{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T16:51:37Z","timestamp":1777135897736,"version":"3.51.4"},"reference-count":55,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T00:00:00Z","timestamp":1771200000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2208159"],"award-info":[{"award-number":["DMS-2208159"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers &amp; Mathematics with Applications"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1016\/j.camwa.2026.02.012","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T12:32:53Z","timestamp":1771936373000},"page":"129-143","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Solving the inverse scattering problem via Carleman-based contraction mapping"],"prefix":"10.1016","volume":"209","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-1856-6162","authenticated-orcid":false,"given":"Phuong M.","family":"Nguyen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0172-8816","authenticated-orcid":false,"given":"Loc H.","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-8123-909X","authenticated-orcid":false,"given":"Huong T.T.","family":"Vu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.camwa.2026.02.012_bib0001","series-title":"Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data","author":"Abney","year":"2023"},{"key":"10.1016\/j.camwa.2026.02.012_bib0002","series-title":"I","first-page":"23","volume":"784","author":"Le","year":"2023"},{"issue":"2","key":"10.1016\/j.camwa.2026.02.012_bib0003","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1515\/jiip-2020-0028","article-title":"A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral cauchy data","volume":"30","author":"Le","year":"2022","journal-title":"J. Inverse Ill-Posed Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0004","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s40306-023-00500-w","article-title":"The Carleman contraction mapping method for quasilinear elliptic equations with over-determined boundary data","volume":"48","author":"Nguyen","year":"2023","journal-title":"Acta Math. Vietnam."},{"key":"10.1016\/j.camwa.2026.02.012_bib0005","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1137\/15M1043959","article-title":"Phased and phaseless domain reconstruction in inverse scattering problem via scattering coefficients","volume":"76","author":"Ammari","year":"2016","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/j.camwa.2026.02.012_bib0006","article-title":"Mathematical and Statistical Methods for Multistatic Imaging","volume":"2098","author":"Ammari","year":"2013"},{"key":"10.1016\/j.camwa.2026.02.012_bib0007","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1137\/100812501","article-title":"Stability and resolution analysis for a topological derivative based imaging functional","volume":"50","author":"Ammari","year":"2012","journal-title":"SIAM J. Control Optim."},{"key":"10.1016\/j.camwa.2026.02.012_bib0008","series-title":"Reconstruction of Small Inhomogeneities from Boundary Measurements","volume":"1846","author":"Ammari","year":"2004"},{"key":"10.1016\/j.camwa.2026.02.012_bib0009","article-title":"Analysis of the Hessian for inverse scattering problems: i. inverse shape scattering of acoustic waves","volume":"28","author":"Bui-Thanh","year":"2012","journal-title":"Inverse Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0010","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1017\/S0956792505006182","article-title":"A survey on level set methods for inverse problems and optimal design","volume":"16","author":"Burger","year":"2005","journal-title":"European J. of Appl. Math."},{"key":"10.1016\/j.camwa.2026.02.012_bib0011","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1088\/0266-5611\/12\/4\/003","article-title":"A simple method for solving inverse scattering problems in the resonance region","volume":"12","author":"Colton","year":"1996","journal-title":"Inverse Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0012","doi-asserted-by":"crossref","first-page":"B722","DOI":"10.1137\/19M129783X","article-title":"Orthogonality sampling method for the electromagnetic inverse scattering problem","volume":"42","author":"Harris","year":"2020","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.camwa.2026.02.012_bib0013","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1088\/0266-5611\/14\/6\/009","article-title":"Characterization of the shape of a scattering obstacle using the spectral data of the far field operator","volume":"14","author":"Kirsch","year":"1998","journal-title":"Inverse Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0014","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/j.jcp.2013.09.048","article-title":"Enhanced multilevel linear sampling methods for inverse scattering problems","volume":"257","author":"Li","year":"2014","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.camwa.2026.02.012_bib0015","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1137\/13093409X","article-title":"Locating multiple multiscale acoustic scatterers","volume":"12","author":"Li","year":"2014","journal-title":"SIAM Multiscale Model. Simul."