A method for reconstructing image data from acquired tomographic projection data measurements is provided. The projection data measurements comprise one or more missing data measurements. The method comprises generating a coarse-resolution projection data set from the acquired projection data measurements and performing an iterative reconstruction on the coarse-resolution projection data set to generate a coarse-resolution reconstructed data set. Then, the method comprises reprojecting the coarse-resolution reconstructed data set to obtain one or more estimates for the one or more missing data measurements. The one or more estimated missing data measurements are then recombined with the acquired projection data measurements, to generate a recombined data set. Then, a direct reconstruction algorithm is applied to the recombined data set to generate the reconstructed image data.