# An Adaptive Denoising and Detection Approach for Underwater Sonar Image

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Non-Local Spatial Information Denoising Method

#### 2.1. Non-Local Spatial Information

#### 2.2. Our Proposed Denoising Method—An Adaptive Non-Local Spatial Information Denoising Algorithm Based on the Golden Ratio

Algorithm 1: the proposed denoising method |

Input: Original sonar image; |

Output: Denoising image; |

Initialization: $r$ (the radius of search window), $s$ (the radius of neighbourhood window); |

Procedure: |

1: For $q=1$ to ${s}^{2}$ do: |

2: Calculate $d$ using Equation (6); |

3: Calculate ${\rho}^{\left(q\right)}$ using Equation (5); |

4: For every search window in the input image, do: |

5: For any two different neighbourhood windows in the search window, do: |

6: Calculate the weighted Euclidean distance using Equation (4); |

7: Calculate the filtering degree parameter $h$ using Equation (9); |

8: Calculate $Ahmin$ and $Ahmax$ when the result of Equation (8) satisfies the golden ratio; |

9: For every search window in the input image, do: |

10: Calculate the filtering degree parameter $h$ using Equation (8); |

11: Calculate $Z$ using Equation (3); |

12: Calculate $w$ using Equation (2); |

13: Calculate non-local spatial information $\overline{x}$ using Equation (1). |

## 3. Culture Algorithm

#### 3.1. Cultural Algorithm Framework

#### 3.2. Our Proposed Cultural Algorithm—A New Adaptive Culture Algorithm

#### 3.2.1. Adaptive Initialization Algorithm Based on Data Field

_{i}= (R

_{i1}, R

_{i2}, ⋯, R

_{iD}), N is the size of R. D is the dimension of a data point. Every data point in R interacts with the data points around it. In this way, a data field is formed according to the interaction of different data points. The interaction between different data points is measured by potential functions in the data field. Generally, the closer data points have stronger interaction and greater potential. In contrast, the further data points have weaker interaction and lower potential. The potential function is defined as:

_{i}= (R

_{i1}, R

_{i2}) at the threshold ${R}_{*}$, R

_{i1}is the grey value of the ith pixel in the underwater sonar image. R

_{i2}is the average of the grey values of pixels in the neighborhood window. The neighborhood window centre is the ith pixel. ${m}_{{R}_{i}}$ is the frequency corresponding to the ith pixel in the two-dimensional histogram of the underwater sonar image. $\parallel {R}_{i}-{R}_{*}\parallel $ is the Euclidean distance and σ is the impact factor.

Algorithm 2: the proposed AIA-DF |

Input: Denoising image; |

Output: Initialized image; |

Initialization: $s$ (the radius of the neighbourhood window), $num$ (the number of the optimal threshold), $U$ (the set of optimal threshold potential solutions); |

Procedure: |

1: For every pixel in the input image, do: |

2: Calculate the mean grey of its neighbourhood; |

3: Establish the two-dimensional grey histogram of the input image; |

4: Establish the data field according to the grey histogram; |

5: repeat: |

6: Calculate the entropy of $H\left(A\right)$ using Equation (15); |

7: Calculate the entropy of $H\left(B\right)$ using Equation (16); |

8: Calculate the optimal threshold when the maximum of Equation (17) is obtained; |

9: Calculate ${U}^{*}$ using Equation (19); |

10: Update $U$ using Equation (18): |

11: Update $num$ using $num=num+1$: |

12: Until: the stopping criteria are met. |

#### 3.2.2. New Update Strategy

_{1}is a random number in [0,1], P(t) is the local attractor, and β is the contraction–expansion coefficient. ${S}_{b}$ is the situational knowledge of the subpopulation on behalf of the local best cultural individual. ${Y}_{w}$ is the local worst cultural individual.

