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Three-dimensional Bayesian inversion with application to subsurface sensing

Publication ,  Journal Article
Yu, Y; Carin, L
Published in: IEEE Transactions on Geoscience and Remote Sensing
May 1, 2007

A Bayesian formalism is considered for inverting for the parameters of a heterogeneity profile based on measured scattering data. It is shown that the typical use of regularization (e.g., Thikonov) corresponds to a maximum a posteriori point approximation to the full-posterior density function on the heterogeneity parameters, given the observed data. In the Bayesian framework considered here, the full posterior is approximated as a multidimensional Gaussian distribution. The mean of this distribution may be used as a point estimate of the heterogeneity profile, with the covariance matrix providing associated "error bars" (a measure of confidence in the inversion). In addition to providing an approximation to the full posterior of the heterogeneity profile, this formalism addresses the proper weighting to apply for inversion regularization. Specifically, an important limitation of previous regularization procedures is the need to place a weight on the importance of the regularization relative to the importance of fitting the data to the underlying model. In the Bayesian analysis outlined here, we also assign such a weight, but now the weight is treated as a random variable, with a statistical prior. The measured data are then used to determine a posterior distribution on the parameter, based on the measured data. We present here the basic Bayesian inversion framework, with several example results presented for subsurface-sensing problems. © 2007 IEEE.

Duke Scholars

Published In

IEEE Transactions on Geoscience and Remote Sensing

DOI

ISSN

0196-2892

Publication Date

May 1, 2007

Volume

45

Issue

5

Start / End Page

1258 / 1270

Related Subject Headings

  • Geological & Geomatics Engineering
  • 40 Engineering
  • 37 Earth sciences
  • 0909 Geomatic Engineering
  • 0906 Electrical and Electronic Engineering
  • 0404 Geophysics
 

Citation

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MLA
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Yu, Y., & Carin, L. (2007). Three-dimensional Bayesian inversion with application to subsurface sensing. IEEE Transactions on Geoscience and Remote Sensing, 45(5), 1258–1270. https://doi.org/10.1109/TGRS.2007.894932
Yu, Y., and L. Carin. “Three-dimensional Bayesian inversion with application to subsurface sensing.” IEEE Transactions on Geoscience and Remote Sensing 45, no. 5 (May 1, 2007): 1258–70. https://doi.org/10.1109/TGRS.2007.894932.
Yu Y, Carin L. Three-dimensional Bayesian inversion with application to subsurface sensing. IEEE Transactions on Geoscience and Remote Sensing. 2007 May 1;45(5):1258–70.
Yu, Y., and L. Carin. “Three-dimensional Bayesian inversion with application to subsurface sensing.” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 5, May 2007, pp. 1258–70. Scopus, doi:10.1109/TGRS.2007.894932.
Yu Y, Carin L. Three-dimensional Bayesian inversion with application to subsurface sensing. IEEE Transactions on Geoscience and Remote Sensing. 2007 May 1;45(5):1258–1270.

Published In

IEEE Transactions on Geoscience and Remote Sensing

DOI

ISSN

0196-2892

Publication Date

May 1, 2007

Volume

45

Issue

5

Start / End Page

1258 / 1270

Related Subject Headings

  • Geological & Geomatics Engineering
  • 40 Engineering
  • 37 Earth sciences
  • 0909 Geomatic Engineering
  • 0906 Electrical and Electronic Engineering
  • 0404 Geophysics