{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T01:40:15Z","timestamp":1787362815906,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-192928"],"award-info":[{"award-number":["DMS-192928"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-20-1-0079"],"award-info":[{"award-number":["FA9550-20-1-0079"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2110773"],"award-info":[{"award-number":["DMS-2110773"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA955020-1-0079"],"award-info":[{"award-number":["FA955020-1-0079"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2008441"],"award-info":[{"award-number":["DMS-2008441"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2024,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of inverse scattering problems with applications to seismic and sonar imaging. One requirement of this approach is that it uses the full square multiple-input\/multiple-output (MIMO) matrix-valued transfer function as the data for multidimensional problems. The synthetic aperture radar (SAR), however, is limited to the single-input\/single-output (SISO) measurements corresponding to the diagonal of the matrix transfer function. Here we present a ROM-based Lippmann\u2013Schwinger approach overcoming this drawback. The ROMs are constructed to match the data for each source-receiver pair separately, and these are used to construct internal solutions for the corresponding source using only the data-driven Gramian. Efficiency of the proposed approach is demonstrated on 2D and 2.5D (3D propagation and 2D reflectors) numerical examples. The new algorithm not only suppresses multiple echoes seen in the Born imaging but also takes advantage of their illumination of some back sides of the reflectors, improving the quality of their mapping.<\/jats:p>","DOI":"10.1137\/23m1564365","type":"journal-article","created":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T04:02:18Z","timestamp":1707364938000},"page":"334-350","source":"Crossref","is-referenced-by-count":4,"title":["Reduced Order Modeling Inversion of Monostatic Data in a Multi-scattering Environment"],"prefix":"10.1137","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2206-100X","authenticated-orcid":true,"given":"Vladimir","family":"Druskin","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8240-7247","authenticated-orcid":true,"given":"Shari","family":"Moskow","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Drexel University, Philadelphia, PA 19104 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikhail","family":"Zaslavsky","sequence":"additional","affiliation":[{"name":"Schlumberger-Doll Research Center, Cambridge, MA 02139-1578 USA, and Department of Mathematics, Southern Methodist University, Dallas, TX 75205 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,2,8]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974829.ch7"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/18\/4\/303"},{"key":"ref3","series-title":"Math. Sci. Res. Inst. Publ. 60","first-page":"55","volume-title":"Inverse Problems and Applications: Inside Out II","author":"Borcea L.","year":"2013"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20073"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/19M1296355"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab750b"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/30\/12\/125011"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aabb16"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.12.021"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-021-01616-7"},{"key":"ref11","unstructured":"L. Borcea, J. Garnier, A. V. Mamonov, and J. Zimmerling, Waveform Inversion with a Data Driven Estimate of the Internal Wave, preprint, https:\/\/arxiv.org\/abs\/2208.11051, 2022."},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1190\/geo2022-0070.1"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/22M1517342"},{"key":"ref14","doi-asserted-by":"crossref","unstructured":"L. Borcea, J. Garnier, A. V. Mamonov, and J. T. Zimmerling, Reduced Order Model Approach for Imaging with Waves, https:\/\/arxiv.org\/abs\/2108.01609, 2021.","DOI":"10.1088\/1361-6420\/ac41d0"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997330792"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/17M1133580"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/15M1039432"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/abfca4"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ac7a59"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/16M1083633"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/6\/065005"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1190\/1.1500380"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/23M1564365","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:28:30Z","timestamp":1787318910000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1564365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,8]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,3,31]]}},"alternative-id":["10.1137\/23M1564365"],"URL":"https:\/\/doi.org\/10.1137\/23m1564365","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,8]]}}}