Fast filtering and back projection for CT image reconstruction
Filtered back projection is a common method for the tomographic images reconstruction. The classical implementation of the algorithm requires $O({{N}^{2}})$ operations, where N is the characteristic linear size of the image. In this paper, we propose methods for reducing the computational complexity of the algorithm to $O({{N}^{2}}\log N)$additions and $O({{N}^{2}})$ multiplications; whereas the previously proposed methods require $O({{N}^{2}}\log N)$ multiplications. We show that the convolution operation with a symmetric filter can be approximated by successive application of two coupled IIR filters. A discrete method for fast calculating the inverse Radon transform is demonstrated. It allows to accelerate the back projection operation.