American Institute of Mathematical Sciences

Advanced
August & September  2019, 12(4&5): 1199-1218. doi: 10.3934/dcdss.2019083

Research on iterative repair algorithm of Hyperchaotic image based on support vector machine

Xin Li 1,, , Ziguan Cui 1, , Linhui Sun 1, , Guanming Lu 1, and  Debnath Narayan 2,

1. 

College of Telecommunications & Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
2. 

Department of Computer Science, Winona State University, Winona, MN 55987, USA

* Corresponding author: Xin Li

Received  August 2017 Revised  December 2017 Published  November 2018

The damaged area of the hyperchaotic image is prone to lack of texture information. It needs to make image restoration design to improve the information expression ability of the image. In this paper, an iterative restoration algorithm of hyperchaotic image based on support vector machine is proposed. The sample blocks in the damaged region of hyperchaotic images are divided into smooth mesh structures according to block segmentation method, and the neighborhood pixels of which points need to repair are ranked efficiently according to gradient values. According to the edge fuzzification features, the position of the important structural information of the damaged area is located. A multi-dimensional spectral peak search method is applied to construct the information feature subspace of image texture, so as to find the best matching block for restoring the damaged region of hyperchaotic image. Considering the features of structural information and texture information, the maximum likelihood algorithm is used to reconstruct the pixel elements in the image region by piecewise fitting. Through the support vector machine algorithm, the image iterative restoration is carried out. The simulation results show that the restoration method for hyperchaotic image can achieve effective restoration of image damaged area, the quality of restorationed image is better, and the computation speed is fast. The image restoration method can effectively ensure the visual effect of the reconstructed image.

Keywords: Support vector machine, hyperchaotic image, image restoration, edge fuzzification, features.
Mathematics Subject Classification: 46N30.
Citation: Xin Li, Ziguan Cui, Linhui Sun, Guanming Lu, Debnath Narayan. Research on iterative repair algorithm of Hyperchaotic image based on support vector machine. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1199-1218. doi: 10.3934/dcdss.2019083
References:
[1]

E. Abiri, Z. Bezareh and A. Darabi, The optimum design of ram cell based on the modified-gdi method using non-dominated sorting genetic algorithm ⅱ (nsga-ⅱ), Journal of Intelligent & Fuzzy Systems, 32 (2017), 4095-4108.   Google Scholar

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[22]

R. C. Tan, T. Lei, Q. M. Zhao, L. H. Gong and Z. H. Zhou, Quantum color image encryption algorithm based on a hyper-chaotic system and quantum fourier transform, International Journal of Theoretical Physics, 55 (2016), 1-17.   Google Scholar

[23]

X. Tang, Spectral analysis of a class of symmetric differential operators with logarithmic coefficients, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 91-102.   Google Scholar

[24]

J. Wang, Z. Lei and G. Chen, A parameter optimization method for an svm based on improved grid search algorithm, Applied Science & Technology, 24 (2012), 231-233.   Google Scholar

[25]

X. Wang and H. L. Zhang, A novel image encryption algorithm based on genetic recombination and hyper-chaotic systems, Nonlinear Dynamics, 83 (2016), 333-346.  doi: 10.1007/s11071-015-2330-8.  Google Scholar

[26]

Y. Wei, Assessment study on brain wave predictive ability to policemena??s safety law enforcement, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 193-204.   Google Scholar

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A. Wong and J. Orchard, A nonlocal-means approach to exemplar-based inpainting, in IEEE International Conference on Image Processing, 2008, 2600-2603. Google Scholar

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Z. Xu and J. Sun, Image inpainting by patch propagation using patch sparsity, IEEE Trans. Image Process, 19 (2010), 1153-1165.  doi: 10.1109/TIP.2010.2042098.  Google Scholar

[29]

L. Zhang and T. Z. Qiao, An binary segmentation algorithm for infrared image, Infrared Technology, 36 (2014), 649-651.   Google Scholar

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Y. Zhao and M. Li, A modified fuzzy c-means algorithm for segmentation of mri, in International Conference on Computational Intelligence and Multimedia Applications, 2003. Iccima 2003. Proceedings, 32 (2003), 146-149. Google Scholar

[31]

Y. Zhou, L. Li and K. Xia, Research on weighted priority of exemplar-based image inpainting, Journal of Electronics(China), 29 (2012), 166-170.   Google Scholar