## 4. Experiments and Discussion

#### 4.1. The Characteristics of the Underwater Sonar Images

#### 4.2. The Effectiveness Verification of the Proposed Denoising Method

#### 4.3. The Effectiveness Demonstration of the Proposed Detection Method

#### 4.4. The Performance Analysis of the New Update Strategy in NACA

#### 4.5. The Adaptability Demonstration of the Proposed Denoising Method and Detection Method

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Wang, X.; Guo, L.; Yin, J.; Liu, Z.; Han, X. Narrowband Chan-Vese model of sonar image segmentation: An adaptive ladder initialization approach. Appl. Acoust.
**2016**, 113, 238–254. [Google Scholar] [CrossRef] - Ye, X.; Zhang, Z.; Liu, P.; Guan, H. Sonar image segmentation based on GMRF and Level-set models. Ocean Eng.
**2010**, 37, 891–901. [Google Scholar] [CrossRef] - Wang, X.; Liu, S.; Teng, X.; Sun, J.; Jiao, J. SFLA with PSO local search for detection sonar image. In Proceedings of the 2016 35th Chinese Control Conference, Chengdu, China, 27–29 July 2016; pp. 3852–3857. [Google Scholar]
- Wu, J.P.; Guo, H. A method for sonar image segmentation based on combination of MRF and region growing. In Proceedings of the 2015 5th International Conference on Communication Systems and Network Technologies, Gwalior, India, 4–6 April 2015; pp. 457–460. [Google Scholar]
- Zhu, Z.; Yin, H.; Chai, Y.; Li, Y.; Qi, G. A novel multi-modality image fusion method based on image decomposition and sparse representation. Inf. Sci.
**2018**, 432, 516–529. [Google Scholar] [CrossRef] - Li, H.; Qiu, H.; Yu, Z.; Li, B. Multifocus image fusion via fixed window technique of multiscale images and non-local means filtering. Signal Process.
**2017**, 138, 71–85. [Google Scholar] [CrossRef] - Wang, X.; Liu, S.; Liu, Z. Underwater sonar image detection: A combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm. PLoS ONE
**2017**, 12, e0177666. [Google Scholar] [CrossRef] - Zhao, F.; Jiao, L.; Liu, H.; Gao, X. A novel fuzzy clustering algorithm with non-local adaptive spatial constraint for image segmentation. Signal Process.
**2011**, 91, 988–999. [Google Scholar] [CrossRef] - Zhao, F. Fuzzy clustering algorithms with self-tuning non-local spatial information for image segmentation. Neurocomputing
**2013**, 106, 115–125. [Google Scholar] [CrossRef] - Wang, L. Segmentation algorithm of fuzzy clustering on side scan sonar image. J. Huazhong Univ. Sci. Technol.
**2012**, 40, 25–29. [Google Scholar] - Mignotte, M.; Collect, C.; Perez, P.; Bouthemy, P. Three-class markovian segmentation of high-resolution sonar image. Comput. Vis. Image Underst.
**1999**, 76, 191–204. [Google Scholar] [CrossRef] - Mignotte, M.; Collect, C.; Perez, P.; Bouthemy, P. Sonar image segmentation using an unsupervised hierarchical MRF model. IEEE Trans. Signal Process.
**2000**, 9, 1216–1231. [Google Scholar] [CrossRef] - Vese, L.; Chan, T. A multiphase level set framework for image segmentation using the mumford and shah model. Int. J. Comput. Vis.
**2002**, 50, 271–293. [Google Scholar] [CrossRef] - Lianantonakis, M.; Petillot, Y. Sidescan sonar segmentation using active contours and level set methods. In Proceedings of the Oceans Europe 2005, Brest, France, France, 20–23 June 2005; pp. 719–724. [Google Scholar]
- Lianantonakis, M.; Petillot, Y. Sidescan sonar segmentation using texture descriptors and active contours. IEEE J. Ocean. Eng.
