An accelerated ordered subsets reconstruction algorithm using an accelerating power factor for emission tomography.

We proposed a speed-enhanced tomographic reconstruction algorithm, ACOSEM (accelerated complete-data ordered-subset expectation-maximization), to accelerate a convergent OS-type algorithm (COSEM). The ACOSEM algorithm was based on modification of the COSEM update by applying an accelerating power factor or a bigger step size. Unlike the limited enhancement of the other speed-enhanced algorithm (E-COSEM), the proposed ACOSEM with an appropriate power factor can lead to a much faster reconstruction speed than COSEM and ECOSEM. Similar to COSEM, there is no free user-entered relaxation parameter needed for ACOSEM to ensure the convergent performance as required in the other type of fast convergent algorithms such as RAMLA. We derived the ACOSEM algorithm, and compared its performance to those of other fast convergent algorithms including COSEM, ECOSEM and RAMLA with optimized relaxation parameters. Though not convergent, OSEM is the current state-of-the-art reconstruction method used in the clinics, and thus included in the noise performance comparison. The results showed that ACOSEM reached the same image quality as in COSEM but two times faster when a power factor of 2.0 was used. An upper limit of 5 for the power factor with monotonically increasing log-likelihood in ACOSEM was observed under various conditions. Although the convergence proof is not available now, the results of log-likelihood values and noise studies showed that ACOSEM performed consistently with COSEM but with an accelerating reconstruction speed.