A method for removing cyclic artefacts in discrete tomography using latin squares

This paper presents a technique to remove image artefacts, formed under the cyclic additive group Z_p, during the inverse Radon reconstruction from prime-dimensioned discrete projections. The cyclic artefacts are circulant matrices that arise from gaps in the known projection data. These artefacts are superimposed periodically on the reconstructed image. The summed value of unknown artefacts at an arbitrary image pixel location is determined using other, overlapping artefact combinations that are located at image positions where their component values are known. Latin squares are used to optimise the selection of these known elements. The result requires an irregular sampling to obtain the known correction values, but, once found, provides a multitude of exact solutions, as the sampling pattern for artefact corrections is translation invariant.