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Volumn 53, Issue 3, 2015, Pages 1608-1628

A recursive algorithm for multifrequency acoustic inverse source problems

Author keywords

Helmholtz equation; Inverse source problems; Multiple frequency

Indexed keywords

ACOUSTIC FIELDS; ACOUSTIC NOISE; ALGORITHMS; HELMHOLTZ EQUATION; ITERATIVE METHODS;

EID: 84937872089     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/140993648     Document Type: Article
Times cited : (93)

References (35)
  • 1
    • 84863812534 scopus 로고    scopus 로고
    • On the multi-frequency inverse source problem in heterogeneous media
    • S. Acosta, S. Chow, J. Taylor, and V. Villamizar, On the multi-frequency inverse source problem in heterogeneous media, Inverse Problems, 28 (2012), 075013.
    • (2012) Inverse Problems , vol.28
    • Acosta, S.1    Chow, S.2    Taylor, J.3    Villamizar, V.4
  • 2
    • 78650800558 scopus 로고    scopus 로고
    • Full identification of acoustic sources with multiple frequencies and boundary measurements
    • C. J. S. Alves, N. F. M. Martins, and N. C. Roberty, Full identification of acoustic sources with multiple frequencies and boundary measurements, Inverse Problems Imaging, 3 (2009), pp. 275-294.
    • (2009) Inverse Problems Imaging , vol.3 , pp. 275-294
    • Alves, C.J.S.1    Martins, N.F.M.2    Roberty, N.C.3
  • 3
    • 0036553053 scopus 로고    scopus 로고
    • Inverse source problem for Maxwell's equation in magnetoencephalography
    • H. Ammari, G. Bao, and J. Fleming, Inverse source problem for Maxwell's equation in magnetoencephalography, SIAM J. Appl. Math., 62 (2002), pp. 1369-1382.
    • (2002) SIAM J. Appl. Math , vol.62 , pp. 1369-1382
    • Ammari, H.1    Bao, G.2    Fleming, J.3
  • 5
    • 84880720585 scopus 로고    scopus 로고
    • Resolution and stability analysis in full-aperture, linearized conductivity and wave imaging
    • H. Ammari, J. Garnier, and K. Sølna, Resolution and stability analysis in full-aperture, linearized conductivity and wave imaging, Proc. Amer. Math. Soc., 141 (2013), pp. 3431-3446.
    • (2013) Proc. Amer. Math. Soc , vol.141 , pp. 3431-3446
    • Ammari, H.1    Garnier, J.2    Sølna, K.3
  • 6
    • 0032638277 scopus 로고    scopus 로고
    • Optical tomography in medical imaging
    • S. Arridge, Optical tomography in medical imaging, Inverse Problems, 15 (1999), pp. R41-93.
    • (1999) Inverse Problems , vol.15 , pp. R41-93
    • Arridge, S.1
  • 8
    • 79951798591 scopus 로고    scopus 로고
    • Numerical solution of an inverse medium scattering problem with a stochastic source
    • G. Bao, S. N. Chow, P. Li, and H. Zhou, Numerical solution of an inverse medium scattering problem with a stochastic source, Inverse Problems, 26 (2010), 074014.
    • (2010) Inverse Problems , vol.26
    • Bao, G.1    Chow, S.N.2    Li, P.3    Zhou, H.4
  • 9
    • 84888033208 scopus 로고    scopus 로고
    • An inverse random source problem for the Helmholtz equation
    • G. Bao, S. N. Chow, P. Li, and H. Zhou, An inverse random source problem for the Helmholtz equation, Math. Comp., 83 (2014), pp. 215-233.
    • (2014) Math. Comp , vol.83 , pp. 215-233
    • Bao, G.1    Chow, S.N.2    Li, P.3    Zhou, H.4
  • 10
    • 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
  • 11
    • 78049297003 scopus 로고    scopus 로고
    • A multi-frequency inverse source problem
    • G. Bao, J. Lin, and F. Triki, A multi-frequency inverse source problem, J. Differential Equations, 249 (2010), pp. 3443-3465.
    • (2010) J. Differential Equations , vol.249 , pp. 3443-3465
    • Bao, G.1    Lin, J.2    Triki, F.3
  • 12
    • 84871727944 scopus 로고    scopus 로고
    • Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data
