Two-Dimensional Reproducing Kernel-Based Interpolation Approximation for Best Regularization Parameter in Electrical Tomography Algorithm

The regularization parameter plays an important role in regularization-based electrical tomography (ET) algorithms, but the existing methods generally cannot determine the parameter. Moreover, these methods are not real-time since a thorough search must be performed for the best parameter. To address the issue, a reproducing kernel-based interpolation approximation method is proposed to efficiently estimate the best regularization parameter from a group of representative samples. The optimization and generation of the new method have been verified by theoretical analysis and experimental demonstration. The theoretical evaluation is conducted in a Hilbert space with a known reproducing kernel, and its symmetry ensures the uniqueness of the interpolation. And experimental validation is carried out using both simulated and actual models, each with a range of distinct features. Results indicate that the new method can approximately find the best regularization parameter. Consequently, when using the regularization parameter, the new method can effectively improve both the spatial resolution and steadiness of ET imaging process.