Removing Motion Blur using Natural Image Statistics

We tackle deconvolution of motion blur in hand-held consumer photography with a Bayesian framework combining sparse gradient and color priors for regularization. We develop a closed-form optimization utilizing iterated re-weighted least squares (IRLS) with a Gaussian approximation of the regularization priors. The model parameters of the priors can be learned from a set of natural images which resemble common image statistics. We throughly evaluate and discuss the effect of different regularization factors and make suggestions for reasonable values. Both gradient and color priors are current state-of-the-art. In natural images the magnitude of gradients resembles a kurtotic hyper-Laplacian distribution, and the two-color model exploits the observation that locally any color is a linear approximation between some primary and secondary colors. Our contribution is integrating both priors into a single optimization framework and providing a more detailed derivation of their optimization functions. Our re-implementation reveals different model parameters than previously published, and the effectiveness of the color priors alone are explicitly examined. Finally, we propose a context-adaptive parameterization of the regularization factors in order to avoid over-smoothing the deconvolution result within highly textured areas.