Variations on Image Reconstruction:Weighted Back Projection and Fourier Expectation Maximization

Abstract

Expectation Maximization and Filtered Back Projection are two common techniques for Tomographic reconstruction of images and volumes. While papers often demonstrat that EM produces higher quality reconstructions, particularly from lower numbers of projections, FBP remains popular due to its low computational complexity. In the following work we present and analyse a modified Expectation Maximization approach which takes advantage of the Fourier Slice Theorem to reduce the bottleneck of forward and back projection. We also investigate Weighted Back Projection, a variation of Filtered Back Projection which uses a weighted average approach to avoid the use of arbitrarily chosen filters.