Fast Blind Deconvolution with Huber Super Gaussian Priors


Xu Zhou1Miguel Vega2, Fugen Zhou1, Rafael Molina2, and Aggelos K. Katsaggelos3
1 Beihang  University,  2University of Granada3Northwestern University

Abstract

    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

    
 Methods SSD Error  Error Ratio
 With Known h 392.15  1 
 This work 590.39   1.41
 Perrone & Favaro 635.27   1.71
 Sun et al 618.92   2.01
 Babacan et al  792.27  2.27
 Zhou et al 686.29   1.66

Table 1. Average scores of different methods 

 Kernel Support  11x11 21x21  27x27 
 Babacan et al (MATLAB) 116.48   302.85 535.71 
 Levin et al (MATLAB) 111.75  240.72   425.58
 Perrone & Favaro (MATLAB) 2382.85  3447.20  3745.64 
 Xu et al (C++) 2.24  3.13  2.93 
 This work (MATLAB) 9.45 15.6 15.12 

Table 2. Running time (in seconds) of different methods for a 512x512 image 
  
 
  
Results on real data
           
 

                                         Input                                                                           Babacan et al                                                                             Xu et al                        

                    
 
                                         Zhou et al                                                           Perrone & Favaro                                                                          This work




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References
 [1] L. Xu, et al., “Unnatural l0 sparse representation for natural image deblurring,” in CVPR, 2013.
 [2] L. Sun, et al, “Edge-based blur kernel estimation using patch priors,” in ICCP, 2013.
 [3] S. Babacan, et al., “Bayesian blind deconvolution with general sparse image priors,” in ECCV, 2012.
 [4] A. Levin, et al., “Efficient marginal likelihood optimization in blind deconvolution,” in CVPR, 2011.
 [5] D. Perrone and P. Favaro, “A logarithmic image prior for blind deconvolution,” IJCV, pp. 1–14, 2015.
 [6] 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.