RATIONAL APPROXIMATIONS FOR TOMOGRAPHIC RECONSTRUCTIONS

Abstract. We use optimal rational approximations of projection data col-lected in X-ray tomography to improve image resolution. Under the assump-tion that the object of interest is described by functions with jump discontinu-ities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algo-rithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp-Logan phantom, we provide a comparison between the new algorithm and the standard Filtered Back-Projection (FBP) algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. 1