Reduced order models for inverse problems

Waveform inversion:

• L. Borcea, J. Garnier, A. Mamonov, J. Zimmerling, When data driven reduced order modeling meets full waveform inversion , submitted in February 2023.
• L. Borcea, J. Garnier, A. Mamonov, J. Zimmerling, Waveform inversion with a data driven estimate of the internal wave , SIAM J. Imaging Sciences, 16(1), 2023, p. 280-312.
• L. Borcea, J. Garnier, A. Mamonov, J. Zimmerling, Waveform inversion via reduced order modeling, Geophysics, 88(2), (MARCH-APRIL 2023), p. R175–R191.
• L. Borcea, V. Druskin, A. Mamonov, M Zaslavsky, J. Zimmerling, Reduced Order Model Approach to Inverse Scattering , SIAM Journal on Imaging Sciences 13 (2), 2020, 685-723.

Imaging with waves:

• L. Borcea, J. Garnier, A. Mamonov, J. Zimmerling, Reduced order model approach for imaging with waves, Inverse Problems 38(2), 2022, p. 025004.
• L. Borcea, V. Druskin, A. Mamonov, M. Zaslavsky, Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models, Journal of Computational Physics 381, 2019, p.1-26.
• L. Borcea, V. Druskin, A. Mamonov, M. Zaslavsky, Untangling the nonlinearity in inverse scattering with data-driven reduced order models, Inverse Problems, 34, 2018, p. 065008.

Diffusive inverse problems:

• L. Borcea, V. Druskin, J. Zimmerling, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientific Computing 89(1), 2021, p.1, 36 pp.
• L. Borcea, V. Druskin, A. Mamonov, S. Moskow, M. Zaslavsky, Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data, Inverse Problems 36 (5), 2020, p. 055010.
• L. Borcea, V. Druskin, A. Mamonov, M. Zaslavsky, A model reduction approach to numerical inversion for a parabolic partial differential equation, Inverse Problems 30, 2014, p. 125011.

Inversion on optimal grids:

• L. Borcea, F. Guevara Vasquez, A. Mamonov, A discrete Liouville transform for numerical reconstruction of Schroedinger potentials, Inverse Problems and Imaging, 11 (4), 2017, p. 623-641.
• L. Borcea, F. Guevara Vasquez, A. Mamonov, Study of noise effects in electrical impedance tomography with resistor networks, Inverse Problems and Imaging, 7(2), 2013, p. 417-443.
• L. Borcea, V. Druskin, F. Guevara Vasquez, A. Mamonov, Resistor network approaches to electrical impedance tomography, Inside Out II, MSRI Publications, Volume 60, 2012, p. 55-118.
• L. Borcea, A. Mamonov, V. Druskin, F. Guevara-Vasquez, Pyramidal resistor networks for electrical impedance tomography with partial boundary measurements, Inverse Problems, 26(10), 2010, p. 105009.
• L. Borcea, A. Mamonov, V. Druskin, Circular resistor networks for electrical impedance tomography with partial boundary measurements, Inverse Problems, 26(4), 2010, p. 045010.
• L. Borcea, V. Druskin, F. Guevara Vasquez, Electrical impedance tomography with resistor networks, Inverse Problems, 24(4), 2008, p. 035013.
• L. Borcea, V. Druskin, L. Knizhnerman, On the continuum limit of a discrete inverse spectral problem on optimal finite difference grids , Communications in Pure and Applied Mathematics, 58 (9), 2005, p. 1231-1279.
• L. Borcea, V. Druskin, Optimal finite difference grids for direct and inverse Sturm Liouville problems, Inverse Problems, 18(4), 2002, p.979-1001.

Waves in random media and applications

Waves in random waveguides:

• L. Borcea, J. Garnier, K. Solna, Onset of energy equipartition among surface and body waves, Proceedings of the Royal Society A 477, 2021, 20200775 (28 pages).
• L. Borcea, J. Garnier, Wave propagation in randomly perturbed weakly coupled waveguides, SIAM Multiscale Model. Simul., 18 (1), 2020, p. 44-78.
• L. Borcea, J. Garnier, D. Wood, Transport of power in random waveguides with turning points, Commun. Math. SCI., Vol 15 (8), 2017, p. 2327-2371.
• L. Borcea, J. Garnier, Pulse reflection in a random waveguide with a turning point, SIAM Multiscale Model. Simul., 15(4), 2017, 1472-1501.
• R. Alonso, L. Borcea, Electromagnetic wave propagation in random waveguides, SIAM Multiscale Modeling Simul., 13 (3), 2015, p. 847-889.
• L. Borcea, Imaging and wave propagation in random waveguides, Lecture notes from session ”Etats de la Recherche” at Institut Henri Poincare, Panoramas et Syntheses 44, Societe mathematique de France, 2014, p. 1-61.
• L. Borcea, J. Garnier, Paraxial coupling of propagating modes in three-dimensional waveguides with random boundaries, SIAM Multiscale Modeling Simul., 12(2), 2014, p.832-878.
• R. Alonso, L. Borcea, J. Garnier, Wave propagation in waveguides with random boundaries, Communications in Mathematical Sciences, 11(1), 2013, p. 233-267.

Imaging in random waveguides:

• L. Borcea, J. Garnier, A ghost imaging modality in a random waveguide, Inverse Problems, 34, 2018, p. 124007,.
• S. Acosta, R. Alonso, L. Borcea, Source estimation with incoherent waves in random waveguides, Inverse Problems, 31(3), 2015, p.035013.
• L. Borcea, J. Garnier, C. Tsogka, A quantitative study of source imaging in random waveguides, Comm. Math. Sci, 13(3), 2015, p. 749-776.
• L. Borcea, L. Issa, C. Tsogka, Source localization in random acoustic waveguides, SIAM Multiscale Modeling Simulations, 8(5), 2010, p. 1981-2022.

Beam propagation:

• L. Borcea, J. Garnier, K. Solna, Paraxial wave propagation in random media with long-range correlations, SIAM J. Applied Math, 83 (1), 2023, p. 25-51.
• L. Borcea, J. Garnier, Derivation of a one-way radiative transfer equation in random media, Phys. Rev. E 93, 022115, 2016.
• L. Borcea, J. Garnier, Polarization effects for electromagnetic wave propagation in random media, Wave Motion, 63, 2016, p. 179-208.

Time dependent random media:

• L. Borcea, J. Garnier, K. Solna, Sound propagation in a weakly turbulent flow in a waveguide, SIAM J. Applied Math., 79(6), 2019, 2663–2687.
• L. Borcea, J. Garnier, K. Solna, Wave propagation and imaging in moving media, SIAM Multiscale Model. Simul., 17(1), 2019, p. 31-67.
• L. Borcea, K. Solna, Pulse propagation in time dependent randomly layered media, SIAM Multiscale Model. Simul.,14(1), 2016, p. 265-300.

Filtering scattering effects:

• L. Borcea, F. Gonzales del Cueto, G. Papanicolaou, C. Tsogka, Filtering deterministic layering effects in imaging, SIAM Review, 54 (2012), p. 757-798.
• L. Borcea, , F. Gonzalez del Cueto, G. Papanicolaou, C. Tsogka, Filtering random layering effects in imaging, SIAM Multiscale Model. Simul., 8(3), p. 751-781, 2010.
• L. Borcea, F. Gonzalez del Cueto, G. Papanicolaou, C. Tsogka, Filtering deterministic layering effects in imaging SIAM Multiscale Model. Simul., Vol7, No 3, 2009, p. 1267-1301.

Imaging in random media:

