메뉴 건너뛰기




Volumn 8, Issue 1, 2015, Pages 280-298

Inverse obstacle scattering in two dimensions with multiple frequency data and multiple angles of incidence

Author keywords

Acoustics; Inverse scattering; Newton s method; Recursive linearization; Regularization

Indexed keywords

ACOUSTICS; CONSTRAINED OPTIMIZATION; INTEGRAL EQUATIONS; INVERSE PROBLEMS; LINEARIZATION; PROBLEM SOLVING;

EID: 84926374677     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/140982787     Document Type: Article
Times cited : (21)

References (57)
  • 1
    • 0033293734 scopus 로고    scopus 로고
    • Hybrid Gauss-trapezoidal quadrature rules
    • B. K. Alpert, Hybrid Gauss-trapezoidal quadrature rules, SIAM J. Sci. Comput., 20 (1999), pp. 1551-1584.
    • (1999) SIAM J. Sci. Comput , vol.20 , pp. 1551-1584
    • Alpert, B.K.1
  • 2
    • 84889083830 scopus 로고    scopus 로고
    • An O(NlogN) fast direct solver for partial hierarchically semi-separable matrices: With application to radial basis function interpolation
    • S. Ambikasaran and E. Darve, An O(NlogN) fast direct solver for partial hierarchically semi-separable matrices: With application to radial basis function interpolation, J. Sci. Comput., 57 (2013), pp. 477-501.
    • (2013) J. Sci. Comput , vol.57 , pp. 477-501
    • Ambikasaran, S.1    Darve, E.2
  • 4
    • 35348858124 scopus 로고    scopus 로고
    • Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm
    • G. Bao, S. Hou, and P. Li, Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm, J. Comput. Phys., 227 (2007), pp. 755-762.
    • (2007) J. Comput. Phys , vol.227 , pp. 755-762
    • Bao, G.1    Hou, S.2    Li, P.3
  • 5
    • 25444524908 scopus 로고    scopus 로고
    • Inverse medium scattering for the Helmholtz equation at fixed frequency
    • G. Bao and P. Li, Inverse medium scattering for the Helmholtz equation at fixed frequency, Inverse Problems, 21 (2005), pp. 1621-1641.
    • (2005) Inverse Problems , vol.21 , pp. 1621-1641
    • Bao, G.1    Li, P.2
  • 6
    • 25444503549 scopus 로고    scopus 로고
    • Inverse medium scattering problems for electromagnetic waves
    • G. Bao and P. Li, Inverse medium scattering problems for electromagnetic waves, SIAM J. Appl. Math., 65 (2005), pp. 2049-2066.
    • (2005) SIAM J. Appl. Math , vol.65 , pp. 2049-2066
    • Bao, G.1    Li, P.2
  • 7
    • 67349126602 scopus 로고    scopus 로고
    • Numerical solution of an inverse medium scattering problem for Maxwell’s equations at fixed frequency
    • G. Bao and P. Li, Numerical solution of an inverse medium scattering problem for Maxwell’s equations at fixed frequency, J. Comput. Phys., 228 (2009), pp. 4638-4648.
    • (2009) J. Comput. Phys , vol.228 , pp. 4638-4648
    • Bao, G.1    Li, P.2
  • 8
    • 84926307402 scopus 로고    scopus 로고
    • Shape reconstruction of inverse medium scattering for the Helmholtz equation
    • Y. Bai, G. Bao, and J. J. Cao, eds., De Gruyter, Berlin, Boston
    • G. Bao and P. J. Li, Shape reconstruction of inverse medium scattering for the Helmholtz equation, in Computational Methods for Applied Inverse Problems, Y. Bai, G. Bao, and J. J. Cao, eds., De Gruyter, Berlin, Boston, 2012, pp. 283-306.
