Fast iterative tomographic reconstruction algorithm

We use a series-expansion approach and an operator framework to derive a new, fast and accurate, iterative tomographic reconstruction algorithm applicable for parallel-ray projections that have been collected at a finite number of arbitrary view angles and have been radially sampled at a rate high enough so that aliasing errors are small. We use the conjugate gradient algorithm to minimize a regularized least squares criterion, and we prove that the main step in each iteration is equivalent to a 2-D discrete convolution, which can be cheaply and exactly implemented via the FFT. The proposed algorithm requires qq(N² log N) multiplies per iteration to reconstruct an N × N image from P view angles, and requires the storage of half of a 2N × 2N PSF.