{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T14:56:28Z","timestamp":1776437788187,"version":"3.51.2"},"reference-count":63,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T00:00:00Z","timestamp":1720656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MIUR Progetti di Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2022","award":["2022T3FHLH"],"award-info":[{"award-number":["2022T3FHLH"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We propose an artificial intelligence approach based on deep neural networks to tackle a canonical 2D scalar inverse source problem. The learned singular value decomposition (L-SVD) based on hybrid autoencoding is considered. We compare the reconstruction performance of L-SVD to the Truncated SVD (TSVD) regularized inversion, which is a canonical regularization scheme, to solve an ill-posed linear inverse problem. Numerical tests referring to far-field acquisitions show that L-SVD provides, with proper training on a well-organized dataset, superior performance in terms of reconstruction errors as compared to TSVD, allowing for the retrieval of faster spatial variations of the source. Indeed, L-SVD accommodates a priori information on the set of relevant unknown current distributions. Different from TSVD, which performs linear processing on a linear problem, L-SVD operates non-linearly on the data. A numerical analysis also underlines how the performance of the L-SVD degrades when the unknown source does not match the training dataset.<\/jats:p>","DOI":"10.3390\/s24144496","type":"journal-article","created":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T15:59:48Z","timestamp":1720713588000},"page":"4496","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Learned-SVD Approach to the Electromagnetic Inverse Source Problem"],"prefix":"10.3390","volume":"24","author":[{"given":"Amedeo","family":"Capozzoli","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria Elettrica e delle Tecnologie dell\u2019Informazione (DIETI), Universit\u00e0 di Napoli Federico II, Via Claudio 21, I 80125 Napoli, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9031-9992","authenticated-orcid":false,"given":"Ilaria","family":"Catapano","sequence":"additional","affiliation":[{"name":"Consiglio Nazionale delle Ricerche, Istituto per il Rilevamento Elettromagnetico dell\u2019Ambiente (IREA), Via Diocleziano 328, I 80124 Napoli, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-1588-271X","authenticated-orcid":false,"given":"Eliana","family":"Cinotti","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Elettrica e delle Tecnologie dell\u2019Informazione (DIETI), Universit\u00e0 di Napoli Federico II, Via Claudio 21, I 80125 Napoli, Italy"},{"name":"Consiglio Nazionale delle Ricerche, Istituto per il Rilevamento Elettromagnetico dell\u2019Ambiente (IREA), Via Diocleziano 328, I 80124 Napoli, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7174-0178","authenticated-orcid":false,"given":"Claudio","family":"Curcio","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Elettrica e delle Tecnologie dell\u2019Informazione (DIETI), Universit\u00e0 di Napoli Federico II, Via Claudio 21, I 80125 Napoli, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8806-2895","authenticated-orcid":false,"given":"Giuseppe","family":"Esposito","sequence":"additional","affiliation":[{"name":"Consiglio Nazionale delle Ricerche, Istituto per il Rilevamento Elettromagnetico dell\u2019Ambiente (IREA), Via Diocleziano 328, I 80124 Napoli, Italy"}]},{"given":"Gianluca","family":"Gennarelli","sequence":"additional","affiliation":[{"name":"Consiglio Nazionale delle Ricerche, Istituto per il Rilevamento Elettromagnetico dell\u2019Ambiente (IREA), Via Diocleziano 328, I 80124 Napoli, Italy"}]},{"given":"Angelo","family":"Liseno","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Elettrica e delle Tecnologie dell\u2019Informazione (DIETI), Universit\u00e0 di Napoli Federico II, Via Claudio 21, I 80125 Napoli, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5672-2721","authenticated-orcid":false,"given":"Giovanni","family":"Ludeno","sequence":"additional","affiliation":[{"name":"Consiglio Nazionale delle Ricerche, Istituto per il Rilevamento Elettromagnetico dell\u2019Ambiente (IREA), Via Diocleziano 328, I 80124 Napoli, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0377-3127","authenticated-orcid":false,"given":"Francesco","family":"Soldovieri","sequence":"additional","affiliation":[{"name":"Consiglio Nazionale delle Ricerche, Istituto per il Rilevamento Elettromagnetico dell\u2019Ambiente (IREA), Via Diocleziano 328, I 80124 Napoli, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1088\/0266-5611\/10\/3\/004","article-title":"On the inverse source method of solving inverse scattering problems","volume":"10","author":"Chew","year":"1994","journal-title":"Inv. 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