    • (2012) Computational Methods for Applied Inverse Problems , pp. 283-306
    • Bao, G.1    Li, P.J.2
  • 9
    • 78650206365 scopus 로고    scopus 로고
    • Error estimates for the recursive linearization of inverse medium problems
    • G. Bao and F. Triki, Error estimates for the recursive linearization of inverse medium problems, J. Comput. Math., 28 (2010), pp. 725-744.
    • (2010) J. Comput. Math , vol.28 , pp. 725-744
    • Bao, G.1    Triki, F.2
  • 10
    • 18844431881 scopus 로고    scopus 로고
    • Hierarchical LU decomposition-based preconditioners for BEM
    • M. Bebendorf, Hierarchical LU decomposition-based preconditioners for BEM, Computing, 74 (2005), pp. 225-247.
    • (2005) Computing , vol.74 , pp. 225-247
    • Bebendorf, M.1
  • 11
    • 0018515704 scopus 로고
    • Algorithms for reporting and counting geometric intersections
    • J. L. Bentley and T. A. Ottmann, Algorithms for reporting and counting geometric intersections, IEEE Trans. Comput., 28 (1979), pp. 643-647.
    • (1979) IEEE Trans. Comput , vol.28 , pp. 643-647
    • Bentley, J.L.1    Ottmann, T.A.2
  • 12
    • 84926339881 scopus 로고    scopus 로고
    • Technical Report YALEU/DCS/TR-1480, Department of Computer Science, Yale University, New Haven, CT
    • D. Beylkin and V. Rokhlin, Fitting a Bandlimited Curve to Points in a Plane, Technical Report YALEU/DCS/TR-1480, Department of Computer Science, Yale University, New Haven, CT, 2013.
    • (2013) Fitting a Bandlimited Curve to Points in a Plane
    • Beylkin, D.1    Rokhlin, V.2
  • 14
    • 18844441348 scopus 로고    scopus 로고
    • Lecture note 21/2003, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
    • S. Börm, L. Grasedyck, and W. Hackbusch, Hierarchical matrices, Lecture note 21/2003, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany, 2003; available online from http://www.mis.mpg.de/publications/other-series/ln/lecturenote-2103.html.
    • (2003) Hierarchical Matrices
    • Börm, S.1    Grasedyck, L.2    Hackbusch, W.3
  • 17
    • 55549132964 scopus 로고    scopus 로고
    • Fast computation of Fourier integral operators
    • E. Candès, L. Demanet, and L. Ying, Fast computation of Fourier integral operators, SIAM J. Sci. Comput., 29 (2007), pp. 2464-2493.
    • (2007) SIAM J. Sci. Comput , vol.29 , pp. 2464-2493
    • Candès, E.1    Demanet, L.2    Ying, L.3
  • 19
    • 34547225006 scopus 로고    scopus 로고
    • A fast ULV decomposition solver for hierarchically semiseparable representations
    • S. Chandrasekaran, M. Gu, and T. Pals, A fast ULV decomposition solver for hierarchically semiseparable representations, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 603-622.
    • (2006) SIAM J. Matrix Anal. Appl , vol.28 , pp. 603-622
    • Chandrasekaran, S.1    Gu, M.2    Pals, T.3
  • 20
    • 0000199057 scopus 로고    scopus 로고
    • Inverse scattering via Heisenberg’s uncertainty principle
    • Y. Chen, Inverse scattering via Heisenberg’s uncertainty principle, Inverse Problems, 13 (1997), pp. 253-282.
    • (1997) Inverse Problems , vol.13 , pp. 253-282
    • Chen, Y.1
  • 21
    • 0000978411 scopus 로고    scopus 로고
    • A simple method for solving inverse scattering problems in the resonance region
    • D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, 12 (1996), pp. 383-393.
