How do I interpolate Spiral MRI images? (3D images with missing chunks of data)

I have Spiral MR Images of the brain in 3D, such that I have an image of the brain with missing chunks of data in the form of stripes. The stripes are at a different angle depending on the image acquisition and the orientation which the patient was in the MR machine. In some case I also have more missing data than actual data. I have tried sinc interpolation with VARIOUS windows and parameters but this resulted in aliasing artefacts which are difficult, or impossible to correct.