Truong, Trung; Nguyen, Dinh-Liem; Klibanov, Michael V. Convexification numerical algorithm for a 2D inverse scattering problem with backscatter data. (English) Zbl 07484730 Inverse Probl. Sci. Eng. 29, No. 13, 2656-2675 (2021). MSC: 35R30 78A46 65C20 PDF BibTeX XML Cite \textit{T. Truong} et al., Inverse Probl. Sci. Eng. 29, No. 13, 2656--2675 (2021; Zbl 07484730) Full Text: DOI arXiv OpenURL
Khoa, Vo Anh; Bidney, Grant W.; Klibanov, Michael V.; Nguyen, Loc H.; Nguyen, Lam H.; Sullivan, Anders J.; Astratov, Vasily N. An inverse problem of a simultaneous reconstruction of the dielectric constant and conductivity from experimental backscattering data. (English) Zbl 1478.78033 Inverse Probl. Sci. Eng. 29, No. 5, 712-735 (2021). MSC: 78A46 65N21 35J05 35J65 42B05 78-05 35R30 35Q60 PDF BibTeX XML Cite \textit{V. A. Khoa} et al., Inverse Probl. Sci. Eng. 29, No. 5, 712--735 (2021; Zbl 1478.78033) Full Text: DOI arXiv OpenURL
Thành, Nguyen T.; Klibanov, Michael V. Solving a 1-D inverse medium scattering problem using a new multi-frequency globally strictly convex objective functional. (English) Zbl 1461.35245 J. Inverse Ill-Posed Probl. 28, No. 5, 693-711 (2020). Reviewer: Andreas Kleefeld (Jülich) MSC: 35R30 35J05 78A46 35P25 PDF BibTeX XML Cite \textit{N. T. Thành} and \textit{M. V. Klibanov}, J. Inverse Ill-Posed Probl. 28, No. 5, 693--711 (2020; Zbl 1461.35245) Full Text: DOI arXiv OpenURL
Smirnov, A. V.; Klibanov, M. V.; Sullivan, Anders J.; Nguyen, L. H. Convexification for an inverse problem for a 1D wave equation with experimental data. (English) Zbl 1452.65214 Inverse Probl. 36, No. 9, Article ID 095008, 32 p. (2020). MSC: 65M32 65M30 65M06 65M12 65K10 65J20 35L10 78A45 78A46 78M20 78M50 PDF BibTeX XML Cite \textit{A. V. Smirnov} et al., Inverse Probl. 36, No. 9, Article ID 095008, 32 p. (2020; Zbl 1452.65214) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Kolesov, Aleksandr E. Convexification of a 3-D coefficient inverse scattering problem. (English) Zbl 1442.78007 Comput. Math. Appl. 77, No. 6, 1681-1702 (2019). MSC: 78A46 65N21 PDF BibTeX XML Cite \textit{M. V. Klibanov} and \textit{A. E. Kolesov}, Comput. Math. Appl. 77, No. 6, 1681--1702 (2019; Zbl 1442.78007) Full Text: DOI arXiv OpenURL
Nguyen, Loc H.; Li, Qitong; Klibanov, Michael V. A convergent numerical method for a multi-frequency inverse source problem in inhomogenous media. (English) Zbl 1423.35453 Inverse Probl. Imaging 13, No. 5, 1067-1094 (2019). MSC: 35R30 78A46 PDF BibTeX XML Cite \textit{L. H. Nguyen} et al., Inverse Probl. Imaging 13, No. 5, 1067--1094 (2019; Zbl 1423.35453) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Li, Jingzhi; Zhang, Wenlong Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data. (English) Zbl 1410.65432 Inverse Probl. 35, No. 3, Article ID 035005, 33 p. (2019). MSC: 65N21 65N20 65J20 65K10 65N12 90C52 65N15 78A70 PDF BibTeX XML Cite \textit{M. V. Klibanov} et al., Inverse Probl. 35, No. 3, Article ID 035005, 33 p. (2019; Zbl 1410.65432) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Nguyen, Dinh-Liem; Nguyen, Loc H. A coefficient inverse problem with a single measurement of phaseless scattering data. (English) Zbl 1419.35248 SIAM J. Appl. Math. 79, No. 1, 1-27 (2019). Reviewer: Roland Pulch (Greifswald) MSC: 35R30 65N21 35J05 78A46 PDF BibTeX XML Cite \textit{M. V. Klibanov} et al., SIAM J. Appl. Math. 79, No. 1, 1--27 (2019; Zbl 1419.35248) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Koshev, Nikolay