    • (1996) Inverse Problems , vol.12 , pp. 383-393
    • Colton, D.1    Kirsch, A.2
  • 25
    • 0003315567 scopus 로고    scopus 로고
    • Numerical Methods for Unconstrained Optimization and Nonlinear Equations
    • SIAM, Philadelphia, corrected reprint of the 1983 original
    • J. E. Dennis Jr. and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics Appl. Math. 16, SIAM, Philadelphia, 1996; corrected reprint of the 1983 original.
    • (1996) Classics Appl. Math , vol.16
    • Dennis, J.E.1    Schnabel, R.B.2
  • 26
    • 84858439345 scopus 로고    scopus 로고
    • A direct solver with O(N) complexity for integral equations on one-dimensional domains
    • A. Gillman, P. Young, and P.-G. Martinsson, A direct solver with O(N) complexity for integral equations on one-dimensional domains, Front. Math. China, 7 (2012), pp. 217-247.
    • (2012) Front. Math. China , vol.7 , pp. 217-247
    • Gillman, A.1    Young, P.2    Martinsson, P.-G.3
  • 27
    • 77949624887 scopus 로고    scopus 로고
    • Fast direct solvers for integral equations in complex three-dimensional domains
    • L. Greengard, D. Gueyffier, P.-G. Martinsson, and V. Rokhlin, Fast direct solvers for integral equations in complex three-dimensional domains, Acta Numer., 18 (2009), pp. 243-275.
    • (2009) Acta Numer , vol.18 , pp. 243-275
    • Greengard, L.1    Gueyffier, D.2    Martinsson, P.-G.3    Rokhlin, V.4
  • 29
    • 50249139169 scopus 로고    scopus 로고
    • Corner singularities for elliptic problems: Integral equations, graded meshes, and compressed inverse preconditioning
    • J. Helsing and R. Ojala, Corner singularities for elliptic problems: Integral equations, graded meshes, and compressed inverse preconditioning, J. Comput. Phys., 227 (2008), pp. 8820-8840.
    • (2008) J. Comput. Phys , vol.227 , pp. 8820-8840
    • Helsing, J.1    Ojala, R.2
  • 30
    • 84869743113 scopus 로고    scopus 로고
    • A fast direct solver for structured linear systems by recursive skeletonization
    • K. L. Ho and L. Greengard, A fast direct solver for structured linear systems by recursive skeletonization, SIAM J. Sci. Comput., 34 (2012), pp. A2507-A2532.
    • (2012) SIAM J. Sci. Comput , vol.34 , pp. A2507-A2532
    • Ho, K.L.1    Greengard, L.2
  • 31
    • 0000670255 scopus 로고    scopus 로고
    • Logarithmic convergence rates of the iteratively regularized Gauss-Newton method for an inverse potential and an inverse scattering problem
    • T. Hohage, Logarithmic convergence rates of the iteratively regularized Gauss-Newton method for an inverse potential and an inverse scattering problem, Inverse Problems, 13 (1997), pp. 1279-1299.
    • (1997) Inverse Problems , vol.13 , pp. 1279-1299
    • Hohage, T.1
  • 32
    • 0000035310 scopus 로고    scopus 로고
    • Reconstruction of an obstacle from the scattering amplitude at a fixed frequency
    • M. Ikehata, Reconstruction of an obstacle from the scattering amplitude at a fixed frequency, Inverse Problems, 14 (1998), pp. 949-954.
    • (1998) Inverse Problems , vol.14 , pp. 949-954
    • Ikehata, M.1
  • 33
    • 84973553839 scopus 로고    scopus 로고
    • Inverse Problems for Partial Differential Equations
    • Springer, New York
    • V. Isakov, Inverse Problems for Partial Differential Equations, Appl. Math. Sci. 127, Springer, New York, 1998.
    • (1998) Appl. Math. Sci , pp. 127
    • Isakov, V.1
  • 34
    • 77349110960 scopus 로고    scopus 로고
    • Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle
    • O. Ivanyshyn and T. Johansson, Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle, J. Integral Equations Appl., 19 (2007), pp. 289-308.