**2007**, 32, 744–752. [Google Scholar] [CrossRef] - Liu, G.; Bian, H.; Shi, H. Sonar image segmentation based on an improved level set method. Phys. Procedia
**2012**, 33, 1168–1175. [Google Scholar] [CrossRef] - Awad, N.; Ali, M.; Suganthan, P.; Reynolds, R. CADE: A Hybridization of cultural algorithm and differential evolution for numerical optimization. Inf. Sci.
**2017**, 378, 215–241. [Google Scholar] [CrossRef] - Khatami, A.; Mirghasemi, S.; Khosravi, A.; Lim, C.P.; Nahavandi, S. A new PSO-based approach to fire flame detection using K-Medoids clustering. Expert Syst. Appl.
**2017**, 68, 69–80. [Google Scholar] [CrossRef] - Morra, L.; Coccia, N.; Cerquitelli, T. Optimization of computer aided detection systems: An evolutionary approach. Expert Syst. Appl.
**2018**, 100, 45–156. [Google Scholar] [CrossRef] - Wei, Z.; Bu, Y. Cultural particle swarm optimization algorithm and its application. In Proceedings of the 2012 24th Chinese Control and Decision Conference, Taiyuan, China, 23–25 May 2012; pp. 740–744. [Google Scholar]
- Liu, T.; Jiao, L.; Ma, W.; Ma, J.; Shang, R. A new quantum-behaved particle swarm optimization based on cultural evolution mechanism for multiobjective problems. Knowl. Based Syst.
**2016**, 101, 90–99. [Google Scholar] [CrossRef] - Wang, X.; Hao, W.; Li, Q. An adaptive cultural algorithm with improved quantum-behaved particle swarm optimization for sonar image detection. Sci. Rep.
**2017**, 7, 17733. [Google Scholar] [CrossRef] - Wang, S.; Wang, D.; Li, C.; Li, Y.; Ding, G. Clustering by fast search and find of density peaks with data field. Chin. J. Electron.
**2016**, 25, 397–402. [Google Scholar] [CrossRef] - Zhang, Y.; Lu, K.; Gao, Y. Quantum algorithms and quantum-inspired algorithms. Chin. J. Comput.
**2013**, 36, 1835–1842. [Google Scholar] [CrossRef] - Wang, X.; Liu, S.; Li, Q.; Liu, Z. Underwater sonar image detection: A novel quantum-inspired shuffled frog leaping algorithm. Chin. J. Electron.
**2018**, 27, 588–594. [Google Scholar] [CrossRef] - Ding, W.; Wang, J.; Guan, Z.; Shi, Q. Enhanced minimum attribute reduction based on quantum-inspired shuffled frog leaping algorithm. J. Syst. Eng. Electron.
**2013**, 24, 426–434. [Google Scholar] [CrossRef] - Ding, W.; Wang, J.; Guan, Z. A minimum attribute self-adaptive cooperative co-evolutionary reduction algorithm based on quantum elitist frogs. J. Comput. Res. Dev.
**2014**, 51, 743–753. [Google Scholar] - Zhang, B.; Qi, H.; Sun, S.; Ruan, L.; Tan, H. Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using improved quantum particle swarm optimization. Int. J. Heat Mass Transf.
**2015**, 85, 300–310. [Google Scholar] [CrossRef]

