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Scr."],"published-print":{"date-parts":[[2025,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The inverse transmission problem of scattering an acoustic wave by a penetrable object has several applications in various fields such as radar, sonar, geophysical exploration, medical imaging and non destructive testing. Here we propose a numerical hybrid method to inverse acoustic scattering by penetrable obstacles from far-field data in two-dimensions, that extends an iterative decomposition method to the transmission problem. The proposed method starts by reconstructing the scattered and interior field by imposing the far-field equation and one of the transmission conditions and, in the second step it uses the second transmission condition to update the position of the approximated boundary, by linearization. Also, we compared two approaches for the linearization step: a Newton-type method; and a gradient-type method with a penalty term for high oscillations of the solution. We also support the methods by a convergence result for a related optimization problem. Numerical results from eight incident directions show the method is feasible, though sensitive to noise.<\/jats:p>","DOI":"10.1088\/1402-4896\/adbc2b","type":"journal-article","created":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T22:53:32Z","timestamp":1741042412000},"page":"045228","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["A hybrid method for the time-harmonic inverse acoustic transmission problem"],"prefix":"10.1088","volume":"100","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-4618-9881","authenticated-orcid":true,"given":"Jo\u00e3o","family":"Paix\u00e3o","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2176-3923","authenticated-orcid":true,"given":"Pedro","family":"Serranho","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2025,3,18]]},"reference":[{"key":"psadbc2bbib1","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/978-1-4614-6393-1","article-title":"A hybrid method for inverse scattering problem for a dielectric","author":"Altundag","year":"2013"},{"key":"psadbc2bbib2","doi-asserted-by":"publisher","first-page":"115\u201325","DOI":"10.17350\/HJSE19030000013","article-title":"A second degree newton method for an inverse scattering problem for a dielectric cylinder","volume":"2","author":"Altundag","year":"2015","journal-title":"Hittite Journal of Science Engineering"},{"key":"psadbc2bbib3","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1515\/jip-2012-0031","article-title":"An iterative method for a two-dimensional inverse scattering problem for a dielectric","volume":"20","author":"Altundag","year":"2012","journal-title":"J. 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