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Bayesian seismic multi-scale inversion in complex Laplace mixed domains
Petroleum Science, 2017 Seismic inversion performed in the time or frequency domain cannot always recover the long-wavelength background of subsurface parameters due to the lack of low-frequency seismic records.
Kun Li, Xing-Yao Yin, Zhao-Yun Zong
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Hierarchical Bayesian level set inversion [PDF]
Statistics and Computing, 2016 The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the quantification of uncertainty within the reconstruction of interfaces. However the Bayesian approach is very sensitive to
Matthew M. Dunlop +2 more
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Generalized Modes in Bayesian Inverse Problems [PDF]
SIAM/ASA Journal on Uncertainty Quantification, 2019 Uncertainty quantification requires efficient summarization of high- or even infinite-dimensional (i.e., non-parametric) distributions based on, e.g., suitable point estimates (modes) for posterior distributions arising from model-specific prior distributions. In this work, we consider non-parametric modes and MAP estimates for priors that do not admit
Christian Clason +3 more
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Structural Gaussian priors for Bayesian CT reconstruction of subsea pipes
Applied Mathematics in Science and Engineering, 2023 A non-destructive testing (NDT) application of X-ray computed tomography (CT) is inspection of subsea pipes in operation via 2D cross-sectional scans. Data acquisition is time-consuming and costly due to the challenging subsea environment. While reducing
Silja L. Christensen +3 more
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Comparison of deterministic and stochastic approaches to crosshole seismic travel-time inversions
Earth and Planetary Physics, 2019 The Bayesian inversion method is a stochastic approach based on the Bayesian theory. With the development of sampling algorithms and computer technologies, the Bayesian inversion method has been widely used in geophysical inversion problems.
YanZhe Zhao, YanBin Wang
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Bayesian spatiotemporal modeling for inverse problems
Statistics and Computing, 2023 38 pages, 23 ...
Shiwei Lan, Shuyi Li, Mirjeta Pasha
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Inverse problems: A Bayesian perspective [PDF]
Acta Numerica, 2010 The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Typically some form of regularization is required to ameliorate ill-posed behaviour.
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Bayesian inversion with α-stable priors
Inverse Problems, 2023 Abstract We propose using Lévy α-stable distributions to construct priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian distributions, with stability indices α = 1, and α = 2, respectively. Our target is to show that these priors
Jarkko Suuronen +3 more
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Bayesian Inference for Inverse Problems [PDF]
AIP Conference Proceedings, 2002 Inverse problems arise everywhere we have indirect measurement. Regularization and Bayesian inference methods are two main approaches to handle inverse problems. Bayesian inference approach is more general and has much more tools for developing efficient methods for difficult problems.
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On the Well-posedness of Bayesian Inverse Problems [PDF]
SIAM/ASA Journal on Uncertainty Quantification, 2020 30 pages, 7 ...
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