Reconstruction of a uniform star object from interior x-ray data

We consider the reconstruction of objects with uniform density from limited projection data. Using the differential-backprojection (DBP), we show that a 2D star-shaped object of uniform but unknown density is determined by its 2D Radon transform sampled over a 2 angular range with a detector that only covers an interior field-of-view (FOV). A stability estimate is obtained using the Cramer-Rao bound and a reconstruction algorithm based on the DBP is described. The accuracy and stability of this algorithm are evaluated using simulated data. In the special case where the object density is known beforehand, the DBP algorithm is compared to DART, an iterative algebraic method for discrete tomography, which is shown to provide superior stability in the presence of noise.