{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:32:49Z","timestamp":1760149969527,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T00:00:00Z","timestamp":1695859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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 R2 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.<\/jats:p>","DOI":"10.3390\/a16100461","type":"journal-article","created":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T07:50:26Z","timestamp":1695887426000},"page":"461","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Comparison of Different Radial Basis Function Networks for the Electrical Impedance Tomography (EIT) Inverse Problem"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-3373-4492","authenticated-orcid":false,"given":"Chowdhury Abrar","family":"Faiyaz","sequence":"first","affiliation":[{"name":"Department of Physics, Shahjalal University of Science and Technology, 3100 Sylhet, Bangladesh"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9444-6799","authenticated-orcid":false,"given":"Pabel","family":"Shahrear","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shahjalal University of Science and Technology, 3114 Sylhet, Bangladesh"}]},{"given":"Rakibul Alam","family":"Shamim","sequence":"additional","affiliation":[{"name":"Department of Physics, Shahjalal University of Science and Technology, 3100 Sylhet, Bangladesh"}]},{"given":"Thilo","family":"Strauss","sequence":"additional","affiliation":[{"name":"ETAS Research, Robert Bosch GMBH, 70469 Stuttgart, Germany"}]},{"given":"Taufiquar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, UNC Charlotte, Charlotte, NC 28223, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1137\/S0036144598333613","article-title":"Electrical impedance tomography","volume":"41","author":"Cheney","year":"1999","journal-title":"SIAM Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1088\/0143-0815\/8\/4A\/020","article-title":"Applications of applied potential tomography (APT) in respiratory medicine","volume":"8","author":"Harris","year":"1987","journal-title":"Clin. 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