Application Of Interpolation In Ct Tomography Reconstruction

Since the birth of the first CT (Computed Tomography) scanner in 1972, CT has been widely used in the world. The wide uses of CT also generate great impetus for CT research. Several big changes have taken placed during the past 30 years. The changes mainly involve in two aspects-speed and image quality.The Radon transform was introduced by J. Radon in 1917. Little computation attention was given to it until the advent of computers enabled the fast evaluation of Fourier transform and their convolutions. The Radon transform is now a mainstay of computerized tomography in medical imaging as well as many other remote-imaging sciences. So far, many reliable reconstruction methods based on Radon transform have been developed.Firstly we introduce the reverse discrete Fourier transform reconstruction, and then we study the two dimensions filtered back projected, at last we propose the method of local convex combination interpolation. Radon domain can be filled by the Fourier transforms for projection images in a polar gridding format (radial lines for parallel projections, radon arcs for fan-beam projections). The Radon-based tomographic reconstruction requires regridding a polar radon domain into a rectilinear lattice before inverse Fourier transform. Since the radon domain is irregularly sampled by Fourier-transformed projections, i.e, oversampled around the central regions and undersampled at the peripheral regions, the polar-to-Cartesian coordinate grid conversion involves rebinning for oversampled central region, interpolation for undersampled peripheral region, and extrapolation for extending the peripheral boundary. In this paper, we propose a general data interpolation or extrapolation scheme to deal with the radon domain regridding, which is a local convex combination with weights determined by a function of inverse distances. For filling the unavailable entries at peripheral regions, we propose to calculate the corresponding entries in the projection domain, rather than in the radon domain, by interpolations and extrapolations. The interpolation for peripheral region allows us investigate the angular sampling for computed tomography scanning. The extrapolation leads to super-resolution tomographic reconstruction. We find that data interpolation in projection domain may produce better results than in radon domain. This finding may be justified by the fact that the data distribution is more continuous in projection domain than in Fourier domain.Finally the feasibility and correctness of the interpolation are validated by using Matlab programs.