A.; Nguyen, Dinh-Liem; Nguyen, Loc H.; Brettin, Aaron; Astratov, Vasily N. A numerical method to solve a phaseless coefficient inverse problem from a single measurement of experimental data. (English) Zbl 1419.35247 SIAM J. Imaging Sci. 11, No. 4, 2339-2367 (2018). MSC: 35R30 78A46 65C20 PDF BibTeX XML Cite \textit{M. V. Klibanov} et al., SIAM J. Imaging Sci. 11, No. 4, 2339--2367 (2018; Zbl 1419.35247) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Nguyen, Dinh-Liem; Nguyen, Loc H.; Liu, Hui A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data. (English) Zbl 1395.35216 Inverse Probl. Imaging 12, No. 2, 493-523 (2018). MSC: 35R30 78A46 65C20 PDF BibTeX XML Cite \textit{M. V. Klibanov} et al., Inverse Probl. Imaging 12, No. 2, 493--523 (2018; Zbl 1395.35216) Full Text: DOI arXiv OpenURL
Nguyen, Dinh-Liem; Klibanov, Michael V.; Nguyen, Loc H.; Fiddy, Michael A. Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method. (English) Zbl 1393.35288 J. Inverse Ill-Posed Probl. 26, No. 4, 501-522 (2018). MSC: 35R30 78A46 65C20 PDF BibTeX XML Cite \textit{D.-L. Nguyen} et al., J. Inverse Ill-Posed Probl. 26, No. 4, 501--522 (2018; Zbl 1393.35288) Full Text: DOI arXiv OpenURL
Nguyen, Dinh-Liem; Klibanov, Michael V.; Nguyen, Loc H.; Kolesov, Aleksandr E.; Fiddy, Michael A.; Liu, Hui Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm. (English) Zbl 1378.78039 J. Comput. Phys. 345, 17-32 (2017). MSC: 78M25 78A46 78-05 PDF BibTeX XML Cite \textit{D.-L. Nguyen} et al., J. Comput. Phys. 345, 17--32 (2017; Zbl 1378.78039) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Nguyen, Loc H.; Sullivan, Anders; Nguyen, Lam A globally convergent numerical method for a 1-d inverse medium problem with experimental data. (English) Zbl 1355.34040 Inverse Probl. Imaging 10, No. 4, 1057-1085 (2016). MSC: 34A55 78A46 34B05 34B40 PDF BibTeX XML Cite \textit{M. V. Klibanov} et al., Inverse Probl. Imaging 10, No. 4, 1057--1085 (2016; Zbl 1355.34040) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Nguyen, Loc H.; Pan, Kejia Nanostructures imaging via numerical solution of a 3-D inverse scattering problem without the phase information. (English) Zbl 1352.78008 Appl. Numer. Math. 110, 190-203 (2016). MSC: 78A46 92C55 35J05 65N21 78A45 44A12 78M50 35R30 PDF BibTeX XML Cite \textit{M. V. Klibanov} et al., Appl. Numer. Math. 110, 190--203 (2016; Zbl 1352.78008) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Romanov, Vladimir G. Two reconstruction procedures for a 3D phaseless inverse scattering problem for the generalized Helmholtz equation. (English) Zbl 1332.35394 Inverse Probl. 32, No. 1, Article ID 015005, 16 p. (2016). MSC: 35R30 35P25 35J05 78A46 PDF BibTeX XML Cite \textit{M. V. Klibanov} and \textit{V. G. Romanov}, Inverse Probl. 32, No. 1, Article ID 015005, 16 p. (2016; Zbl 1332.35394) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Romanov, Vladimir G. Reconstruction procedures for two inverse scattering problems without the phase information. (English) Zbl 1331.35388 SIAM J. Appl. Math. 76, No. 1, 178-196 (2016). MSC: 35R30 78A46 PDF BibTeX XML Cite \textit{M. V. Klibanov} and \textit{V. G. Romanov}, SIAM J. Appl. Math. 76, No. 1, 178--196 (2016; Zbl 1331.35388) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Thành, Nguyen Trung Recovering dielectric constants of explosives via a globally strictly convex cost functional. (English) Zbl 1328.35315 SIAM J. Appl. Math. 75, No. 2, 518-537 (2015). MSC: 35R30 35L05 78A46 PDF BibTeX XML Cite \textit{M. V. Klibanov} and \textit{N. T. Thành}, SIAM J. Appl. Math. 75, No. 2, 518--537 (2015; Zbl 1328.35315) Full Text: DOI arXiv OpenURL