[32]

H. Zhu, X. Zhang, H. Yu and et al., An image encryption algorithm based on compound homogeneous hyper-chaotic system, Nonlinear Dynamics, 89 (2017), 61-79. Google Scholar

show all references

References:
[1]

E. Abiri, Z. Bezareh and A. Darabi, The optimum design of ram cell based on the modified-gdi method using non-dominated sorting genetic algorithm ⅱ (nsga-ⅱ), Journal of Intelligent & Fuzzy Systems, 32 (2017), 4095-4108.   Google Scholar

[2]

S. Asawasamrit and C. Promsakon, On quasi-commutative kk-algebra, Journal of Discrete Mathematical Sciences & Cryptography, 19 (2016), 385-395.  doi: 10.1080/09720529.2015.1102885.  Google Scholar

[3]

M. N. A. Basheer Ahmad—Hugerat, The effectiveness of teachers' use of demonstrations for enhancing students' understanding of and attitudes to learning the oxidation-reduction concept, Eurasia Journal of Mathematics Science & Technology Education, 13 (2017), 555-570.   Google Scholar

[4]

J. Bensmail, R. Duvignau and S. Kirgizov, The complexity of deciding whether a graph admits an orientation with fixed weak diameter, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 31-42.   Google Scholar

[5]

L. Cai, H. Zhai, L. Yang and X. Tian, Assets evaluation credibility method based on the interpersonal relationship model, Journal of Interdisciplinary Mathematics, 20 (2017), 1047-1058.   Google Scholar

[6]

J. Chen, Z. H. Yuan, C. Yuan-Bo and S. O. Automation, Control method design of aircraft stability, Computer Simulation, 34 (2017), 39-43.   Google Scholar

[7]

L. Chen and F. Zhao, Application of local binary pattern weighting algorithm in face recognition based on support vector machine, Bulletin of Science & Technology, 237-240. Google Scholar

[8]

Y. Chen, Y. Zhou, X. Wang and L. Guo, Video information hiding algorithm based on diamond coding, Journal of Computer Applications, 37 (2017), 2806-2812.   Google Scholar

[9]

A. Criminisi, P. Perez and K. Toyama, Object Removal by Exemplar-Based Image Inpainting, Zunic J, Computer Vision and Pattern Recognition, Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Wisconsin: IEEE Computer Society, 2003. Google Scholar

[10]

P. Ferrara, T. Bianchi, A. D. Rosa and A. Piva, Image forgery localization via fine-grained analysis of cfa artifacts, IEEE Transactions on Information Forensics & Security, 7 (2012), 1566-1577.   Google Scholar

[11]

Y. Huang, Z. Wu, L. Wang and T. Tan, Feature coding in image classification: A comprehensive study., IEEE Transactions on Pattern Analysis & Machine Intelligence, 36 (2014), 493-506.   Google Scholar

[12]

M. A. Jian-Hong and J. I. Li-Xia, Study on agent immune network monitoring system model, Computer Simulation, 30 (2013), 213-216.   Google Scholar

[13]

T. H. Kwok, H. Sheung and C. C. L. Wang, Fast Query for Exemplar-Based Image Completion, vol. 19, IEEE Press, 2010. doi: 10.1109/TIP.2010.2052270.  Google Scholar

[14]

L. Lei, P. C. Wei, L. I. Li and S. Yin, Fast image encryption algorithm based on a second secret key, Science Technology & Engineering, 16 (2016), 259-263.   Google Scholar

[15]

T. Li, X. He, Q. Teng and X. Wu, Adaptive bi-lp-l2-norm based blind super-resolution reconstruction for single blurred image, Journal of Computer Applications, 37 (2016), 2313-2318.   Google Scholar

[16]

L. I. Liu-Qing and Z. L. Chen, Risk early warning of stampedes based on visual image, Computer Simulation, 32 (2015), 429-432.   Google Scholar

[17]

T. Long, W. Jiao, G. He and W. Wang, Automatic line segment registration using gaussian mixture model and expectation-maximization algorithm, IEEE Journal of Selected Topics in Applied Earth Observations & Remote Sensing, 7 (2014), 1688-1699.   Google Scholar

[18]

S. Lyu, X. Pan and X. Zhang, Exposing region splicing forgeries with blind local noise estimation, International Journal of Computer Vision, 110 (2014), 202-221.   Google Scholar

