A method for iteratively reconstructing image data acquired by a computed tomography system is provided. The method comprises generating a calculated sinogram from an image estimate and generating an error sinogram based on the calculated sinogram and a measured sinogram. Then, one or more backprojections are performed, each based upon a reconstruction parameter. The reconstruction parameter impacts at least one of convergence speed and computational cost of each iterative step and corresponding reconstruction. A filtering step is performed prior to performing the one or more backprojections. Finally, the initial image is updated by adding corresponding results of the one or more backprojections to the image estimate to obtain the reconstructed image.