EDGE-PROMOTING ADAPTIVE BAYESIAN EXPERIMENTAL DESIGN FOR X-RAY IMAGING

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 diffusiv-ity 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 informa-tion 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 deter-minant 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.