{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T23:58:40Z","timestamp":1776470320285,"version":"3.51.2"},"reference-count":63,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,15]],"date-time":"2021-09-15T00:00:00Z","timestamp":1631664000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["MTM2017-84446-C2-1-R"],"award-info":[{"award-number":["MTM2017-84446-C2-1-R"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2020-112796RB-C21"],"award-info":[{"award-number":["PID2020-112796RB-C21"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2020-114173RB-I00."],"award-info":[{"award-number":["PID2020-114173RB-I00."]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Detecting objects hidden in a medium is an inverse problem. Given data recorded at detectors when sources emit waves that interact with the medium, we aim to find objects that would generate similar data in the presence of the same waves. In opposition, the associated forward problem describes the evolution of the waves in the presence of known objects. This gives a symmetry relation: if the true objects (the desired solution of the inverse problem) were considered for solving the forward problem, then the recorded data should be returned. In this paper, we develop a topological derivative-based multifrequency iterative algorithm to reconstruct objects buried in attenuating media with limited aperture data. We demonstrate the method on half-space configurations, which can be related to problems set in the whole space by symmetry. One-step implementations of the algorithm provide initial approximations, which are improved in a few iterations. We can locate object components of sizes smaller than the main components, or buried deeper inside. However, attenuation effects hinder object detection depending on the size and depth for fixed ranges of frequencies.<\/jats:p>","DOI":"10.3390\/sym13091702","type":"journal-article","created":{"date-parts":[[2021,9,15]],"date-time":"2021-09-15T12:00:44Z","timestamp":1631707244000},"page":"1702","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multifrequency Topological Derivative Approach to Inverse Scattering Problems in Attenuating Media"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8623-6521","authenticated-orcid":false,"given":"Ana","family":"Carpio","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Facultad de Matem\u00e1ticas, Universidad Complutense de Madrid, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5787-5252","authenticated-orcid":false,"given":"Mar\u00eda-Luisa","family":"Rap\u00fan","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada a la Ingenier\u00eda Aeroespacial, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,15]]},"reference":[{"key":"ref_1","first-page":"3","article-title":"Ultrasonic tissue characterization: A review","volume":"26","author":"Jones","year":"1984","journal-title":"Acta Electron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1697","DOI":"10.1080\/17415977.2017.1281269","article-title":"Multifrequency near-field acoustic tomography and holography of 3D subbottom inhomogeneities","volume":"25","author":"Gaikovich","year":"2017","journal-title":"Inverse Probl. 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