Efficient marginal likelihood optimization in blind deconvolution

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Abstract
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\y) and not only its mode. This leads to a distinction between MAPx, k strategies which estimate the mode pair x, k and often lead to undesired results, and MAPk strategies which select the best k while marginalizing over all possible x images. The MAPk principle is significantly more robust than the MAPx, k one, yet, it involves a challenging marginalization over latent images. As a result, MAPk techniques are considered complicated, and have not been widely exploited. This paper derives a simple approximated MAPk algorithm which involves only a modest modification of common MAPx, k algorithms. We show that MAPk can, in fact, be optimized easily, with no additional computational complexity.