Tomographic image reconstruction from a limited number of projections

This paper addresses the reconstruction of a function from its rectangularly sampled Radon transform. After reviewing the Radon transform sampling requirements and describing a convolution/backprojection reconstruction algorithm, two basic issues are addressed. First it is shown that even when the Radon transform of an image is adequately sampled (in the Nyquist sense), the standard convolution/backprojection algorithm may lead to a poor reconstruction unless the Radon transform is first reconstructed to a required set of projections. Secondly, when the Radon transform is undersampled in projections, reconstruction approaches are illustrated which span the range from those which achieve a high uniform-resolution reconstruction with large amounts of aliasing artifacts to those which achieve a low nonuniform-resolution reconstruction with virtually no aliasing artifacts. Reconstruction filters which seek a compromise between those two extremes are defined.