Analysis of Digital Breast Tomosynthesis Acquisition Geometries in Sampling Fourier space

Tomosynthesis acquires projections over a limited angular range and thus samples an incomplete projection set of the object. For a given acquisition geometry, the extent of tomosynthesis sampling can be measured in the frequency domain based on the Fourier Slice Theorem (FST). In this paper we propose a term, "sampling comprehensiveness", to describe how comprehensively an acquisition geometry samples the Fourier domain, and we propose two measurements to assess the sampling comprehensiveness: the volume of the null space and the nearest sampled plane. Four acquisition geometries, conventional (linear), T-shape, bowtie, and circular geometries, were compared on their comprehensiveness. The volume of the null space was estimated as the percentage of voxels subtended by zero slices in the sampled Fourier space. For each voxel in the frequency space, the nearest sampled plane and the distance to that plane were recorded. Among the four, the circular geometry was determined to be the most comprehensive based on the two measurements. We review tomosynthesis sampling with a finite number of projections and discuss how the sampling comprehensiveness should be interpreted. We further suggest that the decision on a system geometry should consider multiple factors including the sampling comprehensiveness, the task to be performed, the thickness of the imaged object, system specifications, and reconstruction algorithm.