Super-resolution of Defocus Blurred Images

Document Type : Original Article


Image Processing and Data Mining (IPDM) Research Lab, Faculty of Computer Engineering and Information Technology, Shahrood University of Technology, Shahrood, Iran


Super-resolution is a process that combines information from some low-resolution images in order to produce an image with higher resolution. In most of the previous related work, the blurriness that is associated with low resolution images is assumed to be due to the integral effect of the acquisition device’s image sensor. However, in practice there are other sources of blurriness as well, including atmospheric and motion blur that may be applied to low resolution images. The research done in this paper provides a super-resolution image from some low-resolution images suffering from blurriness due to defocus. In contrast to motion blur kernels that are sparse, the defocus blur kernel is non-sparse and continuous. Because of the continuity property of defocus blurring kernel, in this paper, we bound the gradient of blurring kernel using proper regularizers to satisfy this property. Experimental results on synthetic data demonstrate the effectiveness of the proposed method to produce high resolution and de-blurred images from some blurry low-resolution images.


1. Babacan, S.D., Molina, R. and Katsaggelos, A.K., “Variational
Bayesian super resolution”, IEEE Transactions on Image
Processing, Vol. 20, No. 4, (2010), 984–999.  
2. Hassanpour, H. and Seyyedyazdi, S. J., “Improving Superresolution
Information of
the Image”, International Journal of Engineering - Transaction
B: Applications, Vol. 31, No. 2, (2018), 241–249.  
3. Almeida, M.S. and Figueiredo, M., “Deconvolving images with
unknown boundaries using the alternating direction method of
multipliers”, IEEE Transactions on Image Processing, Vol. 22,
No. 8, (2013), 3074–3086.  
4. Tsai, R. Y. and Huang, T. ., “Multipleframe image restoration and
registration.”, Advances in Computer Vision and Image
Processing, Vol. 1, No. 2, (1984), 317–339.  
5. Katsaggelos, A.K., Molina, R. and Mateos, J., “Super resolution
of images and video”, Synthesis Lectures on Image, Video, and
Multimedia Processing, Vol. 1, No. 1, (2007), 1–134.  
6. Farsiu, S., Robinson, M.D., Elad, M. and Milanfar, P., “Fast and
robust multiframe super resolution”, IEEE Transactions on
Image Processing, Vol. 13, No. 10, (2004), 1327–1344.  
7. Wang, Z. and Qi, F., “On ambiguities in super-resolution
modeling”, IEEE Signal Processing Letters, Vol. 11, No. 8,
(2004), 678–681.  
8. Laghrib, A., Ezzaki, M., El Rhabi, M., Hakim, A., Monasse, P.
and Raghay, S., “Simultaneous deconvolution and denoising
using a second order variational approach applied to image super
resolution”, Computer Vision and Image Understanding, Vol.
168, (2018), 50–63.  
9. Fan, J., Wu, Y., Zeng, X., Huangpeng, Q., Liu, Y., Long, X. and
Zhou, J., “A Multi-view Super-Resolution Method with Jointoptimization
of Image Fusion and Blind Deblurring”, KSII
Transactions on Internet and Information Systems (TIIS), Vol.
12, No. 5, (2018), 2366–2395.  
10. Olshausen, B.A. and Field, D. J., “Emergence of simple-cell
receptive field properties by learning a sparse code for natural
images”, Nature, Vol. 381, No. 6583, (1996), 607–609.  
11. Levin, A., Fergus, R., Durand, F. and Freeman, W. T., “Image and
depth from a conventional camera with a coded aperture”, ACM
Transactions on Graphics (TOG), Vol. 26, No. 3, (2007), 1–9.  
12. Krishnan, D. and Fergus, R., “Fast image deconvolution using
hyper-Laplacian priors”, In Neural Information Processing
Systems Conference, (2009), 1033–1041.  
13. Almeida, M.S. and Figueiredo, M. A., “Blind image deblurring
with unknown boundaries using the alternating direction method
of multipliers.”, In 2013 IEEE International Conference on Image
Processing, (2013), 586–590.  
14. Boyd, S., Parikh, N., Chu, E., Peleato, B. and Eckstein, J.,
“Distributed optimization and statistical learning via the
alternating direction method of multipliers”, Foundations and
Trends in Machine Learning, Vol. 3, No. 1, (2011), 1–122.  
15. Boyd, S., Boyd, S.P. and Vandenberghe, L., Convex optimization,
Cambridge university press, (2004). 
16. Javaran, T.A., Hassanpour, H. and Abolghasemi, V., “Local
motion deblurring using an effective image prior based on both
the first-and second-order gradients”, Machine Vision and
Applications, Vol. 28, No. 3–4, (2017), 431–444.  
17. Wan, Z. and Bovik, A., “Mean squared error: love it or leave it?”,
IEEE Signal Processing Magazine, Vol. 28, No. 1, (2009), 98–