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

Funding Information: The work of the first author was supported by the the Academy of Finland through grants 320082 and 326961. The work of the second and third authors was supported by the Academy of Finland through grant 312124. School of Engineering Science, LUT University, Lappeenranta, 53851 Finland (Tapio.Helin@ lut.fi). Department of Mathematics and Systems Analysis, Aalto University, FI-00076 Aalto, Finland (nuutti.hyvonen@aalto.fi, juha-pekka.puska@aalto.fi). Publisher Copyright: © 2022 Society for Industrial and Applied Mathematics.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.Peer reviewe