Grayscale Images Deblurring Using Robust Optimization Problem in Uncertainty Conditions in Blurring Model Parameters
Subject Areas : electrical and computer engineering
Zeinab
Mohammadi
1
(Ferdosi University)
Ebrahim
Daneshifar
2
Abbas
Ebrahimi moghadam
3
(Ferdosi University)
M.
Khademi
4
(Ferdowsi University of Mashhad)
Keywords: Semi-blind de-blurringimage de-blurring filterrobust optimizationworst-case optimization,
Abstract :
Nowadays, one of the most important issues in the field of image processing is image de-blurring. De-blurring of an image can be achieved via two different approaches; blind de-blurring and non-blind de-blurring. In blind de-blurring, the kernel by which the blur has occurred is assumed unknown, while in non-blind de-blurring, this kernel is given. In blind de-blurring, the blurring kernel must be estimated in order to sharpen the corrupted image. This may increase the computational cost of the de-blurring process. Non-blind image de-blurring is an ill-posed problem with linear reverse issues. Therefore, we develop optimization problems in order to estimate the original sharp images. Usually, non-blind de-blurring methods assume that the blurring kernel is error-free, however, in practice our knowledge of the PSF is uncertain. Hence, in this paper, we use a semi-blind method for de-blurring the blurred image that is robust to this uncertainty. The proposed robust optimization model is followed by a filter for image de-blurring that can attain the solution with lowest possible error in the worst case scenarios, that is, the maximum uncertainty about the blurring kernel. Based on the simulation results, our proposed semi-blind model yields more than 4 dB PSNR improvements compared to conventional blind image de-blurring methods.
[1] J. G. N. PerChristian Hansen and D. P. O’Leary, Deblurring Images Matrices, Spectra, and Filtering, Siam, 2006.
[2] M. Gong, X. Jiang, and H. Li, "Optimization methods for regularization-based ill-posed problems: a survey and a multi-objective framework," Front. Comput. Sci., vol. 11, no. 3, pp. 362-391, Jun. 2017.
[3] J. M. Bioucas-Dias, "Blind estimation of motion blur parameters for image deconvolution," in Proc. Iberian Conference on Pattern Recognition and Image Analysis, pp. 604-611, Girona, Spain, 6-8 Jun. 2007.
[4] S. Xie, X. Zheng, W. Z. Shao, Y. D. Zhang, T. Lv, and H. Li, "Non-blind image deblurring method by the total variation deep network," IEEE Access, vol. 7, pp. 37536-37544, 2019.
[5] Y. Q. Liu, X. Du, H. L. Shen, and S. J. Chen, "Estimating generalized Gaussian blur kernels for out-of-focus image deblurring," IEEE Trans. Circuits Syst. Video Technol., vol. 31, no. 3, pp. 829-843, Mar. 2020.
[6] م. دهقان و م. محزون، "حذف تاری از تصاویر تارشده در اثر لرزش دوربین،" هفتمین کنفرانس ماشین بینایی و پردازش تصویر، 5 صص.، تهران، ایران، 26-25 آبان 1390.
[7] M. Welk, "A robust variational model for positive image deconvolution," Signal, Image Video Process., vol. 10, no. 2, pp. 369-378, 2016.
[8] M. Tofighi and O. Yorulmaz, "Phase and TV based convex sets for blind deconvolution of microscopic images," IEEE J. Sel. Top. Signal Process., vol. 4553, no. 1, pp. 1-11, Feb. 2015.
[9] H. Yang, X. Su, and S. Chen, "Blind image deconvolution algorithm based on sparse optimization with an adaptive blur kernel estimation," Appl. Sci., vol. 10, no. 7, p. 2437, 2020.
[10] L. Chen, F. Fang, T. Wang, and G. Zhang, "Blind image deblurring with local maximum gradient prior," in Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition, pp. 1742-1750, Long Beach, CA, USA, 15-20 Jun. 2019.