Beilina, Larisa; Thành, Nguyen Trung; Klibanov, Michael V.; Malmberg, John Bondestam Globally convergent and adaptive finite element methods in imaging of buried objects from experimental backscattering radar measurements. (English) Zbl 1332.78020 J. Comput. Appl. Math. 289, 371-391 (2015). Reviewer: Luis Filipe Pinheiro de Castro (Aveiro) MSC: 78A46 65M30 78M10 PDF BibTeX XML Cite \textit{L. Beilina} et al., J. Comput. Appl. Math. 289, 371--391 (2015; Zbl 1332.78020) Full Text: DOI arXiv OpenURL
Beilina, Larisa; Thành, Nguyen Trung; Klibanov, Michael V.; Malmberg, John Bondestam Methods of quantitative reconstruction of shapes and refractive indices from experimental data. (English) Zbl 1319.78012 Beilina, Larisa (ed.), Inverse problems and applications. Selected papers based on the presentations at the third annual workshop on inverse problems, Stockholm, Sweden, May 2–6, 2013. Cham: Springer (ISBN 978-3-319-12498-8/hbk; 978-3-319-12499-5/ebook). Springer Proceedings in Mathematics & Statistics 120, 13-41 (2015). MSC: 78A46 78A40 35Q61 78A45 78M10 78M20 65M60 65M55 78M50 PDF BibTeX XML Cite \textit{L. Beilina} et al., Springer Proc. Math. Stat. 120, 13--41 (2015; Zbl 1319.78012) Full Text: DOI OpenURL
Nguyen Trung Thành; Beilina, Larisa; Klibanov, Michael V.; Fiddy, Michael A. Imaging of buried objects from experimental backscattering time-dependent measurements using a globally convergent inverse algorithm. (English) Zbl 1432.35259 SIAM J. Imaging Sci. 8, No. 1, 757-786 (2015). MSC: 35R30 35L05 78A46 PDF BibTeX XML Cite \textit{Nguyen Trung Thành} et al., SIAM J. Imaging Sci. 8, No. 1, 757--786 (2015; Zbl 1432.35259) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Romanov, Vladimir G. Explicit formula for the solution of the phaseless inverse scattering problem of imaging of nano structures. (English) Zbl 1328.35314 J. Inverse Ill-Posed Probl. 23, No. 2, 187-193 (2015). MSC: 35R30 78A46 PDF BibTeX XML Cite \textit{M. V. Klibanov} and \textit{V. G. Romanov}, J. Inverse Ill-Posed Probl. 23, No. 2, 187--193 (2015; Zbl 1328.35314) Full Text: DOI OpenURL
Thành, Nguyen Trung; Beilina, Larisa; Klibanov, Michael V.; Fiddy, Michael A. Reconstruction of the refractive index from experimental backscattering data using a globally convergent inverse method. (English) Zbl 1410.78018 SIAM J. Sci. Comput. 36, No. 3, B273-B293 (2014). MSC: 78A46 35L15 35R30 65M32 PDF BibTeX XML Cite \textit{N. T. Thành} et al., SIAM J. Sci. Comput. 36, No. 3, B273--B293 (2014; Zbl 1410.78018) Full Text: DOI arXiv OpenURL
Klibanov, Michael V.; Kamburg, Vladimir G. Uniqueness of a one-dimensional phase retrieval problem. (English) Zbl 1295.78008 Inverse Probl. 30, No. 7, Article ID 075004, 10 p. (2014). MSC: 78A46 65R10 65R32 PDF BibTeX XML Cite \textit{M. V. Klibanov} and \textit{V. G. Kamburg}, Inverse Probl. 30, No. 7, Article ID 075004, 10 p. (2014; Zbl 1295.78008) Full Text: DOI OpenURL
Beilina, Larisa; Thành, Nguyen Trung; Klibanov, Michael V.; Fiddy, Michael A. Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation. (English) Zbl 1292.78011 Inverse Probl. 30, No. 2, Article ID 025002, 24 p. (2014). MSC: 78A46 35J25 65N30 PDF BibTeX XML Cite \textit{L. Beilina} et al., Inverse Probl. 30, No. 2, Article ID 025002, 24 p. (2014; Zbl 1292.78011) Full Text: DOI arXiv OpenURL
