Tomographic reconstruction using incremental and NFFT methods

Projection and backprojection operators are the numerically intensive part of iterative methods in tomographic reconstruction.Some alternatives based on interpolation over a regular grid on the Fourier space or on nonequispaced fast Fourier transforms were developed in order to alleviate the computational cost.Both approaches substantially speed up the computation of the iterations of classical algorithms, but the incremental methods, such as osem, ramla, saem, among others, cannot benefit from these techniques.In this paper, it is presented an efficient approach where the nonequispaced fast Fourier transform (nfft) is used in each sub-iteration of the incremental method "ordered subsets for transmission tomography" (ostr) to perform the most expensive calculations: the projection and backprojection.The proposed method is applied to synchrotron radiation tomography and the results show a good performance.