[19]

H. Qin, H. Zhao, H. Zhao and C. N. University, Research on the digital image encryption algorithm based on double chaos, Bulletin of Science & Technology, 32 (2016), 169-173.   Google Scholar

[20]

Z. Q. Song, Y. F. Long, K. Wang and T. S. Department, Modeling and performance research on hysteresis system basing on svm, Computer Simulation, 32 (2015), 398-402.   Google Scholar

[21]

Z. Sun, Z. X. Wang, M. Bai and J. S. Zhang, Image inpainting method based on self-organizing maps and k-means clustering, Science Technology & Engineering, 12 (2012), 1790-1794.   Google Scholar

[22]

R. C. Tan, T. Lei, Q. M. Zhao, L. H. Gong and Z. H. Zhou, Quantum color image encryption algorithm based on a hyper-chaotic system and quantum fourier transform, International Journal of Theoretical Physics, 55 (2016), 1-17.   Google Scholar

[23]

X. Tang, Spectral analysis of a class of symmetric differential operators with logarithmic coefficients, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 91-102.   Google Scholar

[24]

J. Wang, Z. Lei and G. Chen, A parameter optimization method for an svm based on improved grid search algorithm, Applied Science & Technology, 24 (2012), 231-233.   Google Scholar

[25]

X. Wang and H. L. Zhang, A novel image encryption algorithm based on genetic recombination and hyper-chaotic systems, Nonlinear Dynamics, 83 (2016), 333-346.  doi: 10.1007/s11071-015-2330-8.  Google Scholar

[26]

Y. Wei, Assessment study on brain wave predictive ability to policemena??s safety law enforcement, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 193-204.   Google Scholar

[27]

A. Wong and J. Orchard, A nonlocal-means approach to exemplar-based inpainting, in IEEE International Conference on Image Processing, 2008, 2600-2603. Google Scholar

[28]

Z. Xu and J. Sun, Image inpainting by patch propagation using patch sparsity, IEEE Trans. Image Process, 19 (2010), 1153-1165.  doi: 10.1109/TIP.2010.2042098.  Google Scholar

[29]

L. Zhang and T. Z. Qiao, An binary segmentation algorithm for infrared image, Infrared Technology, 36 (2014), 649-651.   Google Scholar

[30]

Y. Zhao and M. Li, A modified fuzzy c-means algorithm for segmentation of mri, in International Conference on Computational Intelligence and Multimedia Applications, 2003. Iccima 2003. Proceedings, 32 (2003), 146-149. Google Scholar

[31]

Y. Zhou, L. Li and K. Xia, Research on weighted priority of exemplar-based image inpainting, Journal of Electronics(China), 29 (2012), 166-170.   Google Scholar

[32]

H. Zhu, X. Zhang, H. Yu and et al., An image encryption algorithm based on compound homogeneous hyper-chaotic system, Nonlinear Dynamics, 89 (2017), 61-79. Google Scholar

Figure 1.  The principle diagram of block segmentation of hyperchaotic image
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Figure 2.  Comparison of image "Cow" restoration effect
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Figure 3.  Comparison of image "Rabbit" restoration effect
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Figure 4.  Comparison of image "Golf" restoration effect
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Figure 5.  Comparison of image "Wall" restoration effect
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Figure 6.  Comparison of image "Stripes" restoration effect
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Table 1.  Comparison of experiment data in the first group
SVM iterative restoration algorithm Criminisi algorithm
Image data set Computing time
$T1$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Computing time
$T2$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Ratio of restoration restoration time
$R = T2/T1$		 Comparison of signal-to-noise ratio:
$(U-V)/$
$ V(\%)$
Cow($512\times 384$) 209.656 22.564 1545.233 21.544 8.24 $\uparrow 3.54$
Rabbit($402\times 336)$ 20.53 33.241 174.324 33.232 8.35 $\uparrow 1.56$
Golf($262\times 350)$ 12.234 30.665 85.245 30.344 7.02 $\downarrow 0.57$
Wall($190\times 186)$ 6.323 28.543 46.314 30.454 7.34 $\downarrow 5.96$
Stripes($176\times 155)$ 2.453 42.032 16.543 43.445 6.64 $\downarrow 3.76$
Table Options

