
Previous Article
Sampling type methods for an inverse waveguide problem
 IPI Home
 This Issue
 Next Article
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. 
[2] 
G. Alessandrini and L. Rondi, Determining a soundsoft polyhedral scatterer by a single farfield 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. 
[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. 
[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 frequencyhopping approach for microwave imaging of large inhomogeneous bodies,, IEEE Microwave and Guided Wave Letters, 5 (1995), 439. 
[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 FaberKrahn 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/s0020801207860. 
[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 soundsoft polyhedral scatterer by a single farfield 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. 
[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. 
[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 frequencyhopping approach for microwave imaging of large inhomogeneous bodies,, IEEE Microwave and Guided Wave Letters, 5 (1995), 439. 
[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 FaberKrahn 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/s0020801207860. 
[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. 
[1] 
Masaru Ikehata, Esa Niemi, Samuli Siltanen. Inverse obstacle scattering with limitedaperture data. Inverse Problems & Imaging, 2012, 6 (1) : 7794. doi: 10.3934/ipi.2012.6.77 
[2] 
Brian Sleeman. The inverse acoustic obstacle scattering problem and its interior dual. Inverse Problems & Imaging, 2009, 3 (2) : 211229. doi: 10.3934/ipi.2009.3.211 
[3] 
François Genoud. Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems  A, 2009, 25 (4) : 12291247. doi: 10.3934/dcds.2009.25.1229 
[4] 
Michele Di Cristo. Stability estimates in the inverse transmission scattering problem. Inverse Problems & Imaging, 2009, 3 (4) : 551565. doi: 10.3934/ipi.2009.3.551 
[5] 
Masaru Ikehata. The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain. Inverse Problems & Imaging, 2016, 10 (1) : 131163. doi: 10.3934/ipi.2016.10.131 
[6] 
Jun Lai, Ming Li, Peijun Li, Wei Li. A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers. Inverse Problems & Imaging, 2018, 12 (3) : 635665. doi: 10.3934/ipi.2018027 
[7] 
Peijun Li, Ganghua Yuan. Increasing stability for the inverse source scattering problem with multifrequencies. Inverse Problems & Imaging, 2017, 11 (4) : 745759. doi: 10.3934/ipi.2017035 
[8] 
Frederic Weidling, Thorsten Hohage. Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems. Inverse Problems & Imaging, 2017, 11 (1) : 203220. doi: 10.3934/ipi.2017010 
[9] 
Ali Fuat Alkaya, Dindar Oz. An optimal algorithm for the obstacle neutralization problem. Journal of Industrial & Management Optimization, 2017, 13 (2) : 835856. doi: 10.3934/jimo.2016049 
[10] 
Ennio Fedrizzi. High frequency analysis of imaging with noise blending. Discrete & Continuous Dynamical Systems  B, 2014, 19 (4) : 979998. doi: 10.3934/dcdsb.2014.19.979 
[11] 
M. Montaz Ali. A recursive topographical differential evolution algorithm for potential energy minimization. Journal of Industrial & Management Optimization, 2010, 6 (1) : 2946. doi: 10.3934/jimo.2010.6.29 
[12] 
T. J. Christiansen. Resonances and balls in obstacle scattering with Neumann boundary conditions. Inverse Problems & Imaging, 2008, 2 (3) : 335340. doi: 10.3934/ipi.2008.2.335 
[13] 
Francesco Demontis, Cornelis Van der Mee. Novel formulation of inverse scattering and characterization of scattering data. Conference Publications, 2011, 2011 (Special) : 343350. doi: 10.3934/proc.2011.2011.343 
[14] 
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa, Akito Suzuki, Kanako Suzuki. Scattering and inverse scattering for nonlinear quantum walks. Discrete & Continuous Dynamical Systems  A, 2018, 38 (7) : 36873703. doi: 10.3934/dcds.2018159 
[15] 
Leonardo Marazzi. Inverse scattering on conformally compact manifolds. Inverse Problems & Imaging, 2009, 3 (3) : 537550. doi: 10.3934/ipi.2009.3.537 
[16] 
Deconinck Bernard, Olga Trichtchenko. Highfrequency instabilities of smallamplitude solutions of Hamiltonian PDEs. Discrete & Continuous Dynamical Systems  A, 2017, 37 (3) : 13231358. doi: 10.3934/dcds.2017055 
[17] 
Guillaume Bal. Homogenization in random media and effective medium theory for high frequency waves. Discrete & Continuous Dynamical Systems  B, 2007, 8 (2) : 473492. doi: 10.3934/dcdsb.2007.8.473 
[18] 
Meng Yu, Jack Xin. Stochastic approximation and a nonlocally weighted softconstrained recursive algorithm for blind separation of reverberant speech mixtures. Discrete & Continuous Dynamical Systems  A, 2010, 28 (4) : 17531767. doi: 10.3934/dcds.2010.28.1753 
[19] 
Peter Monk, Jiguang Sun. Inverse scattering using finite elements and gap reciprocity. Inverse Problems & Imaging, 2007, 1 (4) : 643660. doi: 10.3934/ipi.2007.1.643 
[20] 
Simopekka Vänskä. Stationary waves method for inverse scattering problems. Inverse Problems & Imaging, 2008, 2 (4) : 577586. doi: 10.3934/ipi.2008.2.577 
2016 Impact Factor: 1.094
Tools
Metrics
Other articles
by authors
[Back to Top]