    • G. Bao, J. Lin, and F. Triki, Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data, Contemp. Math., 548 (2011), pp. 45-60.
    • (2011) Contemp. Math , vol.548 , pp. 45-60
    • Bao, G.1    Lin, J.2    Triki, F.3
  • 13
    • 36749117056 scopus 로고
    • Nonuniqueness in the inverse source problem in acoustics and electromagnetics
    • N. Bleistein and J. K. Cohen, Nonuniqueness in the inverse source problem in acoustics and electromagnetics, J. Math. Phys., 18 (1977), pp. 194-201.
    • (1977) J. Math. Phys , vol.18 , pp. 194-201
    • Bleistein, N.1    Cohen, J.K.2
  • 14
    • 0020188742 scopus 로고
    • A survey of the near-field far-field inverse scattering inverse source integral equation
    • N. N. Bojarski, A survey of the near-field far-field inverse scattering inverse source integral equation, IEEE Trans. Antennas Prop., 30 (1982), pp. 975-979.
    • (1982) IEEE Trans. Antennas Prop , vol.30 , pp. 975-979
    • Bojarski, N.N.1
  • 16
    • 85068000760 scopus 로고    scopus 로고
    • Inverse acoustic and electromagnetic scattering theory
    • 3rd ed., Springer, New York
    • D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed., Appl. Math. Sci. 93, Springer, New York, 2010.
    • (2010) Appl. Math. Sci , vol.93
    • Colton, D.1    Kress, R.2
  • 17
    • 0345179899 scopus 로고
    • A note on stopping rules for iterative regularization methods and filtered SVD
    • P. C. Sabatier, ed. Academic Press, New York
    • M. Defrise and C. De Mol, A note on stopping rules for iterative regularization methods and filtered SVD, in Inverse Problems: An Interdisciplinary Study, P. C. Sabatier, ed., Academic Press, New York, 1987, pp. 261-268.
    • (1987) Inverse Problems: An Interdisciplinary Study , pp. 261-268
    • Defrise, M.1    De Mol, C.2
  • 18
    • 0345875999 scopus 로고    scopus 로고
    • A convergence analysis of iterative methods for the solutions of nonlinear ill-posed problems under affinely invariant conditions
    • P. Deuflhard, H. W. Engl, and O. Scherzer, A convergence analysis of iterative methods for the solutions of nonlinear ill-posed problems under affinely invariant conditions, Inverse Problems, 14 (1998), pp. 1081-1106.
    • (1998) Inverse Problems , vol.14 , pp. 1081-1106
    • Deuflhard, P.1    Engl, H.W.2    Scherzer, O.3
  • 19
    • 35349031125 scopus 로고    scopus 로고
    • Inverse source problem in non-homogeneous background media
    • A. J. Devaney, E. Marengo, and M. Li, Inverse source problem in non-homogeneous background media, SIAM J. Appl. Math., 67 (2007), pp. 1353-1378.
    • (2007) SIAM J. Appl. Math , vol.67 , pp. 1353-1378
    • Devaney, A.J.1    Marengo, E.2    Li, M.3
  • 20
    • 33845342497 scopus 로고
    • Radiating and nonradiating classcial current distribution and the fields they generate
    • A. J. Devaney and E. Wolf, Radiating and nonradiating classcial current distribution and the fields they generate, Phys. Rev. D, 8 (1973), pp. 1044-1047.
    • (1973) Phys. Rev. D , vol.8 , pp. 1044-1047
    • Devaney, A.J.1    Wolf, E.2
  • 21
    • 0042430708 scopus 로고    scopus 로고
    • Some remarks on the problem of source identification from boundary measurements
    • A. El Badia and T. H. Duong, Some remarks on the problem of source identification from boundary measurements, Inverse Problems, 14 (1998), pp. 883-891.
    • (1998) Inverse Problems , vol.14 , pp. 883-891
    • El Badia, A.1    Duong, T.H.2
  • 22
    • 70450193186 scopus 로고    scopus 로고
    • Acoustic source identification using multiple frequency information
    • M. Eller and N. P. Valdivia, Acoustic source identification using multiple frequency information, Inverse Problems, 25 (2009), 115005.
    • (2009) Inverse Problems , vol.25
    • Eller, M.1    Valdivia, N.P.2
  • 23
