Iterative Non-negative Deconvolution Algorithms with Alpha-Divergence

This paper presents a class of iterative deconvolution algorithms based on Amari´s alpha-divergence in the condition of non-negativity constraints. The alpha-divergence is actually a family of divergences indexed by alpha is real number that can measure the discrepancy between two distributions or nonnegative sequences. We consider it to model the difference between the deblurred image and its estimate. By iterative minimization, a general update rule is derived by constructing a surrogate function. The well-known Richardson-Lucy (RL) algorithm arises as a special case of our method. The proposed algorithms monotonically decrease the cost functions and automatically meet the non-negativity constraints. The experiments were performed on both simulated and real medical images to investigate the interesting and useful behavior of the algorithms when different parameters (alpha) were used. The results showed that some chosen ones exhibited much better performance than the RL algorithm.