Backprojection - filtered vs unfiltered

I previously posted about the concept of reconstructing a CT image using the sinogram by performing the inverse Radon transform. The Radon transform is implemented using backprojection, taking the scan projections <sinogram> to reconstruct the original image. Because the data are digital, simply backprojecting the rays does not properly reconstruct the original image. In the examples shown below, the original image is a square at the centre of the field and the videos below show image reconstruction using backprojection, with and without filtering.

Very simply, because the rays used to collect and reconstruct the image are of finite, constant width, backprojecting the rays over-represents the central portion of the image, giving a blurry-central image of a square.

Filtering the rays before backprojecting cleans up the image considerably:

The matlab code for the filtered and unfiltered videos were created for a section of a graduate course I taught at UBC.