Source and coded aperture joint optimization for compressive X-ray tomosynthesis

Compressive X-ray tomosynthesis is an emerging technique to reconstruct three-dimensional (3D) objects from two-dimensional projection measurements generated by a set of spatially distributed X-ray sources, where coded apertures are used in front of each source to modulate a set of X-rays to interrogate an object with a reduced radiation dose without loss of image reconstruction quality. The reconstruction performance in compressive tomosynthesis is influenced by several factors including the locations of the X-ray sources, their incident angles, and the coded apertures that determine the structured illumination patterns. This paper develops a source and coded aperture joint optimization (SCO) approach to improve the image reconstruction performance of compressive X-ray tomosynthesis. Based on compressive sensing theory, the synergy among the source pattern, source orientation, and the coded apertures is utilized to minimize the coherence of the sensing matrix of the imaging system. In concert with a gradient-based optimization algorithm, regularization methods are used to reduce the convergence error and achieve uniform sensing of the object under inspection. Compared to the optimization of either the source orientation, or the coded aperture individually, the proposed method effectively increases the degree of optimization freedom, and thus achieves considerable improvement in the 3D imaging reconstruction accuracy.