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We introduce a level set based approach to Bayesian geometric inverse problems.
An inverse problem for the steady state diffusion equation
G. R. Richter · 1981
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On the identification of the leading coefficient of an elliptic equation
G. Alessandrini · 1985
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Inverse Source Problems
V. Isakov · 1990
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Motion of level sets by mean curvature I
L.C. Evansand and J. Spruck · 1991
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A computed example of nonuniqueness of mean curvature flow in ℝ 3 \mathbb{R}^{3}
T. Ilmanen S. Angenent and D. L. Chopp · 1995
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Regularization of Inverse Problems
H. W. Engl, M. Hanke, and A. Neubauer · 1996
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Iterative methods for the reconstruction of an inverse potential problem
F. Hettlich and W. Rundell · 1996
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A level-set approach for inverse problems involving obstacles
F. Santosa · 1996
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Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences
T. Arbogast, M. F. Wheeler, and I. Yotov · 1997
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A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems
M. Hanke · 1997
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Gaussian Measures
V. I. Bogachev · 1998
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General methods for monitoring convergence of iterative simulations
S.P. Brooks and A. Gelman · 1998
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Level set methods, with an application to modeling the growth of thin films
B. Merriman, R. Caflisch, and S. Osher · 1998
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A level set method for inverse problems
M. Burger · 2001
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Electrical impedance tomography
L. Borcea · 2002
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A multiphase level set framework for image segmentation using the mumford-shah model
L. A. Vese and T. F. Chan · 2002
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A framework for the construction of level set methods for shape optimization and reconstruction
M. Burger · 2003
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Level set methods for geometric inverse problems in linear elasticity
H. B. Ameur, M. Burger, and B. Hackl · 2004
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A survey on multiple level set methods with applications for identifying piecewise constant functions
X. C. Tai and T. F. Chan · 2004
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A survey on level set methods for inverse problems and optimal design
M. Burger and S. Osher · 2005
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Electrical impedance tomography using level set representation and total variational regularization
An iterative representer-based scheme for data inversion in reservoir modeling
M. A. Iglesias and C. Dawson · 2009
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Real Analysis : Measure Theory, Integration, and Hilbert Spaces
E. M. Stein and R. Shakarchi · 2009
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Inverse problems: A Bayesian perspective
A. M. Stuart · 2010
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Plurigaussian Simulations in Geosciences
M. Armstrong, A. Galli, H. Beucher, G. Le Loc’h, D. Renard, B. Doligez, R. Eschard, and F. Geffroy · 2011
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Level-set techniques for facies identification in reservoir modeling
M. A. Iglesias and D. McLaughlin · 2011
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Uncertainty quantification in history matching of channelized reservoirs using markov chain level set approaches
J. Xie, Y. Efendiev, A. Datta-Gupta, et al · 2011
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E. T. Chung, T. F. Chan, and X. C. Tai · 2005
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Statistical and Computational Inverse Problems
J. P. Kaipio and E. Somersalo · 2005
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Ensemble kalman filter for automatic history matching of geologic facies
Ning Liu and Dean S Oliver · 2005
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Level set methods for inverse scattering
O. Dorn and D. Lesselier · 2006
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Inverse Problems for Partial Differential Equations
V. Isakov · 2006
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A binary level set method and some applications for mumford-shah image segmentation
J. Lie, M. Lysaker, and X. C. Tai · 2006
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A variant of the level set method and applications to image segmentation
J. Lie, M. Lysaker, and X. C. Tai · 2006
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Adaptive finite element methods for elliptic problems with discontinuous coefficients
A. Bonito, R. A. DeVore, and R. H. Nochetto · 2013
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MCMC methods for functions: modifying old algorithms to make them faster
S. L. Cotter, G. O. Roberts, A. M. Stuart, and D. White · 2013
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Ensemble Kalman methods for inverse problems
M. A. Iglesias, K. Law, and A. M. Stuart · 2013
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Evaluation of Gaussian approximations for data assimilation in reservoir models
M. A. Iglesias, K. J. H. Law, and A. M. Stuart · 2013
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Ensemble Kalman methods for inverse problems
M.A. Iglesias, K.J.H. Law, and A.M. Stuart · 2013
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Conditioning truncated pluri-Gaussian models to facies observations in ensemble-Kalman-based data assimilation
A. Astrakova and D.S. Oliver · 2014
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Well-posed Bayesian geometric inverse problems arising in subsurface flow
M. A. Iglesias, K. Lin, and A. M. Stuart · 2014
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Binary tomography reconstructions with stochastic level-set methods
L. Wang, B. Sixou, and F. Peyrin · 2015
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The Bayesian approach to inverse problems
M. Dashti and A. M. Stuart · 2016
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