Subspace-based non-blind deconvolution

Peixian Zhuang; Xinghao Ding; Jinming Duan; Peixian Zhuang; Xinghao Ding; Jinming Duan

doi:10.3934/mbe.2019108

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2202-2218. doi: 10.3934/mbe.2019108

Previous Article Next Article

Research article Special Issues

Subspace-based non-blind deconvolution

1.
School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Ningliu Road, Nanjing, Jiangsu, 210044, P. R. China
2.
School of Information Science and Engineering, Xiamen University, Haiyun Garden, Xiamen, Fujian, 361005, P. R. China
3.
School of Computer Science, University of Nottingham, Wollaton Road, Nottingham, NG8 1BB, United Kingdom

Received: 05 January 2019 Accepted: 19 February 2019 Published: 14 March 2019

In this paper, we develop a novel subspace-based recovery algorithm for non-blind deconvolution (named SND). With considering visual importance difference between image structures and smoothing areas, we propose subspace data fidelity for protecting image structures and suppressing both noise and artifacts. Meanwhile, with exploiting the difference of subspace priors, we put forward differentiation modelings on different subspace priors for improving deblurring performance. Then we utilize the least square integration method to fuse deblurred estimations and to compensate information loss of subspace deblurrings. In addition, we derive an e cient optimization scheme for addressing the proposed objective function by employing the methods of least square and fast Fourier transform. Final experimental results demonstrate that the proposed method outperforms several classical and state-of-the-art algorithms in both subjective and objective assessments.
- non-blind deconvolution,
- subspace fidelity,
- subspace prior,
- least square integration,
- fast Fourier transform
Citation: Peixian Zhuang, Xinghao Ding, Jinming Duan. Subspace-based non-blind deconvolution[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2202-2218. doi: 10.3934/mbe.2019108

Related Papers:

Abstract

In this paper, we develop a novel subspace-based recovery algorithm for non-blind deconvolution (named SND). With considering visual importance difference between image structures and smoothing areas, we propose subspace data fidelity for protecting image structures and suppressing both noise and artifacts. Meanwhile, with exploiting the difference of subspace priors, we put forward differentiation modelings on different subspace priors for improving deblurring performance. Then we utilize the least square integration method to fuse deblurred estimations and to compensate information loss of subspace deblurrings. In addition, we derive an e cient optimization scheme for addressing the proposed objective function by employing the methods of least square and fast Fourier transform. Final experimental results demonstrate that the proposed method outperforms several classical and state-of-the-art algorithms in both subjective and objective assessments.

