Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.

Paper.

Code (Updated on 20/12/2014).

Results on dataset from Levin et. al. [1].

Results on dataset from Sun et. al. [4].

@inproceedings{perrone_emmcvpr2015,
  author = {Daniele Perrone and Remo Diethelm and Paolo Favaro},
  title = {Blind Deconvolution via Lower-Bounded Logarithmic Image Priors},
  booktitle = {International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR)},
  year = {2015}
}

[1] A. Levin, Y. Weiss, F. Durand and W.T. Freeman: Understanding and evaluating blind deconvolution algorithms, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2009.

[2] D. P. Wipf and H Zhang: Analysis of Bayesian Blind Deconvolution, International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), 2013.

[3] S. D. Babacan, R. Molina, M. N. Do and . K. Katsaggelos: Bayesian Blind Deconvolution with General Sparse Image Priors, European Conference on Computer Vision (ECCV), 2012.

[4] L. Sun, S. Cho, J. Wang; and J. Hays: Edge-based blur kernel estimation using patch priors, International Conference on Computational Photography (ICCP), 2013.