###### Abstract  
This paper aims to determine whether regularization improves image reconstruction in electrical impedance tomography (EIT) using a radial basis network. The primary purpose is to investigate the effect of regularization to estimate the network parameters of the radial basis function network to solve the inverse problem in EIT. Our approach to studying the efficacy of the radial basis network with regularization is to compare the performance among several different regularizations, mainly Tikhonov, Lasso, and Elastic Net regularization. We vary the network parameters, including the fixed and variable widths for the Gaussian used for the network. We also perform a robustness study for comparison of the different regularizations used. Our results include (1) determining the optimal number of radial basis functions in the network to avoid overfitting; (2) comparison of fixed versus variable Gaussian width with or without regularization; (3) comparison of image reconstruction with or without regularization, in particular, no regularization, Tikhonov, Lasso, and Elastic Net; (4) comparison of both mean square and mean absolute error and the corresponding variance; and (5) comparison of robustness, in particular, the performance of the different methods concerning noise level. We conclude that by looking at the \(R^{2}\) score, one can determine the optimal number of radial basis functions. The fixed-width radial basis function network with regularization results in improved performance. The fixed-width Gaussian with Tikhonov regularization performs very well. The regularization helps reconstruct the images outside of the training data set. The regularization may cause the quality of the reconstruction to deteriorate; however, the stability is much improved. In terms of robustness, the RBF with Lasso and Elastic Net seem very robust compared to Tikhonov. Electricalimpedance tomography; radial basis function; deep learning; regularization 2023  
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[PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT)  
This is the EIT inverse problem. There are many technical problems related to EIT image reconstruction, such as finding the best arrangement of electrode positions [10], seeing the impact of boundary surface and electrode contact [11], hardware development [12], a stable reconstruction algorithm, and much more. The EIT inverse problem is known to be highly nonlinear and exponentially ill posed. Here, we focus mainly on solving the inverse problem mathematically without investigating the practical issues associated with EIT imaging. To solve the inverse problem in the machine learning setting, one must solve the forward problem, which involves finding the NtD map from a given conductivity. This is also useful for the verification of the inverse solution. In our case, this is used for generating the training data for the neural network. There are a few analytical solutions to the forward problem for some selected configurations [13; 14]. This work solves the two-dimensional forward problem using the finite element method to generate the training data. The inverse problem of the EIT image reconstruction was first introduced by [PERSON] [15]. As formulated by [PERSON], the inverse problem is to retrieve the conductivity \(\sigma\) from the NtD map \(\Lambda_{\sigma}\). It is well known that under various assumptions and smoothness for the conductivity, a unique solution to the Calderon problem exists [16]. In particular, for the 2D case, it has been shown that a unique solution exists even with very minimal smoothness assumptions on the conductivity [17]. Furthermore, the two-dimensional Calderon problem is stable when the conjunctivitis is Holder-continuous [18]. Another practical issue is that complete boundary data are never practically measured. We only measure partial data, affecting the inverse solution's accuracy.