References
- Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. 2nd ed. Berlin: Springer-Verlag; 1998.
- Kirsch A, Grinberg N. The factorization method for inverse problems. Oxford: Oxford University Press; 2008.
- Colton D, Haddar H, Monk P. The linear sampling method for solving the electromagnetic inverse scattering problem. SIAM Journal on Scientific Computing. 2003;24(3):719–731.
- Qin HH, Colton D. The inverse scattering problem for cavities. Adv Comput Math. 2012;36(2):157–174.
- Qin H, Colton D. The inverse scattering problem for cavities with impedance boundary condition. Adv Comput Math. 2012;36(2):157–174.
- Zeng F, Suarez P, Sun J. A decomposition method for an interior inverse scattering problem. Inverse Probl Imaging. 2013;7(1):291–303.
- Karageorghis A, Lesnic D, Marin L. The MFS for the identification of a sound-soft interior acoustic scatterer. Eng Anal Boundary Elements. 2017;83:107–112.
- Jakubik P, Potthast R. Testing the integrity of some cavity the cauchy problem and the range test. Appl Numer Math. 2008;58(6):899–914.
- Qin HH, Cakoni F. Nonlinear integral equations for shape reconstruction in the inverse interior scattering problem. Inverse Probl. 2013;27(3):563–648.
- Liu X. The factorization method for cavities. Inverse Probl. 2014;30(30):430–441.
- Ochs RL. The limited aperture problem of inverse acoustic scattering: Dirichlet boundary conditions. SIAM J Appl Math. 1987;47(6):1320–1341.
- Zinn A. On an optimisation method for the full- and the limited-aperture problem in inverse acoustic scattering for a sound-soft obstacle. Inverse Probl. 1999;5(2):239.
- Bao G, Liu J. Numerical solution of inverse scattering problems with multi-experimental limited aperture data. SIAM J Sci Comput. 2006;25(3):1102–1117.
- Guo Y, Ma F, Zhang D. An optimization method for acoustic inverse obstacle scattering problems with multiple incident waves. Inverse Probl Sci Eng. 2011;19(4):461–484.
- Ji X, Liu X, Xi Y. Direct sampling methods for inverse elastic scattering problems. Inverse Probl. 2018;34(3):035008.
- Liu X, Sun J. Data recovery in inverse scattering: from limited-aperture to full-aperture. J Comput Phys. 2019;386:350–364.
- Stuart AM. Inverse problems: a Bayesian perspective. Acta Numer. 2010;5(19):451–559.
- Michalak AM, Kitanidis PK. A method for enforcing parameter nonnegativity in Bayesian inverse problems with an application to contaminant source identification. Water Resour Res. 2003;39(2):1033.
- Kaipio JP, Kolehmainen V, Somersalo E, et al. Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography. Inverse Probl. 2000;16(5):1487–1522.
- Lasanen S. Non-Gaussian statistical inverse problems. part ii: posterior convergence for approximated unknowns. Inverse Probl Imaging. 2013;6(2):267–287.
- Lasanen S. Non-Gaussian statistical inverse problems. Part I: posterior distributions. Inverse Probl Imaging. 2017;6(2):215–266.
- Dashti M, Stuart AM. The Bayesian approach to inverse problems. Cham, Switzerland: Springer International Publishing; 2016. p. 1–118. (Handbook of Uncertainty Quantification).
- Bui-Thanh T, Ghattas O. Analysis of the Hessian for inverse scattering problems: I. Inverse shape scattering of acoustic waves. Inverse Probl. 2012;28(5):055001.
- Wang Y, Ma F, Zheng E. Bayesian method for shape reconstruction in the inverse interior scattering problem. Math Probl Eng. 2015;2:1–12.
- Bui-Thanh T, Ghattas O. An analysis of infinite dimensional Bayesian inverse shape acoustic scattering and its numerical approximation. Siam/Asa J Uncertainty Quantification. 2014;2(1):203–222.
- Li Z, Liu Y, Sun J, et al. Quality-bayesian approach to inverse acoustic source problems with partial data. arXiv:200404609. 2020.
- Li Z, Deng Z, Sun J. Extended-sampling-Bayesian method for limited aperture inverse scattering problems. SIAM J Imaging Sci. 2020;13(1):422–444.
- Christen JA, Capistrán MA, Daza-Torres ML, et al. Posterior distribution existence and error control in Banach spaces in the Bayesian approach to UQ in inverse problems. arxiv:171203299. 2017.
- Smith AFM, Roberts GO. Bayesian computation via the Gibbs sampler and related Markov Chain Monte Carlo methods. J Royal Statist Soc. 1993;55(1):3–23.
- Cotter SL, Roberts GO, Stuart AM, et al. MCMC methods for functions: modifying old algorithms to make them faster. Statist Sci. 2012;28(3):424–446.
- Jia J, Zhao Q, Meng D, et al. Variational Bayes' method for functions with applications to some inverse problems. arXiv:190703889V1. 2019.
- Jin B. A variational Bayesian method to inverse problems with impulsive noise. J Comput Phys. 2012;231(2):423–435.
- Jin B, Zou J. Hierarchical Bayesian inference for ill-posed problems via variational method. J Comput Phys. 2010;229(19):7317–7343.
- Roberts GO, Smith AFM. Simple conditions for the convergence of the Gibbs sampler and Metropolis–Hastings algorithms. Stoch Process Appl. 1994;49(2):207–216.
- Andrieu C, Freitas ND, Doucet A, et al. An introduction to MCMC for machine learning. Mach Learn. 2003;50(1–2):5–43.
- Colton D, Kress R. Integral equation methods in scattering theory. New York: Society for Industrial & Applied Mathematics; 2014.
- Eppler K. Second derivatives and sufficient optimality conditions for shape functionals. Control Cybernet. 2000;29(2):485–511.
- Knapik BT, van der Vaart AW, van Zanten JH, et al. Bayesian inverse problems with Gaussian priors. Ann Statist. 2011;39(5):2626–2657.
- Lassas M, Saksman E, Siltanen S. Discretization-invariant Bayesian inversion and Besov space priors. Inverse Probl Imaging. 2017;3(1):87–122.
- Dashti M, Harris S, Stuart A. Besov priors for Bayesian inverse problems. arXiv:11050889. 2011.
- Lucka F. Fast Markov Chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors. Inverse Probl. 2012;28(12):2407–2423.
- Ray K. Bayesian inverse problems with non-conjugate priors. Electron J Statist. 2013;7:2516–2549.
- Mohammad-Djafari A, Dumitru M. Bayesian sparse solutions to linear inverse problems with non-stationary noise with student-t priors. Digital Signal Process. 2015;47:128–156.
- Bogachev VI. Gaussian measures. Providence, RI: American Mathematical Society; 1998; Mathematical surveys and monographs, v. 62.
- Hairer M. An introduction to stochastic PDES. arXiv:09074178. 2009.
- Kress R. Integral equation methods in inverse obstacle scattering. Eng Anal Bound Elem. 1995;15(2):171–179.