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Multiphase Conductivity Imaging With Electrical Impedance Tomography and B-Spline Level Set Method

This article presents a B-spline level set (BLS)-based reconstruction scheme for multiphase conductivity imaging with electrical impedance tomography (EIT). The EIT inverse problem is recast as a shape reconstruction problem where both the inclusion interface and conductivity values are the unknown. In using this scheme, the unknown conductivity to be reconstructed is assumed to be piecewise constant while the inclusion interface is represented by the zero level set of a BLS surface, which, in turn, is represented as a linear combination of B-spline basis functions. Through such a low-order representation technique, the number of unknowns in the reconstruction problem is significantly reduced compared with the traditional pixel-/voxel-based reconstruction methods. The performance of the BLS scheme is tested with heart-and-lungs phantom studies and the cross section of the industrial pipeline phantom studies. The results demonstrate that the BLS scheme is capable of preserving sharp features of inclusions and providing estimates to both the interface locations and unknown conductivity values with reliable accuracy. In addition, we also found that the BLS scheme is quite robust to the selection of the regularization weighting parameter in the least-square-based optimization regime and the additional parameter in the Heaviside function used for modeling the conductivity profile.