• L. Borcea, J. Garnier, Imaging in random media by two-point coherent interferometry, SIAM Journal on Imaging Sciences 14 (4) (2021), p. 1635-1668.
• L. Borcea, J. Garnier, High-resolution interferometric synthetic aperture imaging in scattering media, SIAM Journal on Imaging Sciences 13 (1), 2020, p. 291-316.
• L. Borcea, Notices of the AMS, Vol 66 (11), December 2019, p. 1800-1812.
• L. Borcea, I. Kocyigit, Passive Array Imaging in Random Media, IEEE Transactions on Computational Imaging, 4(3), 459-469, 2018.
• L. Borcea, I. Kocyigit, Imaging in random media with convex optimization, SIAM J. Imaging Sciences, 10(1), 2017, p. 147-190.
• L. Borcea, G. Papanicolaou, C. Tsogka, Time and direction of arrival detection and filtering for imaging in strongly scattering random media, Waves in Random and Complex Media, 27(4),2017, p. 1-26.
• L. Borcea, W. Li, A. Mamonov, J. Schotland, Second-Harmonic imaging in random media, Inverse Problems, 33(6), 2017, p. 065004.
• L. Borcea, J. Garnier, G. Papanicolaou, C. Tsogka, Enhanced statistical stability in coherent interferometric imaging, Inverse Problems, 27(8), 2011, p. 085003.
• L. Borcea, G. Papanicolaou, C. Tsogka, Adaptive time-frequency detection and filtering for imaging in heavy clutter, SIAM Imaging Science, 4(3), 2011, p. 827-849.
• L. Borcea, J. Garnier, G. Papanicolaou, C. Tsogka, Coherent Interferometric Imaging, Time Gating, and Beamforming, Inverse Problems, 27(6), 2011, p. 065008.
• R. Alonso, L. Borcea, G. Papanicolaou, C. Tsogka, Detection and Imaging in strongly backscattering randomly layered media, Inverse Problems, 27(2), 2011, p. 025004.
• L. Borcea, G. Papanicolaou, C. Tsogka, Optimal illumination and waveform design for imaging in random media, JASA, 122, 2007, p. 3507-3518.
• L. Borcea, G. Papanicolaou, C. Tsogka, Optimal waveform design for array imaging, Inverse Problems 23, 2007, p. 1973-2021.
• L. Borcea, G. Papanicolaou, C. Tsogka, Asymptotics for the space-time Wigner transform with applications to imaging), In Stochastic Differential Equations: Theory and Applications. Volume in Honor of Professor Boris L. Rozovskii, P.H. Baxendale and S.V. Lototsky, Editors, Interdisciplinary Mathematical Sciences, vol 2, World Scientific, 2007.
• L. Borcea, G. Papanicolaou, C. Tsogka, Adaptive interferometric imaging in clutter and optimal illumination , Inverse Problems, Inverse Problems, 22, 2006, p. 1405-1436.
• L. Borcea, G. Papanicolaou, C. Tsogka, Coherent interferometry in finely layered random media, SIAM Multiscale Modeling and Simulation, 5(1), 2006, p. 62-83.
• L. Borcea, G. Papanicolaou, C. Tsogka, Interferometric array imaging in clutter, Inverse Problems 21, 2005, p. 1419-1460.
• L. Borcea, G. Papanicolaou, C. Tsogka, Coherent interferometric imaging , Geophysics, 71, 2006, p. S1165-S1175.
• L. Borcea, G. Papanicolaou, C. Tsogka, Theory and applications of time reversal and interferometric imaging, Inverse Problems, 19, 2003, p. 1-26.
• L. Borcea, G. Papanicolaou, C. Tsogka, A resolution study for imaging and time reversal in random media, Contemporary Math, 333, 2003, p. 63--77.
• L. Borcea, G. Papanicolaou, C. Tsogka, J. Berryman, Imaging and time reversal in random media, Inverse Problems, 18, No. 5, 2002, p. 1247-1279.
• J. Berryman, L. Borcea, G. Papanicolaou, C. Tsogka., Statistically stable ultrasonic imaging in random media, Journal of Acoustical Soc. of America, 112, 2002, p. 1509--1522.

Laser applications in random media:

• L. Borcea, J. Garnier, Laser beam imaging from the speckle pattern of the off-axis scattered intensity, SIAM J. Appl. Math., 78(2), 2018, p. 677-704.
• L. Borcea, J. Garnier, K. Solna, Multimode communication through the turbulent atmosphere, JOSA A 37 (5), 2020, p. 720-730.

Other inverse problems

Electrical impedance tomography:

• L. Borcea, G. Gray, Y. Zhang, Variationally Constrained Numerical Solution of Electrical Impedance Tomography , Inverse Problems, 19(5), 2003, p. 1159--1184.
• L. Borcea, Electrical Impedance Tomography, Topical review , Inverse Problems, 18, No. 6, 2002, p. R99-R136 and the addendum .
• L. Borcea, , Nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency, Inverse Problems, 17, No. 2, 2001, p. 329-359.
• L. Borcea, M. Ortiz, A multiscattering series for impedance tomography in layered media Inverse Problems, 15(2), 1999, p. 515-540.

