Optimal relaxation parameters of DRAMA (dynamic RAMLA) aiming at one-pass image reconstruction for 3D-PET

We have reported a block-iterative algorithm named DRAMA for image reconstruction for emission tomography (Tanaka and Kudo 2003 Phys. Med. Biol. 48 1405-22). DRAMA is a modified version of the row-action maximum likelihood algorithm (RAMLA), in which the relaxation parameter is subset dependent and is changed in such a way that the noise propagation from subsets to the reconstructed image is substantially independent of the access order of the subsets. The algorithm provides fast convergence with a reasonable signal-to-noise ratio. The optimal relaxation parameter has been derived assuming a two-dimensional (2D)-PET model, and detailed performance in three-dimensional (3D) reconstruction has not been clear enough. We have developed the new version 'DRAMA-3D', based on the 3D-PET model. The optimal relaxation parameter is a function of the access order of the subsets and the ring difference, and its value is determined by simple formulas from the design parameters of the PET scanner, the operating conditions and the post-smoothing resolution. In this paper, we present the theory of DRAMA-3D, the results of simulation studies on the performance of DRAMA-3D and the comparative studies of the related algorithms. It is shown that DRAMA-3D is robust for various access orders of subsets and is suitable to realize one-pass (single-iteration) reconstruction.