# American Institute of Mathematical Sciences

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

 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.

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
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##### References:
The principle diagram of block segmentation of hyperchaotic image
Comparison of image "Cow" restoration effect
Comparison of image "Rabbit" restoration effect
Comparison of image "Golf" restoration effect
Comparison of image "Wall" restoration effect
Comparison of image "Stripes" restoration effect
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  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 $\downarrow 3.76$
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 $\downarrow 4.93$
 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 $\downarrow 4.93$
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  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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