Efficient Marginal Likelihood Optimization in Blind Deconvolution

In blind deconvolution one aims to estimate from an input blurred image y a sharp image x and an unknown blur kernel k. Recent research shows that a key to success is to consider the overall shape of the posterior distribution p(x, k vertical bar y) and not only its mode. This leads to a distinction between MAP(x,k) strategies which estimate the mode pair x, k and often lead to undesired results, and MAP(k) strategies which select the best k while marginalizing over all possible x images. The MAP(k) principle is significantly more robust than the MAP(x,k) one, yet, it involves a challenging marginalization over latent images. As a result, MAP(k) techniques are considered complicated, and have not been widely exploited. This paper derives a simple approximated MAP(k) algorithm which involves only a modest modification of common MAP(x,k) algorithms. We show that MAP(k) can, in fact, be optimized easily, with no additional computational complexity.