Synthetic aperture radar:

• L. Borcea, I. Kocyigit, A Multiple Measurement Vector Approach to Synthetic Aperture Radar Imaging, SIAM J. Imaging Sciences, 11(1), 2018, p. 770-801.
• L. Borcea, J. Garnier, G. Papanicolaou, K. Solna, C. Tsogka, Resolution analysis of passive synthetic aperture imaging of fast moving objects, SIAM Imaging Sciences, 10(2), 2017, p. 665-710.
• L. Borcea, J. Garnier, Robust imaging with electromagnetic waves in noisy environments , Inverse Problems, 32(10), p. 105010.
• L. Borcea, M. Moscoso, G. Papanicolaou, C. Tsogka, Synthetic aperture imaging of direction and frequency dependent reflectivities , SIAM J. Imaging Sci., 9(1), 2016, p. 52–81.
• L. Borcea, T. Callaghan, G. Papanicolaou, Motion estimation and imaging of complex scenes with synthetic aperture radar, Inverse Problems, 29(5), 2013, p. 05401.
• L. Borcea, T. Callaghan, G. Papanicolaou, Synthetic Aperture Radar Imaging and Motion Estimation via Robust Principal Component Analysis, SIAM Imaging Science, 6(3), 2013, P. 1445-1476.
• L. Borcea, T. Callaghan, G. Papanicolaou, Synthetic Aperture Radar Imaging with Motion Estimation and Autofocus, Inverse Problems, 28(4), 2012, p. 045006.

Qualitative methods:

• L. Borcea, S. Meng, Factorization method versus migration imaging in a waveguide, Inverse Problems 35(12), 2019, p. 124006.
• L. Borcea, F. Cakoni, S. Meng, A direct approach to imaging in a waveguide with perturbed geometry, Journal of Computational Physics 392, 2019, p.556-577.
• L. Borcea, D.-L. Nguyen, Imaging with electromagnetic waves in terminating waveguides, Inverse problems and imaging, 10, 2016, p.915-941.

Optimization approaches:

• L. Borcea, I. Kocyigit, Resolution analysis of imaging with l1 optimization, SIAM J. Imaging Sciences, 8(4), 2015, p. 3015-3050.
• L. Borcea, T. Callaghan, J. Garnier, G. Papanicolaou, A universal filter for enhanced imaging with small arrays, Inverse Problems, 26(1), 2010, 015006(29pp).
• L. Borcea, G. Papanicolaou, F. Guevara Vasquez, Edge illumination and imaging of extended reflectors, SIAM Imaging Sciences, Vol1, No. 1, p. 75-114, 2008.

High contrast media

• L. Borcea, Y. Gorb, Y. Wang, Asymptotic approximation of the Dirichlet to Neumann map of high contrast conductive media, SIAM Multiscale Modeling Simul., 12(4), 2014, p.1494-1532.
• L. Berlyand, L. Borcea, A. Panchenko, Network approximation for effective viscosity of concentrated suspensions with complex geometry, SIAM Journal on Mathematical Analysis, 36(5), 2005, p. 1580-1628.
• L. Borcea, O. Bruno, On the magneto-elastic properties of elastomer-ferromagnet composites, Journal of the Mechanics and Physics of Solids, Vol. 49, No. 12, 2001, p. 2877-2919.
• L. Borcea, G. Papanicolaou, Low frequency electromagnetic fields in high contrast media, Surveys on Solution Methods for Inverse Problems, D. Colton, H. W. Engl, A. Louis, J. R. McLaughlin, W. Rundell editors, Springer Vienna/New York, 2000.
• L. Borcea, J. Berryman, G. Papanicolaou, Matching pursuit for imaging high contrast conductivities, Inverse Problems 15(4), 1999, p. 811-849.
• L. Borcea, Asymptotic Analysis of Quasistatic Transport in High Contrast Conductive Media, SIAM J. Applied Math., 59(2), 1999, p. 597-639.
• L. Borcea, G. Papanicolaou, Network approximation for transport properties of high contrast materials, SIAM J. Applied Math., 58(2), 1998, p. 501-539.
• L. Borcea, G. Papanicolaou, A Hybrid Numerical Method for High Contrast Conductivity Problems , 1997, Journal of Computational and Applied Mathematics 87, no. 1, p. 61-77.
• L. Borcea, J. Berryman, G. Papanicolaou, High Contrast Impedance Tomography, Inverse Problems 12(6), 1996, p. 835-858.