Computation of high overrelaxation parameters in iterative image reconstruction

Single-projection iterative reconstruction allows the use of high overrelaxation parameters. The parameters can be optimized in a pragmatic way by studying their influence on figures of merit extracted from the image. The resulting parameters are high in the beginning and drop down during further iteration. The value of the overrelaxation parameter which gives the best image after one iteration step is easily found. However, this value will change if an optimum image is postulated after two or more iteration steps. A procedure has been developed which rapidly finds the parameters to be used during a sequence of iteration steps to obtain optimum results for a later approximation. Comparing optimization during one and two steps, the initial parameters obtained with two-step optimization are about twice as high as those with one-step optimization, accelerating convergence by nearly a factor of two. Optimization within three or more steps again leads to different parameter sequences which, however, provide only minor convergence improvement. This indicates that different sequences of parameters may result in similar images, and parameters derived from a typical data set may be widely used for other data. Computation of new parameter sequences by the optimizing procedure is recommended if data from new equipment or with new characteristics have to be processed. Index Terms - Image reconstruction, positron emission tomography.