Iterative reconstruction algorithms with α-divergence for PET imaging

This paper presents a class of image reconstruction algorithms based on Amari’s α-divergence for position emission tomography. The α-divergence is actually a family of divergences indexed by α ∈(− ∞ ,  + ∞ ) that can measure discrepancy between two distributions. We consider it to model the discrepancy between projections and their estimates. By iteratively minimizing the α-divergence, a multiplicative updating algorithm is derived using an auxiliary function. The well-known ML-EM algorithm and the SA-WLS algorithm suggested by Zhu et al. arise as two special cases of our method. We prove the monotonic convergence of the algorithm, which Zhu et al. has not provided. The experiments were performed on both simulated and clinical data to study the interesting and useful behavior of the algorithm in cases where different parameters (α) were used. The results showed that some chosen algorithms exhibited much better performance than the prevalent ones.