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Sampling type methods for an inverse waveguide problem
Inverse acoustic obstacle scattering problems using multifrequency measurements
1. | Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria, Austria |
References:
[1] |
H.-D. Alber and A. G. Ramm, Scattering amplitude and algorithm for solving the inverse scattering problem for a class of nonconvex obstacles,, J. Math. Anal. Appl., 117 (1986), 570.
|
[2] |
G. Alessandrini and L. Rondi, Determining a sound-soft polyhedral scatterer by a single far-field measurement,, Proc. Amer. Math. Soc., 133 (2005), 1685.
|
[3] |
H. Ammari, J. Garnier, H. Kang, M. Lim and K. SΦlna, Multistatic imaging of extended targets,, SIAM J. Imaging Sci., 5 (2012), 564. Google Scholar |
[4] |
G. Bao and F. Triki, Error estimates for the recursive linearization of inverse medium problems,, Journal of Computational Mathematics, 28 (2010), 725.
|
[5] |
O. Bucci, L. Crocco, T. Isernia and V. Pascazio, Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,, IEEE Transactions on Geoscience and Remote Sensing, 38 (2000), 1749. Google Scholar |
[6] |
F. Cakoni and D. Colton, "Qualitative Methods in Inverse Scattering Theory. An Introduction,", Interaction of Mechanics and Mathematics, (2006).
|
[7] |
Y. Chen, Inverse scattering via Heisenberg's uncertainty principle,, Inverse Problems, 13 (1997), 253.
|
[8] |
J. Cheng and M. Yamamoto, Global uniqueness in the inverse acoustic scattering problem within polygonal obstacles,, Chinese Ann. Math. Ser. B, 25 (2004), 1.
|
[9] |
W. Chew and J. Lin, A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,, IEEE Microwave and Guided Wave Letters, 5 (1995), 439. Google Scholar |
[10] |
D. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory,", Second edition, 93 (1998).
|
[11] |
D. Colton and B. D. Sleeman, Uniqueness theorems for the inverse problem of acoustic scattering,, IMA J. Appl. Math., 31 (1983), 253.
|
[12] |
G. B. Folland, "Fourier Analysis and its Applications,", The Wadsworth & Brooks/Cole Mathematics Series, (1992).
|
[13] |
D. Gintides, Local uniqueness for the inverse scattering problem in acoustics via the Faber-Krahn inequality,, Inverse Problems, 21 (2005), 1195.
|
[14] |
S. Gutman and A. G. Ramm, Support function method for inverse obstacle scattering problems,, in, (2002), 179.
|
[15] |
F. Hettlich and W. Rundell, A second degree method for nonlinear inverse problems,, SIAM J. Numer. Anal., 37 (2000), 587.
|
[16] |
N. Honda, G. Nakamura and M. Sini, Analytic extension and reconstruction of obstacles from few measurements for elliptic second order operators,, Mathematische Annalen, (2012).
doi: 10.1007/s00208-012-0786-0. |
[17] |
L. Hörmander, "The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis,", Reprint of the second (1990) edition, (1990).
|
[18] |
V. Isakov, "Inverse Problems for Partial Differential Equations,", Second edition, 127 (2006).
|
[19] |
A. Kirsch, The domain derivative and two applications in inverse scattering theory,, Inverse Problems, 9 (1993), 81.
|
[20] |
A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems," Oxford Lecture Series in Mathematics and its Applications, 36,, Oxford University Press, (2008).
|
[21] |
R. Kress, Newton's method for inverse obstacle scattering meets the method of least squares. Special section on imaging,, Inverse Problems, 19 (2003).
|
[22] |
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations,", Cambridge University Press, (2000).
|
[23] |
R. Potthast, A survey on sampling and probe methods for inverse problems,, Inverse Problems, 22 (2006).
|
[24] |
A. G. Ramm, "Multidimensional Inverse Scattering Problems,", Pitman Monographs and Surveys in Pure and Applied Mathematics, 51 (1992).
|
[25] |
E. Sincich and M. Sini, Local stability for soft obstacles by a single measurement,, Inverse Probl. Imaging, 2 (2008), 301.
|
[26] |
P. Stefanov and G. Uhlmann, Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering,, Proc. Amer. Math. Soc., 132 (2004), 1351.
