Xu Zhou1, Miguel Vega2, Fugen Zhou1, Rafael Molina2, and Aggelos K. Katsaggelos3
1 Beihang University, 2University of Granada, 3Northwestern University
Expectation Maximization (EM) based inference has already proven to be a very powerful tool to solve blind image deconvolution (BID) problems. Unfortunately, three important problems still impede the application of EM in BID: the undesirable saddle points and local minima caused by highly nonconvex priors, the instability around zero of some of the most interesting sparsity promoting priors, and the intrinsic high computational cost of the corresponding BID algorithm. In this paper we first show how Super Gaussian priors can be made numerically tractable around zero by introducing the family of Huber Super Gaussian priors and then present a fast EM based blind deconvolution method formulated in the image space. In the proposed computational approach, image and kernel estimation are performed by using the Alternating Direction Method of Multipliers (ADMM), which allows to exploit the advantages of FFT computation. For highly nonconvex priors, we propose a Smooth ADMM (SADMM) approach to avoid poor BID estimates. Extensive experiments demonstrate that the proposed method significantly outperforms state-of-the-art BID methods in terms of quality of the reconstructions and speed.
Results on synthetic data
Sun et al Babacan et al Perrone & Favaro Zhou et al This work
Figure 1. Cumulative histograms of the error ratios across the dataset from Sun et al
Table 1. Average scores of different methods
Table 2. Running time (in seconds) of different methods for a 512x512 image
 L. Xu, et al., “Unnatural l0 sparse representation for natural image deblurring,” in CVPR, 2013.
 L. Sun, et al, “Edge-based blur kernel estimation using patch priors,” in ICCP, 2013.
 S. Babacan, et al., “Bayesian blind deconvolution with general sparse image priors,” in ECCV, 2012.
 A. Levin, et al., “Efficient marginal likelihood optimization in blind deconvolution,” in CVPR, 2011.
 D. Perrone and P. Favaro, “A logarithmic image prior for blind deconvolution,” IJCV, pp. 1–14, 2015.
 X. Zhou, J. Mateos, F. Zhou, R. Molina, and A. Katsaggelos, “Variational dirichlet blur kernel estimation,” IEEE TIP., vol. 24, no. 12, pp. 5127–5139, 2015.