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The localized basis functions for scalar and vector 3D tomography and their ray transforms
Imaging with electromagnetic waves in terminating waveguides
1. | Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, United States |
References:
[1] |
R. Alonso and L. Borcea, Electromagnetic wave propagation in random waveguides, Multiscale Modeling & Simulation, 13 (2015), 847-889.
doi: 10.1137/130941936. |
[2] |
T. Arens, D. Gintides and A. Lechleiter, Direct and inverse medium scattering problems in a planar 3D waveguide, SIAM J. Appl. Math., 71 (2011), 753-772.
doi: 10.1137/100806333. |
[3] |
A.-S. Bonnet-Bendhia and F. Starling, Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem, Mathematical Methods in the Applied Sciences, 17 (1994), 305-338.
doi: 10.1002/mma.1670170502. |
[4] |
L. Borcea, L. Issa and C. Tsogka, Source localization in random acoustic waveguides, Multiscale Model. Simul., 8 (2010), 1981-2022.
doi: 10.1137/100782711. |
[5] |
L. Borcea and J. Garnier, Paraxial coupling of propagating modes in three-dimensional waveguides with random boundaries, Multiscale Modeling & Simulation, 12 (2014), 832-878.
doi: 10.1137/12089747X. |
[6] |
L. Bourgeois, F. L. Louër and E. Lunéville, On the use of Lamb modes in the linear sampling method for elastic waveguides, Inverse Problems, 27 (2011), 055001, 27pp.
doi: 10.1088/0266-5611/27/5/055001. |
[7] |
L. Bourgeois and E. Lunéville, The linear sampling method in a waveguide: A modal formulation, Inverse Problems, 24 (2008), 015018, 20pp.
doi: 10.1088/0266-5611/24/1/015018. |
[8] |
L. Bourgeois and E. Lunéville, On the use of sampling methods to identify cracks in acoustic waveguides, Inverse Problems, 28 (2012), 105011, 18pp.
doi: 10.1088/0266-5611/28/10/105011. |
[9] |
L. Bourgeois and E. Lunéville, On the use of the linear sampling method to identify cracks in elastic waveguides, Inverse Problems, 29 (2013), 025017, 19pp.
doi: 10.1088/0266-5611/29/2/025017. |
[10] |
S. Dediu and J. R. McLaughlin, Recovering inhomogeneities in a waveguide using eigensystem decomposition, Inverse Problems, 22 (2006), 1227-1246, URL http://stacks.iop.org/0266-5611/22/1227.
doi: 10.1088/0266-5611/22/4/007. |
[11] |
L. Evans, Partial Differential Equations (Graduate Studies in Mathematics vol 19)(Providence, RI: American Mathematical Society), Oxford University Press, 1998. |
[12] |
L. Issa, Source Localization in Cluttered Acoustic Waveguides, PhD thesis, Rice University, 2010. |
[13] |
J. D. Jackson, Classical Electrodynamics, 2nd edition, Wiley New York etc., 1975. |
[14] |
A. K. Jordan and L. S. Tamil, Inverse scattering theory for optical waveguides and devices: Synthesis from rational and nonrational reflection coefficients, Radio Science, 31 (1996), 1863-1876.
doi: 10.1029/96RS02501. |
[15] |
U. Kangro and R. Nicolaides, Divergence boundary conditions for vector helmholtz equations with divergence constraints, ESAIM, Math. Model. Numer. Anal., 33 (1999), 479-492.
doi: 10.1051/m2an:1999148. |
[16] |
A. Kirsch, An integral equation approach and the interior transmission problem for Maxwell's equations, Inverse Probl. Imaging, 1 (2007), 159-179.
doi: 10.3934/ipi.2007.1.159. |
[17] |
W. McLean, Strongly Elliptic Systems and Boundary Integral Operators, Cambridge University Press, Cambridge, UK, 2000. |
[18] |
D. W. Mills and L. S. Tamil, Analysis of planar optical waveguides using scattering data, J. Opt. Soc. Am. A, 9 (1992), 1769-1778.
doi: 10.1364/JOSAA.9.001769. |
[19] |
P. Monk, Finite Element Methods for Maxwell's Equations, Oxford Science Publications, Oxford, 2003.
doi: 10.1093/acprof:oso/9780198508885.001.0001. |
[20] |
P. Monk and V. Selgas, Sampling type methods for an inverse waveguide problem, Inverse Probl. Imaging, 6 (2012), 709-747.
doi: 10.3934/ipi.2012.6.709. |
[21] |
P. Roux and M. Fink, Time reversal in a waveguide: Study of the temporal and spatial focusing, J. Acoust. Soc. Am., 107 (2000), 2418-2429.
doi: 10.1121/1.428628. |
[22] |
K. G. Sabra and D. R. Dowling, Blind deconvolution in ocean waveguides using artificial time reversal, The Journal of the Acoustical Society of America, 116 (2004), 262-271.
doi: 10.1121/1.1751151. |
[23] |
L. S. Tamil and A. K. Jordan, Spectral inverse scattering theory for inhomogeneous dielectric waveguides and devices, Proceedings of the IEEE, 79 (1991), 1519-1528.
doi: 10.1109/5.104226. |
[24] |
C. Tsogka, D. A. Mitsoudis and S. Papadimitropoulos, Selective imaging of extended reflectors in two-dimensional waveguides, SIAM Journal on Imaging Sciences, 6 (2013), 2714-2739.
doi: 10.1137/130924238. |
[25] |
Y. Xu, C. Matawa and W. Lin, Generalized dual space indicator method for underwater imaging, Inverse Problems, 16 (2000), 1761-1776.