Beilina, Larisa; Klibanov, Michael V. Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm. (English) Zbl 1209.78010 Inverse Probl. 26, No. 12, Article ID 125009, 30 p. (2010). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78A40 35R30 65M12 65M32 PDF BibTeX XML Cite \textit{L. Beilina} and \textit{M. V. Klibanov}, Inverse Probl. 26, No. 12, Article ID 125009, 30 p. (2010; Zbl 1209.78010) Full Text: DOI Link OpenURL
Klibanov, Michael V.; Fiddy, Michael A.; Beilina, Larisa; Pantong, Natee; Schenk, John Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem. (English) Zbl 1190.78006 Inverse Probl. 26, No. 4, Article ID 045003, 30 p. (2010). MSC: 78A55 65M12 65M32 65D15 PDF BibTeX XML Cite \textit{M. V. Klibanov} et al., Inverse Probl. 26, No. 4, Article ID 045003, 30 p. (2010; Zbl 1190.78006) Full Text: DOI Link OpenURL
Xin, Jianguo; Klibanov, Michael V. Imaging of land mines by the globally convergent convexification method using a simplified mathematical model. (English) Zbl 1258.78005 Inverse Probl. Sci. Eng. 16, No. 5, 631-653 (2008). MSC: 78A46 86A22 65M32 PDF BibTeX XML Cite \textit{J. Xin} and \textit{M. V. Klibanov}, Inverse Probl. Sci. Eng. 16, No. 5, 631--653 (2008; Zbl 1258.78005) Full Text: DOI OpenURL
Kaltenbacher, Barbara; Klibanov, Michael V. An inverse problem for a nonlinear parabolic equation with applications in population dynamics and magnetics. (English) Zbl 1156.35486 SIAM J. Math. Anal. 39, No. 6, 1863-1889 (2008). MSC: 35R30 65M32 82D40 92D25 78A25 PDF BibTeX XML Cite \textit{B. Kaltenbacher} and \textit{M. V. Klibanov}, SIAM J. Math. Anal. 39, No. 6, 1863--1889 (2008; Zbl 1156.35486) Full Text: DOI OpenURL
Shan, Hua; Klibanov, Michael V.; Liu, Hanli; Pantong, Natee; Su, Jianzhong Numerical implementation of the convexification algorithm for an optical diffusion tomograph. (English) Zbl 1154.35473 Inverse Probl. 24, No. 2, Article ID 025006, 18 p. (2008). MSC: 35R30 65N21 78A25 78A70 92C55 78M25 PDF BibTeX XML Cite \textit{H. Shan} et al., Inverse Probl. 24, No. 2, Article ID 025006, 18 p. (2008; Zbl 1154.35473) Full Text: DOI OpenURL
Klibanov, Michael V.; Timonov, Alexandre A unified framework for constructing globally convergent algorithms for multidimensional coefficient inverse problems. (English) Zbl 1064.35208 Appl. Anal. 83, No. 9, 933-955 (2004). MSC: 35R30 35L15 78M50 78A46 92C55 PDF BibTeX XML Cite \textit{M. V. Klibanov} and \textit{A. Timonov}, Appl. Anal. 83, No. 9, 933--955 (2004; Zbl 1064.35208) Full Text: DOI OpenURL
Timonov, Alexandre; Klibanov, Michael V. An efficient algorithm for solving the inverse problem of locating the interfaces using the frequency sounding data. (English) Zbl 1057.86010 J. Comput. Phys. 183, No. 2, 422-437 (2002). MSC: 86A22 78A46 65N21 86-08 78M20 PDF BibTeX XML Cite \textit{A. Timonov} and \textit{M. V. Klibanov}, J. Comput. Phys. 183, No. 2, 422--437 (2002; Zbl 1057.86010) Full Text: DOI OpenURL
Gryazin, Yuriy A.; Klibanov, Michael V.; Lucas, Thomas R. Numerical solution of a subsurface imaging inverse problem. (English) Zbl 0993.35090 SIAM J. Appl. Math. 62, No. 2, 664-683 (2001). MSC: 35R30 35J05 78A46 65N21 PDF BibTeX XML Cite \textit{Y. A. Gryazin} et al., SIAM J. Appl. Math. 62, No. 2, 664--683 (2001; Zbl 0993.35090) Full Text: DOI OpenURL
Bikov, A. A.; Popov, V. Yu.; Sveshnikov, A. G.; Klibanov, M.; Volkova, I. O.; Tikhonravov, A. V. Resonant scattering of electromagnetic waves by a lossy periodic dielectric waveguide. (English) Zbl 0972.78006 Math. Comput. Modelling 32, No. 9, 1059-1070 (2000). MSC: 78A45 78A50 PDF BibTeX XML Cite \textit{A. A. Bikov} et al., Math. Comput. Modelling 32, No. 9, 1059--1070 (2000; Zbl 0972.78006) Full Text: DOI OpenURL
