Sequentially optimized projections in x-ray imaging*The work of MB was supported by the Bundesministerium für Bildung und Forschung under the project id 05M16PMB (MED4D). The work of AH was supported by the Academy of Finland (decision 312123). The work of TH was supported by the Academy of Finland (decisions 320082 and 326961). The work of NH and JP was supported by the Academy of Finland (decision 312124). (22nd June 2021) - Burger, M; Hauptmann, A; Helin, T; Hyvönen, N; Puska, J-P
Abstract: This work applies Bayesian experimental design to selecting optimal projection geometries in (discretized) parallel beam x-ray tomography assuming the prior and the additive noise are Gaussian. The introduced greedy exhaustive optimization algorithm proceeds sequentially, with the posterior distribution corresponding to the previous projections serving as the prior for determining the design parameters, i.e. the imaging angle and the lateral position of the source–receiver pair, for the next one. The algorithm allows redefining the region of interest after each projection as well as adapting parameters in the (original) prior to the measured data. Both A and D -optimality are considered, with emphasis on efficient evaluation of the corresponding objective functions. Two-dimensional numerical experiments demonstrate the functionality of the approach.