to the achievable resolution in the respective area. The idea is to use a coarser model (i.e. a dilated grid) in regions where only a low resolution can be achieved. This is in order to decrease the number of DoF without having an impact on the reconstruction quality. As a measure of the spatial resolution of our ECT-system the point spread function (PSF) is used, which is determined by simulations. We use this information for reconstruction tasks with different meshes to demonstrate that almost equal results can be achieved at a fraction of time. Additionally, we investigate the characteristics of coarser models within the L-curve framework, which is used for the determination of the regularization parameter.