{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:38:49Z","timestamp":1787323129685,"version":"build-2736575974"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"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\/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\/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"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2308200"],"award-info":[{"award-number":["DMS-2308200"]}],"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":[[2024,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>The Lippmann\u2013Schwinger\u2013Lanczos (LSL) algorithm has recently been shown to provide an efficient tool for imaging and direct inversion of synthetic aperture radar data in multiscattering environments [V. Druskin, S. Moskow, and M. Zaslavsky, SIAM J.\u00a0Imaging Sci., 17 (2024), pp.\u00a0334\u2013350], where the data set is limited to the monostatic, a.k.a. single input\/single output (SISO), measurements. The approach is based on constructing data-driven estimates of internal fields via a reduced order model (ROM) framework and then plugging them into the Lippmann\u2013Schwinger integral equation. However, the approximations of the internal solutions may have more error due to missing the off-diagonal elements of the multiple input\/multiple output (MIMO) matrix valued transfer function. This, in turn, may result in multiple echoes in the image. Here we present a ROM-based data completion algorithm to mitigate this problem. First, we apply the LSL algorithm to the SISO data as in [V. Druskin, S. Moskow, and M. Zaslavsky, SIAM J.\u00a0Imaging Sci., 17 (2024), pp.\u00a0334\u2013350] to obtain approximate reconstructions as well as the estimate of internal field. Next, we use these estimates to calculate a forward Lippmann\u2013Schwinger integral to populate the missing off-diagonal data (the lifting step). Finally, to update the reconstructions, we solve the Lippmann\u2013Schwinger equation using the original SISO data, where the internal fields are constructed from the lifted MIMO data. The steps of obtaining the approximate reconstructions and internal fields and populating the missing MIMO data entries can be repeated for complex models to improve the images even further. Efficiency of the proposed approach is demonstrated on two-dimensional and 2.5-dimensional\u00a0numerical examples, where we see reconstructions are improved substantially.<\/jats:p>","DOI":"10.1137\/24m165778x","type":"journal-article","created":{"date-parts":[[2024,11,11]],"date-time":"2024-11-11T04:00:32Z","timestamp":1731297632000},"page":"2196-2211","source":"Crossref","is-referenced-by-count":1,"title":["ROM Inversion of Monostatic Data Lifted to Full MIMO"],"prefix":"10.1137","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2206-100X","authenticated-orcid":true,"given":"V.","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":"S.","family":"Moskow","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Drexel University, Philadelphia, PA 19104 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Zaslavsky","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Southern Methodist University, Dallas, TX 75205 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,11,11]]},"reference":[{"key":"ref1","unstructured":"J. Baker, E. Cherkaev, V. Druskin, S. Moskow, and M. Zaslavsky, Doubly Regularized Lippmann-Schwinger-Lanczos Algorithm for Inverse Scattering Problems in the Frequency Domain, submitted."},{"key":"ref2","first-page":"55","volume":"60","author":"Borcea L.","year":"2011","journal-title":"Inverse Prob. Appl. Inside Out II Math. Sci. Res. Inst. Publ."},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/19M1296355"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab750b"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/30\/12\/125011"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aabb16"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.12.021"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"L. Borcea, J. Garnier, A. V. Mamonov, and J. Zimmerling, Waveform inversion with a data driven estimate of the internal wave, SIAM J. Imaging Sci., 16 (2023), pp. 280\u2013312, https:\/\/doi.org\/10.1137\/22M1517342.","DOI":"10.1137\/22M1517342"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ac41d0"},{"key":"ref10","first-page":"1","author":"Burfeindt M. J.","year":"2024","journal-title":"IEEE Open J. Antennas Propag."},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719406"},{"key":"ref12","unstructured":"M. Cheney and M. J. Burfeindt, A Procedure for Suppressing Multiple Scattering, NRL\/5340\/MR\u20142021\/7, Naval Research Lab, 2021."},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/17M1133580"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/15M1039432"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/abfca4"},{"key":"ref16","volume":"8","author":"Druskin V.","year":"2022","journal-title":"Inverse Problems"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/23M1564365"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1137\/140973025"},{"key":"ref19","doi-asserted-by":"crossref","unstructured":"P. Kepley, L. Oksanen, and M. V. de Hoop, Generating Virtual Interior Point Source Traveltimes and Redatuming Using Boundary Control, Seg Technical Program Expanded Abstracts, 2016, https:\/\/api.semanticscholar.org\/CorpusID:133142134.","DOI":"10.1190\/segam2016-13966222.1"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/CAMA57522.2023.10352835"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TGRS.2021.3055805"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s42519-020-00149-w"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1190\/1.2434780"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1515\/9783110560855-012"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1080\/00207178008922881"},{"key":"ref26","unstructured":"J. Virieux, An Introduction to Full Waveform Inversion, 2016, https:\/\/api.semanticscholar.org\/CorpusID:204892824."},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ad5b83"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M165778X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:43:30Z","timestamp":1787319810000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M165778X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,11]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,12,31]]}},"alternative-id":["10.1137\/24M165778X"],"URL":"https:\/\/doi.org\/10.1137\/24m165778x","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,11]]}}}