References

[1]	G. Wang, D. L. Snyder and J. A. O'Sullivan, et al., Iterative deblurring for CT metal artifact reduction, IEEE Trans. Med. Imag., 28 (1996), 657–664.
[2]	M. Jiang, G. Wang and M. W. Skinner, et al., Blind deblurring of spiral CT images, IEEE Trans. Med. Imag., 22 (2003), 837–845.
[3]	X. Kan, Y. Zhang and L. Zhu, et al., Snow cover mapping for mountainous areas by fusion of MODIS L1B and geographic data based on stacked denoising auto-encoders, Computers, Materials and Continua, 57 (2018), 49–68.
[4]	L. He, D. Ouyang and M. Wang, et al. , A method of identifying thunderstorm clouds in satellite cloud image based on clustering, Computers, Materials and Continua, 57 (2018), 549–570.
[5]	C. Thorpe, F. Li and Z. Li, et al., A coprime blur scheme for data security in video surveillance, IEEE Trans. Pattern Anal. Machine Intell., 35 (2013), 3066–3072.
[6]	J. Wang, T. Li and X. Luo, et al., Identifying computer generated images based on quaternion central moments in color quaternion wavelet domain, IEEE Trans. Circuits Syst. Video Technol., (2018), 1.
[7]	S. Zhou, W. Liang and J. Li, et al., Improved VGG model for road traffic sign recognition, Computers, Materials and Continua, 57 (2018), 11–24.
[8]	J. Liu, N. Sun and X. Li, et al., Rare bird sparse recognition via part-based gist feature fusion and regularized intraclass dictionary learning, Computers, Materials and Continua, 55 (2018), 435–446.
[9]	Q. Shan, J. Jia and A. Agarwala, High-quality motion deblurring from a single image, ACM Trans. Graphics., 27 (2008), 73.
[10]	S. Cho and S. Lee, Fast motion deblurring, ACM Trans. Graphics., 28 (2009), 145.
[11]	I. Caiszar, Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems, Ann. Stat., 8 (1991), 2032–2066.
[12]	J. Li, Z. Shen and R. Yin, et al., A reweighted ${\ell _2}$ method for image restoration with Poisson and mixed Poisson-Gaussian noise, UCLA Preprint 68 (2012).
[13]	P. Zhuang, Y. Huang and D. Zeng, et al., Non-blind deconvolution using `1-norm high-frequency fidelity, Multimed. Tools Appl., 76 (2016), 1–9.
[14]	J. Yang, Y. Zhang and W. Yin, An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise, SIAM J. Sci. Comput., 31 (2009), 2842–2865.
[15]	A. Tikhonov, On the stability of inverse problems, Dokl. Akad. Nauk SSSR, 39 (1943), 195–198.
[16]	S. Osher, L. Rudin and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), 259–268.
[17]	Y. Wang, J. Wang and W. Yin, et al., A new alternating minimization algorithm for total variation image reconstruction, SIAM J. Imaging Sci., 1 (2008), 248–272.
[18]	D. Krishnan and R. Fergus, Fast image deconvolution using hyper-laplacian priors, Adv. Neural Inf. Process. Syst., (2009), 1033–1041.
[19]	D. Krishnan, T. Tay and R. Fergus, Blind deconvolution using a normalized sparsity measure, IEEE Conf. Comput. Vis. Pattern Recognit., (2011), 2657–2664.
[20]	L. Xu, C. Lu and Y. Xu, et al., Image smoothing via `0 gradient minimization, ACM Trans. Graphics., 30 (2011), 174.
[21]	L. Xu, S. Zheng and J. Jia, Unnatural ${\ell _0}$ sparse representation for natural image deblurring, IEEE Conf. Comput. Vis. Pattern Recognit., (2013), 1107–1114.
[22]	W. Dong, L. Zhang and G. Shi, Centralized sparse representation for image restoration, IEEE Int. Conf. Comput. Vis., (2011), 1259–1266.
[23]	W. Dong, L. Zhang and G. Shi, et al., Nonlocally centralized sparse representation for image restoration, IEEE Trans. Image Process., 22 (2013), 1620–1630.
[24]	J. Zhang, D. Zhao and R. Xiong, et al., Image restoration using joint statistical modeling in a space-transform domain, IEEE Trans. Circuits Syst. Video Technol., 24 (2014), 915–928.
[25]	V. M. Patel, R. Maleh and A. C. Gilbert, et al., Gradient-based image recovery methods from incomplete Fourier measurements, IEEE Trans. Image Process. 21 (2012), 94–105.
[26]	Z. Wang, A. C. Bovik and H. R. Sheikh, et al., Image quality assessment: from error visibility to structural similarity, IEEE Trans. Image Process., 13 (2004), 600–612.
[27]	P. Zhuang, X. Fu and Y. Huang,et al., A novel framework method for non-blind deconvolution using subspace images priors, Signal Processing: Image Communication, 46 (2016), 17–28.
[28]	T. Chan, S. Esedoglu and F. Park, et al., Recent developments in total variation image restoration, Mathematical Models of Computer Vision, 17 (2015).
[29]	L. Xu and J. Jia, Two-phase kernel estimation for robust motion deblurring, Eur. Conf. Comput. Vis., (2010), 157–170.
[30]	C. C. Lee and W. L. Hwang, Sparse representation of a blur kernel for out-of-focus blind image restoration, IEEE Int. Conf. Image Process., (2016), 2698–2702.
[31]	S. Cho, J. Wang and S. Lee, Handling outliers in non-blind image deconvolution, IEEE Int. Conf. Comput. Vis., (2011), 495–502.
[32]	A. Levin, Y. Weiss and F. Durand, et al., Understanding and evaluating blind deconvolution algorithms, IEEE Conf. Comput. Vis. Pattern Recognit., (2009), 1964–1971.

Reader Comments

Your name:*

Email:*
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)