|
show all references
References:
[1] |
H.-D. Alber and A. G. Ramm, Scattering amplitude and algorithm for solving the inverse scattering problem for a class of nonconvex obstacles,, J. Math. Anal. Appl., 117 (1986), 570.
|
[2] |
G. Alessandrini and L. Rondi, Determining a sound-soft polyhedral scatterer by a single far-field measurement,, Proc. Amer. Math. Soc., 133 (2005), 1685.
|
[3] |
H. Ammari, J. Garnier, H. Kang, M. Lim and K. SΦlna, Multistatic imaging of extended targets,, SIAM J. Imaging Sci., 5 (2012), 564. Google Scholar |
[4] |
G. Bao and F. Triki, Error estimates for the recursive linearization of inverse medium problems,, Journal of Computational Mathematics, 28 (2010), 725.
|
[5] |
O. Bucci, L. Crocco, T. Isernia and V. Pascazio, Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,, IEEE Transactions on Geoscience and Remote Sensing, 38 (2000), 1749. Google Scholar |
[6] |
F. Cakoni and D. Colton, "Qualitative Methods in Inverse Scattering Theory. An Introduction,", Interaction of Mechanics and Mathematics, (2006).
|
[7] |
Y. Chen, Inverse scattering via Heisenberg's uncertainty principle,, Inverse Problems, 13 (1997), 253.
|
[8] |
J. Cheng and M. Yamamoto, Global uniqueness in the inverse acoustic scattering problem within polygonal obstacles,, Chinese Ann. Math. Ser. B, 25 (2004), 1.
|
[9] |
W. Chew and J. Lin, A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,, IEEE Microwave and Guided Wave Letters, 5 (1995), 439. Google Scholar |
[10] |
D. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory,", Second edition, 93 (1998).
|
[11] |
D. Colton and B. D. Sleeman, Uniqueness theorems for the inverse problem of acoustic scattering,, IMA J. Appl. Math., 31 (1983), 253.
|
[12] |
G. B. Folland, "Fourier Analysis and its Applications,", The Wadsworth & Brooks/Cole Mathematics Series, (1992).
|
[13] |
D. Gintides, Local uniqueness for the inverse scattering problem in acoustics via the Faber-Krahn inequality,, Inverse Problems, 21 (2005), 1195.
|
[14] |
S. Gutman and A. G. Ramm, Support function method for inverse obstacle scattering problems,, in, (2002), 179.
|
[15] |
F. Hettlich and W. Rundell, A second degree method for nonlinear inverse problems,, SIAM J. Numer. Anal., 37 (2000), 587.
|
[16] |
N. Honda, G. Nakamura and M. Sini, Analytic extension and reconstruction of obstacles from few measurements for elliptic second order operators,, Mathematische Annalen, (2012).
doi: 10.1007/s00208-012-0786-0. |
[17] |
L. Hörmander, "The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis,", Reprint of the second (1990) edition, (1990).
|
[18] |
V. Isakov, "Inverse Problems for Partial Differential Equations,", Second edition, 127 (2006).
|
[19] |
A. Kirsch, The domain derivative and two applications in inverse scattering theory,, Inverse Problems, 9 (1993), 81.
|
[20] |
A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems," Oxford Lecture Series in Mathematics and its Applications, 36,, Oxford University Press, (2008).
|
[21] |
R. Kress, Newton's method for inverse obstacle scattering meets the method of least squares. Special section on imaging,, Inverse Problems, 19 (2003).
|
[22] |
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations,", Cambridge University Press, (2000).
|
[23] |
R. Potthast, A survey on sampling and probe methods for inverse problems,, Inverse Problems, 22 (2006).
|
[24] |
A. G. Ramm, "Multidimensional Inverse Scattering Problems,", Pitman Monographs and Surveys in Pure and Applied Mathematics, 51 (1992).
|
[25] |
E. Sincich and M. Sini, Local stability for soft obstacles by a single measurement,, Inverse Probl. Imaging, 2 (2008), 301.
|
[26] |
P. Stefanov and G. Uhlmann, Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering,, Proc. Amer. Math. Soc., 132 (2004), 1351.
|
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