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Stability estimates for the inverse source problem with passive measurements

  • *Corresponding author: Faouzi Triki

    *Corresponding author: Faouzi Triki 

This work was funded by the by The Villum Foundation (grant no. 25893)

Abstract / Introduction Full Text(HTML) Related Papers Cited by
  • We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part of the radiated field on the boundary for multiple frequencies. The proof combines a spectral decomposition with a quantification of the unique continuation of the resolvent as a holomorphic function of the frequency. The obtained results show that the inverse problem is well posed when the frequency band is larger than the spatial frequency of the source.

    Mathematics Subject Classification: Primary: 34A55.

    Citation:

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  • [1] S. AcostaS. ChowJ. Taylor and V. Villamizar, On the multi-frequency inverse source problem in heterogeneous media, Inverse Problems, 28 (2012), 075013. 
    [2] K. Ammari and F. Triki, On weak observability for evolution systems with skew-adjoint generators, SIAM Journal on Mathematical Analysis, 52 (2020), 1884-1902.  doi: 10.1137/19M1241830.
    [3] H. Ammari and H. Zhang, Super-resolution in high-contrast media, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471 (2015), 20140946. 
    [4] G. BaoP. LiJ. Lin and F. Triki, Inverse scattering problems with multi-frequencies, Inverse Problems, 31 (2015), 093001. 
    [5] G. BaoJ. Lin and F. Triki, A multi-frequency inverse source problem, Journal of Differential Equations, 249 (2010), 3443-3465.  doi: 10.1016/j.jde.2010.08.013.
    [6] G. Bao, J. Lin, F. Triki et al., Numerical solution of the inverse source problem for the helmholtz equation with multiple frequency data, Contemp. Math, 548 (2011), 45-60.
    [7] G. Bao and F. Triki, Stability for the multifrequency inverse medium problem, Journal of Differential Equations, 269 (2020), 7106-7128.  doi: 10.1016/j.jde.2020.05.021.
    [8] J. ChengV. Isakov and S. Lu, Increasing stability in the inverse source problem with many frequencies, Journal of Differential Equations, 260 (2016), 4786-4804.  doi: 10.1016/j.jde.2015.11.030.
    [9] M. N. Entekhabi and V. Isakov, On increasing stability in the two dimensional inverse source scattering problem with many frequencies, Inverse Problems, 34 (2018), 055005. 
    [10] J. GarnierH. Haddar and H. Montanelli, The linear sampling method for random sources, SIAM J. Imaging Sci., 16 (2023), 1572-1593. 
    [11] J. Garnier and  G. PapanicolaouPassive Imaging with Ambient Noise, Cambridge University Press, 2016. 
    [12] A. Henrot, Eigenvalues of elliptic operators, Extremum Problems for Eigenvalues of Elliptic Operators, 1-16.
    [13] P. LiJ. Zhai and Y. Zhao, Stability for the acoustic inverse source problem in inhomogeneous media, SIAM Journal on Applied Mathematics, 80 (2020), 2547-2559.  doi: 10.1137/20M1334267.
    [14] W. C. H. McLeanStrongly Elliptic Systems and Boundary Integral Equations, Cambridge university press, 2000. 
    [15] R. Nevanlinna, H. Behnke, H. Grauert, L. V. Ahlfors, D. C. Spencer, L. Bers, K. Kodaira, M. Heins and J. A. Jenkins, Analytic Functions, vol. 11, Springer, 1970.
    [16] A. Osses and F. Triki, An improved spectral inequality for sums of eigenfunctions, arXiv e-prints, arXiv–2312.
    [17] F. Triki and C.-H. Tsou, Inverse inclusion problem: A stable method to determine disks, Journal of Differential Equations, 269 (2020), 3259-3281.  doi: 10.1016/j.jde.2020.02.028.
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