Optimized single site update algorithms for image deblurring

We present optimized algorithms for image deblurring in the case of a separable point spread function (PSF). Our work is in the usual context of Bayesian estimation with Gibbs random fields (GRF). The derived algorithms fall into the class of single site update algorithms (SSUAs), which exhibit a high convergence rate per iteration and small memory requirements, while hard domain constraints such as positivity are easily introduced. On the other hand, standard forms of SSUAs rapidly become intractable when the size of the PSF is large. We show how PSF separability can benefit the SSUAs, in order to reduce the cost of each pixel update from O(2pq) to O(p+q) (p×q is the size of the PSF). We show that the resulting deterministic SSUA compares very favorably with global update algorithms (GUAs). The new separable form can also benefit other SSUAs, especially stochastic versions such as simulated annealing (SA) and Monte Carlo Markov chain (MCMC) algorithms