Preconditioned alternating projection algorithm for solving the penalized-likelihood SPECT reconstruction problem.

PURPOSE: The authors recently developed a preconditioned alternating projection algorithm (PAPA) for solving the penalized-likelihood SPECT reconstruction problem. The proposed algorithm can solve a wide variety of non-differentiable optimization models. This work is dedicated to comparing the performance of PAPA with total variation (TV) regularization (TV-PAPA) and a novel forward-backward algorithm with nested expectation maximization (EM)-TV iteration scheme (FB-EM-TV).

METHODS: Monte Carlo technique was used to simulate multiple noise realizations of the fan-beam collimated SPECT data for a piecewise constant phantom with warm background, and hot and cold spheres with uniform activities at two noise levels. They were reconstructed using the aforementioned algorithms with attenuation, scatter, distance-dependent collimator blurring and sensitivity corrections. Noise suppressing performance, lesion detectability, lesion contrast, contrast recovery coefficient, convergence speed and selection of optimal parameters were evaluated. The conventional EM algorithms with TV post-filter (TVPF-EM) and Gaussian post-filter (GPF-EM) were used as benchmarks.

RESULTS: The TV-PAPA and FB-EM-TV demonstrated similar performance in all investigated categories. Both algorithms outperformed TVPF-EM in terms of image noise suppression, lesion detectability, lesion contrast and convergence speed. We established that the optimal parameters versus information density approximately followed power laws, which offers a guidance in parameter selection for reconstruction methods.

CONCLUSIONS: For the simulated SPECT data, TV-PAPA and FB-EM-TV produced qualitatively and quantitatively similar images. They performed better than the benchmark TVPF-EM and GPF-EM, with only limited loss of lesion contrast.