doi: 10.1088/0266-5611/16/6/311. |
show all references
References:
[1] |
R. Alonso and L. Borcea, Electromagnetic wave propagation in random waveguides, Multiscale Modeling & Simulation, 13 (2015), 847-889.
doi: 10.1137/130941936. |
[2] |
T. Arens, D. Gintides and A. Lechleiter, Direct and inverse medium scattering problems in a planar 3D waveguide, SIAM J. Appl. Math., 71 (2011), 753-772.
doi: 10.1137/100806333. |
[3] |
A.-S. Bonnet-Bendhia and F. Starling, Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem, Mathematical Methods in the Applied Sciences, 17 (1994), 305-338.
doi: 10.1002/mma.1670170502. |
[4] |
L. Borcea, L. Issa and C. Tsogka, Source localization in random acoustic waveguides, Multiscale Model. Simul., 8 (2010), 1981-2022.
doi: 10.1137/100782711. |
[5] |
L. Borcea and J. Garnier, Paraxial coupling of propagating modes in three-dimensional waveguides with random boundaries, Multiscale Modeling & Simulation, 12 (2014), 832-878.
doi: 10.1137/12089747X. |
[6] |
L. Bourgeois, F. L. Louër and E. Lunéville, On the use of Lamb modes in the linear sampling method for elastic waveguides, Inverse Problems, 27 (2011), 055001, 27pp.
doi: 10.1088/0266-5611/27/5/055001. |
[7] |
L. Bourgeois and E. Lunéville, The linear sampling method in a waveguide: A modal formulation, Inverse Problems, 24 (2008), 015018, 20pp.
doi: 10.1088/0266-5611/24/1/015018. |
[8] |
L. Bourgeois and E. Lunéville, On the use of sampling methods to identify cracks in acoustic waveguides, Inverse Problems, 28 (2012), 105011, 18pp.
doi: 10.1088/0266-5611/28/10/105011. |
[9] |
L. Bourgeois and E. Lunéville, On the use of the linear sampling method to identify cracks in elastic waveguides, Inverse Problems, 29 (2013), 025017, 19pp.
doi: 10.1088/0266-5611/29/2/025017. |
[10] |
S. Dediu and J. R. McLaughlin, Recovering inhomogeneities in a waveguide using eigensystem decomposition, Inverse Problems, 22 (2006), 1227-1246, URL http://stacks.iop.org/0266-5611/22/1227.
doi: 10.1088/0266-5611/22/4/007. |
[11] |
L. Evans, Partial Differential Equations (Graduate Studies in Mathematics vol 19)(Providence, RI: American Mathematical Society), Oxford University Press, 1998. |
[12] |
L. Issa, Source Localization in Cluttered Acoustic Waveguides, PhD thesis, Rice University, 2010. |
[13] |
J. D. Jackson, Classical Electrodynamics, 2nd edition, Wiley New York etc., 1975. |
[14] |
A. K. Jordan and L. S. Tamil, Inverse scattering theory for optical waveguides and devices: Synthesis from rational and nonrational reflection coefficients, Radio Science, 31 (1996), 1863-1876.
doi: 10.1029/96RS02501. |
[15] |
U. Kangro and R. Nicolaides, Divergence boundary conditions for vector helmholtz equations with divergence constraints, ESAIM, Math. Model. Numer. Anal., 33 (1999), 479-492.
doi: 10.1051/m2an:1999148. |
[16] |
A. Kirsch, An integral equation approach and the interior transmission problem for Maxwell's equations, Inverse Probl. Imaging, 1 (2007), 159-179.
doi: 10.3934/ipi.2007.1.159. |
[17] |
W. McLean, Strongly Elliptic Systems and Boundary Integral Operators, Cambridge University Press, Cambridge, UK, 2000. |
[18] |
D. W. Mills and L. S. Tamil, Analysis of planar optical waveguides using scattering data, J. Opt. Soc. Am. A, 9 (1992), 1769-1778.
doi: 10.1364/JOSAA.9.001769. |
[19] |
P. Monk, Finite Element Methods for Maxwell's Equations, Oxford Science Publications, Oxford, 2003.
doi: 10.1093/acprof:oso/9780198508885.001.0001. |
[20] |
P. Monk and V. Selgas, Sampling type methods for an inverse waveguide problem, Inverse Probl. Imaging, 6 (2012), 709-747.
doi: 10.3934/ipi.2012.6.709. |
[21] |
P. Roux and M. Fink, Time reversal in a waveguide: Study of the temporal and spatial focusing, J. Acoust. Soc. Am., 107 (2000), 2418-2429.
doi: 10.1121/1.428628. |
[22] |
K. G. Sabra and D. R. Dowling, Blind deconvolution in ocean waveguides using artificial time reversal, The Journal of the Acoustical Society of America, 116 (2004), 262-271.
doi: 10.1121/1.1751151. |
[23] |
L. S. Tamil and A. K. Jordan, Spectral inverse scattering theory for inhomogeneous dielectric waveguides and devices, Proceedings of the IEEE, 79 (1991), 1519-1528.
doi: 10.1109/5.104226. |
[24] |
C. Tsogka, D. A. Mitsoudis and S. Papadimitropoulos, Selective imaging of extended reflectors in two-dimensional waveguides, SIAM Journal on Imaging Sciences, 6 (2013), 2714-2739.
doi: 10.1137/130924238. |
[25] |
Y. Xu, C. Matawa and W. Lin, Generalized dual space indicator method for underwater imaging, Inverse Problems, 16 (2000), 1761-1776.
doi: 10.1088/0266-5611/16/6/311. |
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