Edge-Promoting Adaptive Bayesian Experimental Design for X-ray Imaging

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Abstract

This work considers sequential edge-promoting Bayesian experimental design for (discretized) linear inverse problems, exemplified by X-ray tomography. The process of computing a total variation-type reconstruction of the absorption inside the imaged body via lagged diffusivity iteration is interpreted in the Bayesian framework. Assuming a Gaussian additive noise model, this leads to an approximate Gaussian posterior with a covariance structure that contains information on the location of edges in the posterior mean. The next projection geometry is then chosen through A- or D-optimal Bayesian design, which corresponds to minimizing the trace or the determinant of the updated posterior covariance matrix that accounts for the new projection. Two- and three-dimensional numerical examples based on simulated data demonstrate the functionality of the introduced approach.

Original languageEnglish
Pages (from-to)B506-B530
JournalSIAM Journal on Scientific Computing
Volume44
Issue number3
DOIs
Publication statusPublished - 2022
MoE publication typeA1 Journal article-refereed

Keywords

  • A-optimality
  • adaptivity
  • Bayesian experimental design
  • D-optimality
  • edge-promoting prior
  • lagged diffusivity
  • optimal projections
  • X-ray tomography

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