},{"key":"10.1016\/j.camwa.2026.02.012_bib0016","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1515\/jiip-2020-0114","article-title":"Imaging of bi-anisotropic periodic structures from electromagnetic near field data","volume":"30","author":"Nguyen","year":"2022","journal-title":"J. Inverse Ill-Posed Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0017","series-title":"Synthetic Aperture Radar Signal Processing with MATLAB Algorithms","author":"Soumekh","year":"1999"},{"key":"10.1016\/j.camwa.2026.02.012_bib0018","series-title":"Iterative Methods for Approximate Solutions of Inverse Problems","author":"Bakushinskii","year":"2004"},{"key":"10.1016\/j.camwa.2026.02.012_bib0019","article-title":"Analysis of the Hessian for inverse scattering problems: II. inverse medium scattering of acoustic waves","volume":"28","author":"Bui-Thanh","year":"2012","journal-title":"Inverse Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0020","article-title":"Nonlinear Least Squares for Inverse Problems: Theoretical Foundations and Step-by-Step Guide for Applications, Scientic Computation","author":"Chavent","year":"2009"},{"key":"10.1016\/j.camwa.2026.02.012_bib0021","article-title":"Regularization of Inverse Problems, Mathematics and its Applications","author":"Engl","year":"1996"},{"key":"10.1016\/j.camwa.2026.02.012_bib0022","series-title":"Supercomputer technologies in inverse problems of ultrasound tomography, Inverse Probl","first-page":"075004","volume":"29","author":"Goncharsky","year":"2013"},{"key":"10.1016\/j.camwa.2026.02.012_bib0023","series-title":"Numerical Methods for the Solution of Ill-Posed Problems","author":"Tikhonov","year":"1995"},{"key":"10.1016\/j.camwa.2026.02.012_bib0024","series-title":"Mathematical Methods for Wave Phenomena","author":"Bleistein","year":"1984"},{"key":"10.1016\/j.camwa.2026.02.012_bib0025","series-title":"Waves and Fields in Inhomogeneous Media","author":"Chew","year":"1990"},{"key":"10.1016\/j.camwa.2026.02.012_bib0026","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139047838","article-title":"Mathematical Foundations of Imaging, Tomography and Wavefield Inversion","author":"Devaney","year":"2012"},{"key":"10.1016\/j.camwa.2026.02.012_bib0027","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1080\/00036811.2016.1188286","article-title":"Remarks on the born approximation and the factorization method","volume":"96","author":"Kirsch","year":"2017","journal-title":"Appl. Anal."},{"key":"10.1016\/j.camwa.2026.02.012_bib0028","series-title":"Basic Methods of Tomography and Inverse Problems","first-page":"127","article-title":"Applied inverse problems for acoustic, electromagnetic and elastic wave scattering","author":"Langenberg","year":"1987"},{"key":"10.1016\/j.camwa.2026.02.012_bib0029","doi-asserted-by":"crossref","DOI":"10.1088\/0266-5611\/24\/6\/065005","article-title":"Convergence and stability of the inverse born series for diffuse waves","volume":"24","author":"Moskow","year":"2008","journal-title":"Inverse Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0030","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1088\/0266-5611\/21\/5\/007","article-title":"Inverse medium scattering for the Helmholtz equation at fixed frequency","volume":"21","author":"Bao","year":"2005","journal-title":"Inverse Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0031","doi-asserted-by":"crossref","first-page":"2049","DOI":"10.1137\/040607435","article-title":"Inverse medium scattering problems for electromagnetic waves","volume":"65","author":"Bao","year":"2005","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/j.camwa.2026.02.012_bib0032","doi-asserted-by":"crossref","DOI":"10.1088\/0266-5611\/31\/9\/093001","article-title":"Inverse scattering problems with multi-frequencies","volume":"31","author":"Bao","year":"2015","journal-title":"Inverse Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0033","series-title":"Inverse scattering via heisenberg\u2019s uncertainty principle. Inverse Probl","first-page":"253","volume":"13","author":"Chen","year":"1997"},{"key":"10.1016\/j.camwa.2026.02.012_bib0034","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/ab95aa","article-title":"Convexification and experimental data for a 3D inverse scattering problem with the moving point source","volume":"36","author":"Khoa","year":"2020","journal-title":"Inverse Probl."},{"issue":"5","key":"10.1016\/j.camwa.2026.02.012_bib0035","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1080\/17415977.2020.1802447","article-title":"An inverse problem of a simultaneous reconstruction of the dielectric constant and conductivity from experimental backscattering data","volume":"29","author":"Khoa","year":"2021","journal-title":"Inverse Probl. Sci. Eng."},{"issue":"2","key":"10.1016\/j.camwa.2026.02.012_bib0036","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1137\/19M1303101","article-title":"Convexification for a 3D inverse scattering problem with the moving point source","volume":"13","author":"Khoa","year":"2020","journal-title":"SIAM J. Imaging Sci."