    • (2007) J. Integral Equations Appl , vol.19 , pp. 289-308
    • Ivanyshyn, O.1    Johansson, T.2
  • 35
    • 84860523889 scopus 로고    scopus 로고
    • Statistical and Computational Inverse Problems
    • Springer, New York
    • J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Appl. Math. Sci. 160, Springer, New York, 2010.
    • (2010) Appl. Math. Sci , pp. 160
    • Kaipio, J.1    Somersalo, E.2
  • 36
    • 36149033735 scopus 로고
    • The domain derivative and two applications in inverse scattering theory
    • A Kirsch, The domain derivative and two applications in inverse scattering theory, Inverse Problems, 9 (1993), pp. 81-96.
    • (1993) Inverse Problems , vol.9 , pp. 81-96
    • Kirsch, A.1
  • 37
    • 0000714376 scopus 로고    scopus 로고
    • Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
    • A. Kirsch, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, 14 (1998), pp. 1489-1512.
    • (1998) Inverse Problems , vol.14 , pp. 1489-1512
    • Kirsch, A.1
  • 38
    • 85067935824 scopus 로고    scopus 로고
    • An Introduction to the Mathematical Theory of Inverse Problems
    • Springer, New York
    • A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, 2nd ed., Appl. Math. Sci. 120, Springer, New York, 2011.
    • (2011) Appl. Math. Sci , pp. 120
    • Kirsch, A.1
  • 39
    • 0002595876 scopus 로고
    • An optimization method in inverse acoustic scattering
    • (Stuttgart, 1987), Comput. Mech., Southampton, UK
    • A. Kirsch and R. Kress, An optimization method in inverse acoustic scattering, in Boundary Elements IX, Vol. 3 (Stuttgart, 1987), Comput. Mech., Southampton, UK, 1987, pp. 3-18.
    • (1987) Boundary Elements IX , vol.3 , pp. 3-18
    • Kirsch, A.1    Kress, R.2
  • 40
    • 84880800120 scopus 로고    scopus 로고
    • Quadrature by expansion: A new method for the evaluation of layer potentials
    • A. Klöckner, A. Barnett, L. Greengard, and M. O’Neil, Quadrature by expansion: A new method for the evaluation of layer potentials, J. Comput. Phys., 252 (2013), pp. 332-349.
    • (2013) J. Comput. Phys , vol.252 , pp. 332-349
    • Klöckner, A.1    Barnett, A.2    Greengard, L.3    O’Neil, M.4
  • 41
    • 80052954708 scopus 로고    scopus 로고
    • An adaptive fast direct solver for boundary integral equations in two dimensions
    • W. Y. Kong, J. Bremer, and V. Rokhlin, An adaptive fast direct solver for boundary integral equations in two dimensions, Appl. Comput. Harmon. Anal., 31 (2011), pp. 346-369.
    • (2011) Appl. Comput. Harmon. Anal , vol.31 , pp. 346-369
    • Kong, W.Y.1    Bremer, J.2    Rokhlin, V.3
  • 42
    • 0022059920 scopus 로고
    • Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering
    • R. Kress, Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering, Quart. J. Mech. Appl. Math., 38 (1985), pp. 323-341.
    • (1985) Quart. J. Mech. Appl. Math , vol.38 , pp. 323-341
    • Kress, R.1
  • 43
    • 84942912012 scopus 로고    scopus 로고
    • Linear Integral Equations
    • Springer, New York
    • R. Kress, Linear Integral Equations, Appl. Math. Sci. 82, Springer, New York, 1999.
    • (1999) Appl. Math. Sci , vol.82
    • Kress, R.1
  • 44
    • 0346316880 scopus 로고    scopus 로고
    • Newton’s method for inverse obstacle scattering meets the method of least squares
    • R. Kress, Newton’s method for inverse obstacle scattering meets the method of least squares, Inverse Problems, 19 (2003), pp. S91-S104.
