Sampling of shifted fan beam projections for region of interest reconstruction

The sampling requirements in fan-beam tomography are well known and provide an estimate of the number of projections required for accurate reconstruction of the entire image. Here we consider the problem of reconstructing a small, off-center subregion of the object. We show that a subregion can be reconstructed from a smaller set of projections, reducing the computation required to form the image. The analysis requires the study of the essential support of the Fourier transform of shifted fan beam projections, which have not previously been analyzed.