    • 0003277393 scopus 로고    scopus 로고
    • Regularization of inverse problems
    • Kluwer Academic Publishers, Dordrecht
    • H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Math. Appl. 375, Kluwer Academic Publishers, Dordrecht, 1996.
    • (1996) Math. Appl , vol.375
    • Engl, H.W.1    Hanke, M.2    Neubauer, A.3
  • 24
    • 0003323928 scopus 로고
    • Inverse source problems
    • AMS, Providence, RI
    • V. Isakov, Inverse Source Problems, Math. Surveys Monogr. 34, AMS, Providence, RI, 1990.
    • (1990) Math. Surveys Monogr , vol.34
    • Isakov, V.1
  • 25
    • 84872006751 scopus 로고    scopus 로고
    • Subspaces of stability in the Cauchy problem for the Helmholtz equation
    • V. Isakov and S. Kindermann, Subspaces of stability in the Cauchy problem for the Helmholtz equation, Methods Appl. of Anal., 18 (2011), pp. 1-30.
    • (2011) Methods Appl. of Anal , vol.18 , pp. 1-30
    • Isakov, V.1    Kindermann, S.2
  • 26
    • 0022768343 scopus 로고
    • Non-radiating monochromatic sources and their fields
    • K. Kim and E. Wolf, Non-radiating monochromatic sources and their fields, Optics Commun., 59 (1986), pp. 1-6.
    • (1986) Optics Commun , vol.59 , pp. 1-6
    • Kim, K.1    Wolf, E.2
  • 27
    • 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, Appl. Math. Sci. 120, Springer, New York, 2010.
    • (2010) Appl. Math. Sci , vol.120
    • Kirsch, A.1
  • 28
    • 84898063014 scopus 로고    scopus 로고
    • Regularization theory for ill-posed problems. Selected topics
    • De Gruyter, Berlin
    • S. Lu and S. V. Pereverzev, Regularization theory for ill-posed problems. Selected topics, Inverse Ill-posed Probl. Ser. 58, De Gruyter, Berlin, 2013.
    • (2013) Inverse Ill-posed Probl. Ser , vol.58
    • Lu, S.1    Pereverzev, S.V.2
  • 30
    • 55149099625 scopus 로고    scopus 로고
    • Inverse source problems in nonhomogeneous background media: Part II. Vector formulation and antenna substrate performance characterization
    • E. A. Marengo, M. R. Khodja, and A. Bouherif, Inverse source problems in nonhomogeneous background media: Part II. Vector formulation and antenna substrate performance characterization, SIAM J. Appl. Math., 69 (2008), pp. 81-110.
    • (2008) SIAM J. Appl. Math , vol.69 , pp. 81-110
    • Marengo, E.A.1    Khodja, M.R.2    Bouherif, A.3
  • 31
    • 0000099584 scopus 로고    scopus 로고
    • On the radiating and nonradiating components of scalar electromagnetic, and weak gravitational sources
    • E. A. Marengo and R. W. Ziolkowski, On the radiating and nonradiating components of scalar, electromagnetic, and weak gravitational sources, Phys. Rev. Lett., 83 (1999), pp. 3345-3349.
    • (1999) Phys. Rev. Lett , vol.83 , pp. 3345-3349
    • Marengo, E.A.1    Ziolkowski, R.W.2
  • 32
    • 0006297797 scopus 로고
    • Diffraction-limited scalar image formation with holograms of arbitrary shape
    • R. P. Porter, Diffraction-limited scalar image formation with holograms of arbitrary shape, J. Opt. Soc. Am., 60 (1970), pp. 1051-1059.
    • (1970) J. Opt. Soc. Am , vol.60 , pp. 1051-1059
    • Porter, R.P.1
  • 33
    • 0020098945 scopus 로고
    • Holography and the inverse source problem
    • R. P. Porter and A. J. Devaney, Holography and the inverse source problem, J. Opt. Soc. Am., 72 (1982), pp. 327-330.
    • (1982) J. Opt. Soc. Am , vol.72 , pp. 327-330
    • Porter, R.P.1    Devaney, A.J.2
  • 34
    • 79953654399 scopus 로고    scopus 로고
    • Themoacoustic tomography arising in brain imaging
    • P. Stefanov and G. Uhlmann, Themoacoustic tomography arising in brain imaging, Inverse Problems, 27 (2011), 075011.
    • (2011) Inverse Problems , vol.27
    • Stefanov, P.1    Uhlmann, G.2


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