Fast OPED algorithm for reconstruction of images from Radon data

A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested. The new implementation uses FFT for discrete sine transform and an interpolation step. The convergence of the fast implementation is proved under the condition that the function is mildly smooth. The numerical test shows that the accuracy of the OPED algorithm changes little when the fast implementation is used.