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Inverse acoustic obstacle scattering problems using multifrequency measurements
1.  Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, A4040 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. Google Scholar 
[2] 
G. Alessandrini and L. Rondi, Determining a soundsoft polyhedral scatterer by a single farfield measurement,, Proc. Amer. Math. Soc., 133 (2005), 1685. Google Scholar 
[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. Google Scholar 
[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). Google Scholar 
[7] 
Y. Chen, Inverse scattering via Heisenberg's uncertainty principle,, Inverse Problems, 13 (1997), 253. Google Scholar 
[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. Google Scholar 
[9] 
W. Chew and J. Lin, A frequencyhopping 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). Google Scholar 
[11] 
D. Colton and B. D. Sleeman, Uniqueness theorems for the inverse problem of acoustic scattering,, IMA J. Appl. Math., 31 (1983), 253. Google Scholar 
[12] 
G. B. Folland, "Fourier Analysis and its Applications,", The Wadsworth & Brooks/Cole Mathematics Series, (1992). Google Scholar 
[13] 
D. Gintides, Local uniqueness for the inverse scattering problem in acoustics via the FaberKrahn inequality,, Inverse Problems, 21 (2005), 1195. Google Scholar 
[14] 
S. Gutman and A. G. Ramm, Support function method for inverse obstacle scattering problems,, in, (2002), 179. Google Scholar 
[15] 
F. Hettlich and W. Rundell, A second degree method for nonlinear inverse problems,, SIAM J. Numer. Anal., 37 (2000), 587. Google Scholar 
[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/s0020801207860. Google Scholar 
[17] 
L. Hörmander, "The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis,", Reprint of the second (1990) edition, (1990). Google Scholar 
[18] 
V. Isakov, "Inverse Problems for Partial Differential Equations,", Second edition, 127 (2006). Google Scholar 
[19] 
A. Kirsch, The domain derivative and two applications in inverse scattering theory,, Inverse Problems, 9 (1993), 81. Google Scholar 
[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). Google Scholar 
[21] 
R. Kress, Newton's method for inverse obstacle scattering meets the method of least squares. Special section on imaging,, Inverse Problems, 19 (2003). Google Scholar 
[22] 
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations,", Cambridge University Press, (2000). Google Scholar 
[23] 
R. Potthast, A survey on sampling and probe methods for inverse problems,, Inverse Problems, 22 (2006). Google Scholar 
[24] 
A. G. Ramm, "Multidimensional Inverse Scattering Problems,", Pitman Monographs and Surveys in Pure and Applied Mathematics, 51 (1992). Google Scholar 
[25] 
E. Sincich and M. Sini, Local stability for soft obstacles by a single measurement,, Inverse Probl. Imaging, 2 (2008), 301. Google Scholar 
[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. Google Scholar 
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. Google Scholar 
[2] 
G. Alessandrini and L. Rondi, Determining a soundsoft polyhedral scatterer by a single farfield measurement,, Proc. Amer. Math. Soc., 133 (2005), 1685. Google Scholar 
[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. Google Scholar 
[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). Google Scholar 
[7] 
Y. Chen, Inverse scattering via Heisenberg's uncertainty principle,, Inverse Problems, 13 (1997), 253. Google Scholar 
[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. Google Scholar 
[9] 
W. Chew and J. Lin, A frequencyhopping 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). Google Scholar 
[11] 
D. Colton and B. D. Sleeman, Uniqueness theorems for the inverse problem of acoustic scattering,, IMA J. Appl. Math., 31 (1983), 253. Google Scholar 
[12] 
G. B. Folland, "Fourier Analysis and its Applications,", The Wadsworth & Brooks/Cole Mathematics Series, (1992). Google Scholar 
[13] 
D. Gintides, Local uniqueness for the inverse scattering problem in acoustics via the FaberKrahn inequality,, Inverse Problems, 21 (2005), 1195. Google Scholar 
[14] 
S. Gutman and A. G. Ramm, Support function method for inverse obstacle scattering problems,, in, (2002), 179. Google Scholar 
[15] 
F. Hettlich and W. Rundell, A second degree method for nonlinear inverse problems,, SIAM J. Numer. Anal., 37 (2000), 587. Google Scholar 
[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/s0020801207860. Google Scholar 
[17] 
L. Hörmander, "The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis,", Reprint of the second (1990) edition, (1990). Google Scholar 
[18] 
V. Isakov, "Inverse Problems for Partial Differential Equations,", Second edition, 127 (2006). Google Scholar 
[19] 
A. Kirsch, The domain derivative and two applications in inverse scattering theory,, Inverse Problems, 9 (1993), 81. Google Scholar 
[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). Google Scholar 
[21] 
R. Kress, Newton's method for inverse obstacle scattering meets the method of least squares. Special section on imaging,, Inverse Problems, 19 (2003). Google Scholar 
[22] 
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations,", Cambridge University Press, (2000). Google Scholar 
[23] 
R. Potthast, A survey on sampling and probe methods for inverse problems,, Inverse Problems, 22 (2006). Google Scholar 
[24] 
A. G. Ramm, "Multidimensional Inverse Scattering Problems,", Pitman Monographs and Surveys in Pure and Applied Mathematics, 51 (1992). Google Scholar 
[25] 
E. Sincich and M. Sini, Local stability for soft obstacles by a single measurement,, Inverse Probl. Imaging, 2 (2008), 301. Google Scholar 
[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. Google Scholar 
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