    • (2003) Inverse Problems , vol.19 , pp. SS91-S104
    • Kress, R.1
  • 45
    • 34547190693 scopus 로고    scopus 로고
    • Uniqueness and numerical methods in inverse obstacle scattering
    • R. Kress, Uniqueness and numerical methods in inverse obstacle scattering, J. Phys. Conf. Ser., 73 (2007), 012003.
    • (2007) J. Phys. Conf. Ser , vol.73
    • Kress, R.1
  • 46
    • 84893095558 scopus 로고    scopus 로고
    • The Radon Transform and Medical Imaging, CBMS-NSF Regional Conference Ser
    • SIAM, Philadelphia
    • P. Kuchment, The Radon Transform and Medical Imaging, CBMS-NSF Regional Conference Ser. Appl. Math. 85, SIAM, Philadelphia, 2014.
    • (2014) Appl. Math , vol.85
    • Kuchment, P.1
  • 47
    • 16844371628 scopus 로고    scopus 로고
    • A fast direct solver for boundary integral equations in two dimensions
    • P.-G. Martinsson and V. Rokhlin, A fast direct solver for boundary integral equations in two dimensions, J. Comput. Phys., 205 (2005), pp. 1-23.
    • (2005) J. Comput. Phys , vol.205 , pp. 1-23
    • Martinsson, P.-G.1    Rokhlin, V.2
  • 49
    • 75949119619 scopus 로고    scopus 로고
    • An algorithm for the rapid evaluation of special function transforms
    • M. O’Neil, F. Woolfe, and V. Rokhlin, An algorithm for the rapid evaluation of special function transforms, Appl. Comput. Harmon. Anal., 28 (2010), pp. 203-226.
    • (2010) Appl. Comput. Harmon. Anal , vol.28 , pp. 203-226
    • O’Neil, M.1    Woolfe, F.2    Rokhlin, V.3
  • 50
    • 0000459796 scopus 로고    scopus 로고
    • A fast new method to solve inverse scattering problems
    • R. Potthast, A fast new method to solve inverse scattering problems, Inverse Problems, 12 (1996), pp. 731-742.
    • (1996) Inverse Problems , vol.12 , pp. 731-742
    • Potthast, R.1
  • 51
    • 0032182797 scopus 로고    scopus 로고
    • A point source method for inverse acoustic and electromagnetic obstacle scattering problems
    • R. Potthast, A point source method for inverse acoustic and electromagnetic obstacle scattering problems, IMA J. Appl. Math., 61 (1998), pp. 119-140.
    • (1998) IMA J. Appl. Math , vol.61 , pp. 119-140
    • Potthast, R.1
  • 52
    • 0033874167 scopus 로고    scopus 로고
    • Stability estimates and reconstructions in inverse acoustic scattering using singular sources
    • R. Potthast, Stability estimates and reconstructions in inverse acoustic scattering using singular sources, J. Comput. Appl. Math., 114 (2000), pp. 247-274.
    • (2000) J. Comput. Appl. Math , vol.114 , pp. 247-274
    • Potthast, R.1
  • 55
    • 67849126626 scopus 로고    scopus 로고
    • A geometric nonuniform fast Fourier transform
    • I. Sammis and J. Strain, A geometric nonuniform fast Fourier transform, J. Comput. Phys., 228 (2009), pp. 7086-7108.
    • (2009) J. Comput. Phys , vol.228 , pp. 7086-7108
    • Sammis, I.1    Strain, J.2
  • 57
    • 84870180544 scopus 로고    scopus 로고
    • Inverse acoustic obstacle scattering problems using multifrequency measurements
    • M. Sini and N. G. Thành, Inverse acoustic obstacle scattering problems using multifrequency measurements, Inverse Probl. Imaging, 6 (2012), pp. 749-773.
    • (2012) Inverse Probl. Imaging , vol.6 , pp. 749-773
    • Sini, M.1    Thành, N.G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.