A Fast and Accurate Multilevel Inversion of the Radon Transform

A number of imaging technologies reconstruct an image function from its Radon projection using the convolution backprojection method. The convolution is an O(N2 log N) algorithm, where the image consists of N X N pixels, while the backprojection is an O(N3 ) algorithm, thus constituting the major computational burden of the convolution backprojection method. An O(N2 log N) multilevel backprojection method is presented here. When implemented with a Fourier-domain postprocessing technique, also presented here, the resulting image quality is similar or superior to the image quality of the classical backprojection technique.