A unified minimization framework for single/multi-shot nonparametric blind deblurring

摘要

The nonparametric blind deconvolution, either single or multi-shot, has been intensively studied since Fergus et al.'s variational Bayesian approach to camera shake deblurring [1]. However, in the current literature there is always a gap between the two highly related problems; single and multi-shot blind deconvolution are modeled and solved independently, lacking a unified optimization perspective. We attempt to bridge the gap between the two problems in this paper, via constructing a simple, rigorous and unified minimization functional which couples the variational Bayesian and maximum-a-posteriori principles. The new approach is depicted using a directed graphic model, in which the sharp image and the inverse noise variance associated with each shot are treated as random variables, while the blur-kernel, in difference from existing variational Bayesian methods, is just modeled as a deterministic parameter. With a universal, three-level hierarchical prior on the latent sharp image and a Gamma hyper-prior on each inverse noise variance, the single/multi-shot blind deconvolution is formulated into an ℓ0.5-norm regularized negative log-marginal-likelihood minimization problem. By ideas of expectation-maximization, majorization-minimization, mean field approximation, and iteratively reweighted least squares, all the unknown quantities of interest, including the sharp image, the blur-kernel, the inverse noise variance, as well as other related parameters are estimated automatically. In comparison to existing single/multi-shot methods, the proposed method is not only more flexible, but also more adaptive while with less implementational heuristics. Experimental results on Levin et al.'s [2] benchmark data set demonstrate the effectiveness and superiority of the proposed framework.