Gryazin, Yuriy A.; Klibanov, Michael V.; Lucas, Thomas R. GMRES computation of high frequency electrical field propagation in land mine detection. (English) Zbl 0994.78019 J. Comput. Phys. 158, No. 1, 98-115 (2000). MSC: 78M25 78A55 78A46 65N06 65F10 PDF BibTeX XML Cite \textit{Y. A. Gryazin} et al., J. Comput. Phys. 158, No. 1, 98--115 (2000; Zbl 0994.78019) Full Text: DOI OpenURL
Gutman, Semion; Klibanov, Michael V.; Tikhonravov, Alexander V. Global convexity in a single-source 3-D inverse scattering problem. (English) Zbl 0836.35162 IMA J. Appl. Math. 55, No. 3, 281-302 (1995). MSC: 35R30 35P25 92C50 78A45 PDF BibTeX XML Cite \textit{S. Gutman} et al., IMA J. Appl. Math. 55, No. 3, 281--302 (1995; Zbl 0836.35162) Full Text: DOI OpenURL
Tikhonravov, Alexander V.; Klibanov, Michael V.; Zuev, Ilya V. Numerical study of the phaseless inverse scattering problem in thin-film optics. (English) Zbl 0827.35141 Inverse Probl. 11, No. 1, 251-270 (1995). MSC: 35R30 35P25 78A45 PDF BibTeX XML Cite \textit{A. V. Tikhonravov} et al., Inverse Probl. 11, No. 1, 251--270 (1995; Zbl 0827.35141) Full Text: DOI OpenURL
Gutman, Semion; Klibanov, Michael Iterative method for multi-dimensional inverse scattering problems at fixed frequencies. (English) Zbl 0805.35153 Inverse Probl. 10, No. 3, 573-599 (1994). MSC: 35R30 65J20 35P25 78A45 PDF BibTeX XML Cite \textit{S. Gutman} and \textit{M. Klibanov}, Inverse Probl. 10, No. 3, 573--599 (1994; Zbl 0805.35153) Full Text: DOI OpenURL
Klibanov, M. V. On an inverse diffraction problem. (English. Russian original) Zbl 0734.35154 Differ. Equations 26, No. 10, 1323-1329 (1990); translation from Differ. Uravn. 26, No. 10, 1777-1783 (1990). Reviewer: Hou Zongyi (Shanghai) MSC: 35R30 78A45 35J05 PDF BibTeX XML Cite \textit{M. V. Klibanov}, Differ. Equations 26, No. 10, 1323--1329 (1990; Zbl 0734.35154); translation from Differ. Uravn. 26, No. 10, 1777--1783 (1990) OpenURL
Klibanov, M. V. On the determination of a function of compact support from the argument of its Fourier transform. (English. Russian original) Zbl 0662.42006 Sov. Math., Dokl. 34, 121-123 (1987); translation from Dokl. Akad. Nauk SSSR 289, 539-540 (1986). MSC: 42A38 78A45 42A63 PDF BibTeX XML Cite \textit{M. V. Klibanov}, Sov. Math., Dokl. 34, 121--123 (1987; Zbl 0662.42006); translation from Dokl. Akad. Nauk SSSR 289, 539--540 (1986) OpenURL
Klibanov, M. V. Determination of a function with compact support from the absolute value of its Fourier transform, and an inverse scattering problem. (English. Russian original) Zbl 0618.42012 Differ. Equations 22, 1232-1240 (1986); translation from Differ. Uravn. 22, No. 10, 1790-1798 (1986). Reviewer: R.P.Boas MSC: 42B99 78A45 42A38 PDF BibTeX XML Cite \textit{M. V. Klibanov}, Differ. Equations 22, 1232--1240 (1986; Zbl 0618.42012); translation from Differ. Uravn. 22, No. 10, 1790--1798 (1986) OpenURL
Klibanov, M. V. On uniqueness of the determination of a compactly supported function from the modulus of its Fourier transform. (English. Russian original) Zbl 0617.42005 Sov. Math., Dokl. 32, 668-670 (1985); translation from Dokl. Akad. Nauk SSSR 285, 278-280 (1985). Reviewer: D.K.Ugulawa MSC: 42B10 78A45 PDF BibTeX XML Cite \textit{M. V. Klibanov}, Sov. Math., Dokl. 32, 668--670 (1985; Zbl 0617.42005); translation from Dokl. Akad. Nauk SSSR 285, 278--280 (1985) OpenURL