{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T06:27:53Z","timestamp":1774160873011,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,4,26]],"date-time":"2019-04-26T00:00:00Z","timestamp":1556236800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61571321"],"award-info":[{"award-number":["61571321"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006606","name":"Natural Science Foundation of Tianjin City","doi-asserted-by":"publisher","award":["17JCQNJC03500"],"award-info":[{"award-number":["17JCQNJC03500"]}],"id":[{"id":"10.13039\/501100006606","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>An image reconstruction method is proposed based on Lagrange-Newton method for electrical impedance tomography (EIT) and ultrasound tomography (UT) dual-modality imaging. Since the change in conductivity distribution is usually accompanied with the change in acoustic impedance distribution, the reconstruction targets of EIT and UT are unified to the conductivity difference using the same mesh model. Some background medium distribution information obtained from ultrasound transmission and reflection measurements can be used to construct a hard constraint about the conductivity difference distribution. Then, the EIT\/UT dual-modality inverse problem is constructed by an equality constraint equation, and the Lagrange multiplier method combining Newton-Raphson iteration is used to solve the EIT\/UT dual-modality inverse problem. The numerical and experimental results show that the proposed dual-modality image reconstruction method has a better performance than the single-modality EIT method and is more robust to the measurement noise.<\/jats:p>","DOI":"10.3390\/s19091966","type":"journal-article","created":{"date-parts":[[2019,4,26]],"date-time":"2019-04-26T07:52:59Z","timestamp":1556265179000},"page":"1966","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["A Lagrange-Newton Method for EIT\/UT Dual-Modality Image Reconstruction"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6064-6730","authenticated-orcid":false,"given":"Guanghui","family":"Liang","sequence":"first","affiliation":[{"name":"Tianjin Key Laboratory of Process Measurement and Control, School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2220-3856","authenticated-orcid":false,"given":"Shangjie","family":"Ren","sequence":"additional","affiliation":[{"name":"Tianjin Key Laboratory of Process Measurement and Control, School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shu","family":"Zhao","sequence":"additional","affiliation":[{"name":"Institute of Biomedical Engineering, CAMS &amp; PUMC (Chinese Academy of Medical Sciences and Peking Union Medical College), Tianjin 300192, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8478-8928","authenticated-orcid":false,"given":"Feng","family":"Dong","sequence":"additional","affiliation":[{"name":"Tianjin Key Laboratory of Process Measurement and Control, School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/S0955-5986(03)00024-4","article-title":"Application of electrical resistance tomography to two-phase pipe flow parameters measurement","volume":"14","author":"Dong","year":"2003","journal-title":"Flow Meas. 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