},{"key":"10.1016\/j.camwa.2026.02.012_bib0037","series-title":"Applied Mathematical Sciences","article-title":"Inverse acoustic and electromagnetic scattering theory","author":"Colton","year":"2013"},{"key":"10.1016\/j.camwa.2026.02.012_bib0038","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1137\/S0036141093244039","article-title":"Uniform strict convexity of a cost functional for three-dimensional inverse scattering problem","volume":"26","author":"Klibanov","year":"1995","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/j.camwa.2026.02.012_bib0039","doi-asserted-by":"crossref","first-page":"1579","DOI":"10.3934\/ipi.2021068","article-title":"Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data","volume":"16","author":"Klibanov","year":"2022","journal-title":"Inverse Probl. Imaging"},{"key":"10.1016\/j.camwa.2026.02.012_bib0040","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/18M1168303","article-title":"A coefficient inverse problem with a single measurement of phaseless scattering data","volume":"79","author":"Klibanov","year":"2019","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/j.camwa.2026.02.012_bib0041","first-page":"223","article-title":"A h\u00f6lder stability estimate for a 3D coefficient inverse problem for a hyperbolic equation with a plane wave","volume":"31","author":"Klibanov","year":"2023","journal-title":"J. Inverse Ill-Posed Probl."},{"issue":"5","key":"10.1016\/j.camwa.2026.02.012_bib0042","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1515\/jiip-2017-0067","article-title":"Convexification of restricted dirichlet to neumann map","volume":"25","author":"Klibanov","year":"2017","journal-title":"J. Inverse and Ill-Posed Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0043","series-title":"Technical Report","article-title":"The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients","author":"Le","year":"2023"},{"key":"10.1016\/j.camwa.2026.02.012_bib0044","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.camwa.2022.10.021","article-title":"The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations","volume":"128","author":"Nguyen","year":"2022","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0045","series-title":"Cloaking using Complementary Media for the Helmholtz Equation and a Three Spheres Inequality for Second Order Elliptic Equations","volume":"2","author":"Nguyen","year":"2015"},{"key":"10.1016\/j.camwa.2026.02.012_bib0046","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.camwa.2022.08.032","article-title":"A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications","volume":"125","author":"Le","year":"2022","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0047","series-title":"Shishat\u202f\u00b7\u202fPLXski\u012d. Ill-Posed Problems of Mathematical Physics and Analysis. Translations of Mathematical Monographs","author":"Lavrent\u2019ev","year":"1986"},{"key":"10.1016\/j.camwa.2026.02.012_bib0048","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-7805-9","article-title":"Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems","author":"Beilina","year":"2012"},{"key":"10.1016\/j.camwa.2026.02.012_bib0049","first-page":"244","article-title":"Uniqueness in the large of a class of multidimensional inverse problems","volume":"17","author":"Bukhgeim","year":"1981","journal-title":"Soviet Math. Doklady"},{"key":"10.1016\/j.camwa.2026.02.012_bib0050","series-title":"Inverse Problems and Carleman Estimates: Global Uniqueness, Global Convergence and Experimental Data","author":"Klibanov","year":"2021"},{"key":"10.1016\/j.camwa.2026.02.012_bib0051","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/aafe8f","article-title":"An inverse space-dependent source problem for hyperbolic equations and the Lipschitz-like convergence of the quasi-reversibility method","volume":"35","author":"Nguyen","year":"2019","journal-title":"Inverse Probl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0052","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2021.110828","article-title":"Numerical viscosity solutions to Hamilton-Jacobi equations via a Carleman estimate and the convexification method","volume":"451","author":"Klibanov","year":"2022","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.camwa.2026.02.012_bib0053","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.3934\/ipi.2019048","article-title":"A convergent numerical method for a multi-frequency inverse source problem in inhomogenous media","volume":"13","author":"Nguyen","year":"2019","journal-title":"Inverse Probl. Imaging"},{"key":"10.1016\/j.camwa.2026.02.012_bib0054","doi-asserted-by":"crossref","first-page":"2135","DOI":"10.1016\/j.camwa.2020.09.010","article-title":"A new algorithm to determine the creation or depletion term of parabolic equations from boundary measurements","volume":"80","author":"Nguyen","year":"2020","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.camwa.2026.02.012_bib0055","first-page":"232","article-title":"A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem","volume":"38","author":"Nguyen","year":"2020","journal-title":"J. Inverse Ill-Posed Probl."}],"container-title":["Computers &amp; Mathematics with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122126000805?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122126000805?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T02:40:27Z","timestamp":1775616027000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0898122126000805"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":55,"alternative-id":["S0898122126000805"],"URL":"https:\/\/doi.org\/10.1016\/j.camwa.2026.02.012","relation":{},"ISSN":["0898-1221"],"issn-type":[{"value":"0898-1221","type":"print"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Solving the inverse scattering problem via Carleman-based contraction mapping","name":"articletitle","label":"Article Title"},{"value":"Computers & Mathematics with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.camwa.2026.02.012","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}]}}