Implementing Fast Hierarchical Back Projection

– Filtered back projection (FBP) is a commonly used image reconstruction scheme for parallel beam tomography. The algorithm implemented in this project, called fast hierarchical back projection (FHBP), was proposed in [1] as a fast approximation to the direct FBP technique. Through derivation, implementation and simulation results, I will show a complete picture on this novel algorithm for a classical image reconstruction problem. FHBP divides an image into smaller images and uses the basic fact that smaller images require less data to reconstruct. While the direct FBP technique has computational complexity O(N 3), the computational complexity of this FHBP is O(N 2 log 2 N). The gains achieved for a 512 x 512-pixel image for this specific implementation reached upwards of 100 with a worst case root mean squared error (RMSE) of 13.3/255 gray levels.