Method for rebinning and for correcting cone beam error in a fan beam

Abstract

A method of reconstructing data acquired on a fan beam CT system first rebins the data to parallel beam format using limited angle weighting that fold-over redundant data by adding corner rays of one scan to the center rays of another scan. For each view, now parallel beam data are filtered with a parallel beam kernel, and transformed. The transform is replicated, and multiplied by an interpolation filter. Next, the replicated, multiplied transform is convolved with the gridding function, and added into the Fourier image at an angle corresponding to the view angle. In the case of an n-scan cone beam correction a two-dimensional weighting function is calculated for each view giving the view's contribution to each pixel in the image. Multiplication by this weighting function is accomplished by convolution of the transform of the weighting function with the above transformed view. These steps are repeated for all views, whereafter the two-dimensional inverse Fourier transform is taken to get a preliminary image. The center portion of the preliminary image is then extracted and multiplied by the inverse of the gridding function to get the desired reconstructed image. The image, which is substantially free of cone beam error, is built-up by summing for each view the backprojection of the view times that view's weighting function. Preferably the gridding function is a Kaiser-Bessel function, whose values are pre-calculated and stored in a look-up table.