A Bayesian method for an inverse transmission scattering problem in acoustics

References

• Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. 2nd ed. Berlin: Springer-Verlag; 1998. (Applied mathematical sciences).
   Google Scholar
• Hohage T, Schormann C. A Newton-type method for a transmission problem in inverse scattering. Inverse Probl. 1998;14:1207–1227.
   Google Scholar
• Lee KM. Inverse transmission scattering problem via a Dirichlet-to-Neumann map. Eng Anal Bound Elem. 2019;101:214–220.
   Google Scholar
• Ghosh Roy DN, Warner J, Couchman LS, et al. Inverse obstacle transmission problem in acoustics. Inverse Probl. 1998;14:903–929.
   Google Scholar
• Colton D, Coyle J, Monk P. Recent developments in inverse acoustic scattering theory. SIAM Rev. 2000;42:369–414.
   Google Scholar
• Colton D, Kirsch A. A simple method for solving inverse scattering problems in the resonance region. Inverse Probl. 1996;12:383–393.
   Google Scholar
• Colton D, Piana M, Potthast R. A simple method using Morozov's discrepancy principle for solving inverse scattering problems. Inverse Probl. 1997;13:1477–1493.
   Google Scholar
• Yang J, Zhang B, Zhang R. A sampling method for the inverse transmission problem for periodic media. Inverse Probl. 2012;28:Article ID: 035004.
   Google Scholar
• Colton D, Haddar H, Piana M. The linear sampling method in inverse electromagnetic scattering theory. Inverse Probl. 2003;19:S105–S137.
   Google Scholar
• Dashti M, Stuart AM. The Bayesian approach to inverse problems. In: Handbook of uncertainty quantification. Cham: Springer; 2017.
   Google Scholar
• Kaipio JP, Somersalo E. Statistical and computational inverse problems. New York: Springer-Verlag; 2005. (Applied mathematical sciences).
   Google Scholar
• Stuart AM. Inverse problems: A Bayesian perspective. Acta Numer. 2010;5:451–559.
   Google Scholar
• Bui-Thanh T, Ghattas O. An analysis of infinite dimensional Bayesian inverse shape acoustic scattering and its numerical approximation. SIAM/ASA J Uncertain Quantification. 2014;2:203–222.
   Google Scholar
• Huang J, Deng Z, Xu L. Bayesian approach for inverse interior scattering problems with limited aperture. Appl Anal. 2020;1–14. https://doi.org/https://doi.org/10.1080/00036811.2020.1781828.
   Google Scholar
• Li Z, Deng Z, Sun J. Extended-sampling-Bayesian method for limited aperture inverse scattering problems. SIAM J Imag Sci. 2020;13:422–444.
   Google Scholar
• Li Z, Liu Y, Sun J, et al. Quality-Bayesian approach to inverse acoustic source problems with partial data. SIAM J Sci Comput. 2021;43:A1062–A1080.
   Google Scholar
• Liu J, Liu Y, Sun J. An inverse medium problem using Stekloff eigenvalues and a Bayesian approach. Inverse Probl. 2019;35:Article ID: 94004.
   Google Scholar
• Wang Y. Seismic inversion: theory and applications. Hoboken: John Wiley and Sons; 2016.
   Google Scholar
• Wang Y, Ma F, Zheng E. Bayesian method for shape reconstruction in the inverse interior scattering problem. Math Probl Eng. 2015;2:1–12.
   Google Scholar
• Bui-Thanh T, Ghattas O, Martin J, et al. A computational framework for infinite-dimensional Bayesian inverse problems part I: the linearized case, with application to global seismic inversion. SIAM J Sci Comput. 2013;35:A2494–A2523.
   Google Scholar
• Cui T, Law KJH, Marzouk YM. Dimension-independent likelihood-informed MCMC. J Comput Phys. 2016;304:109–137.
   Google Scholar
• Martin J, Wilcox LC, Burstedde C, et al. A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. SIAM J Sci Comput. 2012;34:A1460–A1487.
   Google Scholar
• Petra N, Martin J, Stadler G, et al. A computational framework for infinite-dimensional Bayesian inverse problems, part II: Stochastic Newton MCMC with application to ice sheet flow inverse problems. SIAM J Sci Comput. 2014;36:A1525–A1555.
   Google Scholar
• Archambeau C, Cornford D, Opper M, et al. Gaussian process approximations of stochastic differential equations. In: JMLR: Workshop and Conference Proceedings, Bletchley Park, UK; 2007; 1:1–16.
   Google Scholar
• Arridge SR, Ito K, Jin B, et al. Variational Gaussian approximation for poisson data. Inverse Probl. 2018;34:Article ID: 025005.
   Google Scholar
• Challis E, Barber D. Gaussian Kullback-Leibler approximate inference. J Mach Learn Res. 2013;14:2239–2286.
   Google Scholar
• Cotter SL, Roberts GO, Stuart AM, et al. MCMC methods for functions: modifying old algorithms to make them faster. Statist Sci. 2012;28:424–446.
   Google Scholar
• Hsiao GC, Xu L. A system of boundary integral equations for the transmission problem in acoustics. Appl Numer Math. 2011;61:1017–1029.
   Google Scholar
• Hsiao GC, Wendland WL. Boundary integral equations. Berlin: Springer-Verlag; 2008.
   Google Scholar
• Hairer M. Introduction to stochastic PDEs. 2009. arXiv:0907.4178.
   Google Scholar