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, ky) 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.