Source Design Optimization for Depth Image Reconstruction in X-ray Imaging

X-ray tomography is an effective non-destructive testing method for industrial quality control. Limited-angle tomography can be used to reduce the amount of data that need to be acquired and thereby speed up the process. In some industrial applications, however, objects are flat and layered, and laminography is preferred. It can deliver 2D images of the structure of a layered object at a particular depth from very limited data. An image at a particular depth is obtained by summing those parts of the data that contribute to that slice. This produces a sharp image of that slice while superimposing a blurred version of structures present at other depths. In this paper, we investigate an Optimal Experimental Design (OED) problem for laminography that aims to determine the optimal source positions. Not only can this be used to mitigate imaging artifacts, it can also speed up the acquisition process in cases where moving the source and detector is time-consuming (e.g., in robotic arm imaging systems). We investigate the imaging artifacts in detail through a modified Fourier Slice Theorem. We address the experimental design problem within the Bayesian risk framework using empirical Bayes risk minimization. Finally, we present numerical experiments on simulated data.