Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse Problem
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...
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MDPI AG
2023-09-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/16/10/461 |
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| author | Chowdhury Abrar Faiyaz Pabel Shahrear Rakibul Alam Shamim Thilo Strauss Taufiquar Khan |
| author_facet | Chowdhury Abrar Faiyaz Pabel Shahrear Rakibul Alam Shamim Thilo Strauss Taufiquar Khan |
| author_sort | Chowdhury Abrar Faiyaz |
| collection | DOAJ |
| description | 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 <i>R</i><sup>2</sup> 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. |
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| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T21:30:48Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-ddd88ab721f848d5acec54b7fbcc71ca2023-11-19T15:23:29ZengMDPI AGAlgorithms1999-48932023-09-01161046110.3390/a16100461Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse ProblemChowdhury Abrar Faiyaz0Pabel Shahrear1Rakibul Alam Shamim2Thilo Strauss3Taufiquar Khan4Department of Physics, Shahjalal University of Science and Technology, 3100 Sylhet, BangladeshDepartment of Mathematics, Shahjalal University of Science and Technology, 3114 Sylhet, BangladeshDepartment of Physics, Shahjalal University of Science and Technology, 3100 Sylhet, BangladeshETAS Research, Robert Bosch GMBH, 70469 Stuttgart, GermanyDepartment of Mathematics and Statistics, UNC Charlotte, Charlotte, NC 28223, USAThis 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 <i>R</i><sup>2</sup> 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.https://www.mdpi.com/1999-4893/16/10/461electricalimpedance tomographyradial basis functiondeep learningregularization |
| spellingShingle | Chowdhury Abrar Faiyaz Pabel Shahrear Rakibul Alam Shamim Thilo Strauss Taufiquar Khan Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse Problem Algorithms electricalimpedance tomography radial basis function deep learning regularization |
| title | Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse Problem |
| title_full | Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse Problem |
| title_fullStr | Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse Problem |
| title_full_unstemmed | Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse Problem |
| title_short | Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse Problem |
| title_sort | comparison of different radial basis function networks for the electrical impedance tomography eit inverse problem |
| topic | electricalimpedance tomography radial basis function deep learning regularization |
| url | https://www.mdpi.com/1999-4893/16/10/461 |
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