Comparison of FBP and iterative algorithms with non-uniform angular sampling

Some people may believe that the filtered backprojection (FBP) algorithm does not work if the projection data are measured non-uniformly. Some may also believe that iterative algorithms can automatically handle the non-uniformly sampled data in the projector/backprojector. This paper claims that the FBP algorithm can effectively handle the situation where the angular sampling is not uniform. This paper compares the images that are reconstructed by both the FBP and the iterative Landweber algorithms when the angular sampling is non-uniform. When the iteration number is low, the iterative algorithms do not handle the non-uniform sampling properly. A weighting strategy is then suggested and it makes the image resolution more isotropic. In few-view tomography, the FBP and iterative algorithms both perform poorly if no other prior information is used. We have made the following observations: 1) When using an iterative algorithm, one must use early solutions due to noise amplification. 2) An early solution can have anisotropic spatial resolution if the angular sampling is not uniform. 3) The anisotropic resolution problem can be solved by introducing angle dependent weighting, which is not noise dependent. 4) The weighting is not effective when the iteration number is large. The weighting only affects the early solutions, and does not affect the converged solution. 5) When the iteration number is large, the model-mismatch errors are amplified and cause artifacts in the image. 6) The FBP algorithm is not sensitive to the model-mismatch errors, and does not have the “early solution” problems. 7) In few-view tomography, both FBP and iterative algorithms perform poorly, while the FBP algorithm gives a sharper image than the iterative algorithm does.