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Imaging Sci."],"published-print":{"date-parts":[[2024,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We consider the inverse scattering problem for time-harmonic acoustic waves in a medium with pointwise inhomogeneities. In the Foldy\u2013Lax model, the estimation of the scatterers\u2019 locations and intensities from far field measurements can be recast as the recovery of a discrete measure from nonlinear observations. We propose a \u201clinearize and locally optimize\u201d approach to perform this reconstruction. We first solve a convex program in the space of measures (known as the Beurling LASSO), which involves a linearization of the forward operator (the far field pattern in the Born approximation). Then, we locally minimize a second functional involving the nonlinear forward map, using the output of the first step as initialization. We provide guarantees that the output of the first step is close to the sought-after measure when the scatterers have small intensities and are sufficiently separated. We also provide numerical evidence that the second step still allows for accurate recovery in settings that are more involved.<\/jats:p>","DOI":"10.1137\/24m1636265","type":"journal-article","created":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T04:16:15Z","timestamp":1721708175000},"page":"1619-1649","source":"Crossref","is-referenced-by-count":1,"title":["Localization of Point Scatterers via Sparse Optimization on Measures"],"prefix":"10.1137","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8612-3663","authenticated-orcid":true,"given":"Giovanni S.","family":"Alberti","sequence":"first","affiliation":[{"name":"MaLGa Center, Department of Mathematics, University of Genoa, Via Dodecaneso 35, 16146 Genoa, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Romain","family":"Petit","sequence":"additional","affiliation":[{"name":"MaLGa Center, Department of Mathematics, University of Genoa, Via Dodecaneso 35, 16146 Genoa, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7257-604X","authenticated-orcid":true,"given":"Matteo","family":"Santacesaria","sequence":"additional","affiliation":[{"name":"MaLGa Center, Department of Mathematics, University of Genoa, Via Dodecaneso 35, 16146 Genoa, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,7,23]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-021-01718-4"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-88201-2"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-022-01896-5"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2019.03.010"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/19M1237259"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5760"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2018.03.007"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/b98245"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/8641"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2014.03.004"},{"key":"ref11","first-page":"1","volume":"18","author":"Bach F.","year":"2017","journal-title":"J. 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