Download as excel

SVM iterative restoration algorithm Criminisi algorithm
Image data set Computing time
$T1$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Computing time
$T2$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Ratio of restoration restoration time
$R = T2/T1$		 Comparison of signal-to-noise ratio:
$(U-V)/$
$ V(\%)$
Cow($512\times 384$) 209.656 22.564 1545.233 21.544 8.24 $\uparrow 3.54$
Rabbit($402\times 336)$ 20.53 33.241 174.324 33.232 8.35 $\uparrow 1.56$
Golf($262\times 350)$ 12.234 30.665 85.245 30.344 7.02 $\downarrow 0.57$
Wall($190\times 186)$ 6.323 28.543 46.314 30.454 7.34 $\downarrow 5.96$
Stripes($176\times 155)$ 2.453 42.032 16.543 43.445 6.64 $\downarrow 3.76$
Table 2.  Comparison of experiment data in the second group
SVM iterative restoration algorithm Criminisi algorithm
Image data set Computing time
$T1$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Computing time
$T2$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Ratio of restoration restoration time
$R = T2/T1$		 Comparison of signal-to-noise ratio:
$(U-V)/$
$V(\%)$
Cow($512\times 384)$ 142.354 22.545 1655.221 21.444 11.85 $\uparrow 1.24$
Rabbit($402\times 336)$ 15.545 32.740 157.545 33.464 11.55 $\downarrow 1.45$
Golf($262\times 350)$ 7.344 30.469 85.565 30.443 11.45 $\uparrow 0.51$
Wall($190\times 186)$ 4.455 30.908 46.877 30.356 9.56 $\downarrow 0.56$
Stripes($176\times 155)$ 1.666 41.876 16.54 43.676 9.65 $\downarrow 4.93$
Table Options

Download as excel

SVM iterative restoration algorithm Criminisi algorithm
Image data set Computing time
$T1$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Computing time
$T2$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Ratio of restoration restoration time
$R = T2/T1$		 Comparison of signal-to-noise ratio:
$(U-V)/$
$V(\%)$
Cow($512\times 384)$ 142.354 22.545 1655.221 21.444 11.85 $\uparrow 1.24$
Rabbit($402\times 336)$ 15.545 32.740 157.545 33.464 11.55 $\downarrow 1.45$
Golf($262\times 350)$ 7.344 30.469 85.565 30.443 11.45 $\uparrow 0.51$
Wall($190\times 186)$ 4.455 30.908 46.877 30.356 9.56 $\downarrow 0.56$
Stripes($176\times 155)$ 1.666 41.876 16.54 43.676 9.65 $\downarrow 4.93$
Table 3.  Comparison of experiment data in the third group
SVM iterative restoration algorithm Criminisi algorithm
Image data set Computing time
$T1$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Computing time
$T2$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Ratio of restoration restoration time
$R = T2/T1$		 Comparison of signal-to-noise ratio:
$(U-V)/$
$V(\%)$
Cow($512\times 384)$ 109.464 22.454 1232.243 22.976 11.63 $\uparrow 1.12$
Rabbit($402\times 336)$ 13.045 31.554 163.465 32.566 12.34 $\downarrow 2.67$
Golf($262\times 350)$ 6.454 30.464 81.354 30.654 13.43 $\uparrow 0.34$
Wall($190\times 186)$ 3.833 28.578 40.456 28.533 10.46 $\downarrow 0.45$
Stripes($176\times 155)$ 1.354 40.665 15.566 43.355 9.76 $\downarrow 5.45$
Table Options

Download as excel

SVM iterative restoration algorithm Criminisi algorithm
Image data set Computing time
$T1$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Computing time
$T2$(S)		 The signal to noise ratio of the restored image:
V($dB$)		 Ratio of restoration restoration time
$R = T2/T1$		 Comparison of signal-to-noise ratio:
$(U-V)/$
$V(\%)$
Cow($512\times 384)$ 109.464 22.454 1232.243 22.976 11.63 $\uparrow 1.12$
Rabbit($402\times 336)$ 13.045 31.554 163.465 32.566 12.34 $\downarrow 2.67$
Golf($262\times 350)$ 6.454 30.464 81.354 30.654 13.43 $\uparrow 0.34$
Wall($190\times 186)$ 3.833 28.578 40.456 28.533 10.46 $\downarrow 0.45$
Stripes($176\times 155)$ 1.354 40.665 15.566 43.355 9.76 $\downarrow 5.45$
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