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arXiv · 2104.00301

Edge-promoting adaptive Bayesian experimental design for X-ray imaging

Tapio Helin·Nuutti Hyvönen·Juha-Pekka Puska
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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-optimal Bayesian design, which corresponds to minimizing the trace 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.

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Tapio Helin, Nuutti Hyvönen, Juha-Pekka Puska. 2021-04-01. Edge-promoting adaptive Bayesian experimental design for X-ray imaging. https://arxiv.org/abs/2104.00301

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