[11] ز. دلخسته و م. طالبی، "حذف اثر تاری ناشی از حرکت در تصاویر،" چهارمین کنفرانس ملی فناوری اطلاعات، کامپیوتر و مخابرات ،18 صص.، مشهد، دانشگاه تربت حیدریه، 22 تير 1396.
[12] R. M. Kudupudi and A. K. Jagannatham, "Robust blurred image recovery using minimax and semi-definite programming approaches," in Proc. IEEE Int. Conf. on Multimedia and Expo, ICME’13, 6 pp., San Jose, CA, USA, 15-19 Jul. 2013.
[13] K. B. Petersen and M. S. Pedersen, The Matrix Cookbook, Technical University of Denmark, Nov. 2012.
[14] Y. Shi and Q. Chang, "Acceleration methods for image restoration problem with different boundary conditions," Appl. Numer. Math., vol. 58, no. 5, pp. 602-614, 2008.
[15] Y. Xue-Fei, X. Ting-Fa, and B. Ting-Zhu, "Improved fixed point method for image restoration," Chinese J. Opt. Appl. Opt., vol. 6, no. 3, pp. 318-324, 2013.
[16] R. C. Gonzalez, Digital Image Processing, vol. 14, no. 3. 2002.
[17] L. E. L. Ghaoui, "Robust Solutions to Least-Squares Problems with Uncertain Data," 1997.
[18] H. Ji and K. Wang, "Robust image deblurring with an inaccurate blur kernel," IEEE Trans. on Image Processing, vol. 21, no. 4, pp. 1624-1634, Apr. 2012.
[19] A. Ben-Tal, L. El Ghaoui, and A. Nemirovski, Robust Optimization, Princeton University Press, 2009.
[20] E. A. Gharavol, Y. C. Liang, and K. Mouthaan, "Robust linear transceiver design in MIMO Ad Hoc cognitive radio networks," in Proc. IEEE 71st Veh. Technol. Conf., 5 pp, Taipei, Taiwan, 16-19 May 2010.
[21] B. Zhang, Z. He, K. Niu, and L. Zhang, "Robust linear beamforming for MIMO relay broadcast channel with limited feedback," IEEE Signal Process. Lett., vol. 17, no. 2, pp. 209-212, Feb. 2010.
[22] J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," pp. 1-24, 1998.
[23] M. H. Al-Towaiq and Y. S. Abu, "Two improved classes of Broyden's methods for solving nonlinear systems of equations," J. Math. Comput. Sci., vol. 17, pp. 22-31, 2017.
[24] F. Toutounian, J. Saberi-Nadjafi, and S. H. Taheri, "A hybrid of the newton-GMRES and electromagnetic meta-heuristic methods for solving systems of nonlinear equations," J. Math. Model. Algorithms, vol. 8, no. 4, pp. 425-443, 2009.
[25] A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, Siam, 2001.
[26] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
[27] A. Hore and D. Ziou, "Image quality metrics: PSNR vs. SSIM," in Proc. Int. Conf. Pattern Recognit., pp. 2366-2369, Istanbul, Turkey, 23-26 Aug. 2010.
[28] U. Sara, M. Akter, and M. S. Uddin, "Image quality assessment through FSIM, SSIM, MSE and PSNR-a comparative study," J. Journal of Computational Chemistry., vol. 7, no. 3, pp. 8-18, 2019.
[29] Z. Al-Ameen, "Faster deblurring for digital images using an ameliorated Richardson-Lucy algorithm," IEIE Trans. Smart Process. Comput., vol. 7, no. 4, pp. 289-295, 2018.
[30] E. A. Gharavol, Y. C. Liang, and K. Mouthaan, "Robust downlink beamforming in multiuser MISO cognitive radio networks," in Proc. IEEE 20th In. Symp. on Personal, Indoor, and Mobile Radio Communications pp. 808-812, Tokyo, Japan,13-16 Sept. 2009.