Filtered backprojection algorithm can outperform iterative maximum likelihood expectation-maximization algorithm

The iterative maximum-likelihood expectation-maximization (ML-EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML-EM in certain occasions, when the least-squared difference from the true image, that is, the least-squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML-EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML-EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML-EM images. For the noiseless projections, the FBP algorithms outperform the ML-EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML-EM algorithm.