A particle filter approach for tomographic imaging based on different state-space representations

In electrical capacitance tomography (ECT) the main focus is on the reconstruction of distinct objects with sharp transitions between different phases. Being inherently ill-posed, the reconstruction algorithm requires some sort of regularization to stabilize the solution of the inverse problem. However, introducing regularization may counteract the reconstruction of well-defined contours for grid-based methods. Level set propagation approaches which also rely on regularization are able to model sharp phase boundaries but suffer from high computational demands. In this contribution, two different state-space representations of closed contours based on B-splines and on Fourier descriptors are investigated. Both approaches allow us to describe the problem with only a small set of state-space variables. Regularization is incorporated implicitly which can be directly interpreted in the object domain as it relates to smooth contours. To solve the inverse problem, statistical inversion is performed by means of particle filtering providing the opportunity to conveniently incorporate prior information and to take measurement uncertainties into account. The proposed particle filter approach is compared to an extended Kalman filter realization in terms of complexity, computation time and estimation accuracy.