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

TL;DR

This paper introduces an adaptive Bayesian experimental design method for X-ray imaging that actively selects projection angles to improve edge detection in reconstructed images, using a Gaussian approximation of the posterior.

Contribution

It develops a novel edge-promoting Bayesian design framework that optimizes projection geometry based on posterior covariance, enhancing image reconstruction quality.

Findings

Effective edge detection in simulated X-ray data

Improved projection selection via A-optimal design

Demonstrated in 2D and 3D numerical examples

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.