**Figure 1.**The estimated values of the optimal threshold (image size: 277 × 325): (

**a**) Original sonar image; (

**b**) The estimated values of the optimal threshold.

**Figure 2.**The estimated values of the optimal threshold (image size: 173 × 167): (

**a**) Original sonar image; (

**b**) The estimated values of the optimal threshold.

**Figure 3.**The estimated values of the optimal threshold (image size: 197 × 211): (

**a**) Original sonar image; (

**b**) The estimated values of the optimal threshold.

**Figure 4.**The estimated values of the optimal threshold (image size: 205 × 201): (

**a**) Original sonar image; (

**b**) The estimated values of the optimal threshold.

**Figure 5.**The estimated values of the optimal threshold (image size: 130 × 106): (

**a**) Original sonar image; (

**b**) The estimated values of the optimal threshold.

**Figure 6.**The estimated values of the optimal threshold (image size: 146 × 135): (

**a**) Original sonar image; (

**b**) The estimated values of the optimal threshold.

**Figure 7.**The result of the linear fitting based on Table 1.

**Figure 9.**The denoising results based on Figure 1a of the proposed denoising method in this paper and the previous denoising method: (

**a**) The denoising result of the denoising method proposed in this paper; (

**b**) The result of filtering the degree parameter is selected by two adaptive thresholds in the proposed denoising method; (

**c**) The denoising result of the previous denoising method; (

**d**) The result of the filtering degree parameter is selected by two previous thresholds in the previous denoising method.

**Figure 10.**The detection results of the fuzzy c-means (FCM) based on Figure 9b,d: (

**a**) FCM detection result when $h=0.01$; (

**b**) FCM detection result when $h=0.019$; (

**c**) FCM detection result when $h=0.032$; (

**d**) FCM detection result when $h=0.05$.

**Figure 11.**Detection results of the image shown in Figure 9a: (

**a**) Detection result of NACA (new adaptive cultural algorithm); (

**b**) Detection result of QSFLA-NSM (quantum-inspired shuffled frog leaping algorithm combining the new search mechanism); (

**c**) Detection result of ACA-IQPSO (adaptive cultural algorithm with improved quantum-behaved particle swarm optimization); (

**d**) Detection result of QSFLA (quantum-inspired shuffled frog leaping algorithm); (

**e**) Detection result of CPSO (cultural particle swarm optimization algorithm); (

**f**) Detection result of QPSO (quantum-behaved particle swarm optimization).

**Figure 12.**The chart of the best fitness function values in Table 2.

**Figure 13.**Detection results of the underwater sonar image (image size: 112×117): (

**a**) Original sonar image; (

**b**) The denoising result of the denoising method proposed in this paper; (

**c**) Detection result of NACA; (

**d**) Detection result of QSFLA-NSM; (

**e**) Detection result of ACA-IQPSO; (

**f**) Detection result of QSFLA; (

**g**) Detection result of CPSO; (

**h**) Detection result of QPSO.

**Figure 14.**The chart of the best fitness function values in Table 3.

**Figure 15.**Detection result after the first iteration in the detection process of Figure 11: (

**a**) Detection result of NACA; (

**b**) Detection result of QSFLA-NSM; (

**c**) Detection result of ACA-IQPSO; (

**d**) Detection result of QSFLA; (

**e**) Detection result of CPSO; (

**f**) Detection result of QPSO.

**Figure 16.**The distribution of particle positions in the new update strategy and old update strategy: (

**a**) Position distribution of particles on Sphere function; (

**b**) Position distribution of particles on Griewank function.

**Figure 17.**The result of the fitness value calculation in the new update strategy and old update strategy: (

**a**) The optimization results of the Sphere function; (

**b**) The optimization results of the Griewank function.

**Figure 18.**Detection results of the underwater sonar image (image size: 259×368): (

**a**) Original sonar image; (

**b**) The denoising result of the denoising method proposed in this paper; (

**c**) Detection result of NACA.

**Figure 19.**Detection results of the underwater sonar image (image size: 259×368): (

**a**) Original sonar image; (

**b**) The denoising result of the denoising method proposed in this paper; (

**c**) Detection result of NACA.

**Figure 20.**Detection results of the underwater sonar image (image size: 203×101): (

**a**) Original sonar image; (

**b**) The denoising result of the denoising method proposed in this paper; (

**c**) Detection result of NACA.

- | $\mathit{h}\mathit{m}\mathit{i}\mathit{n}$ | $\mathit{h}\mathit{m}\mathit{a}\mathit{x}$ | $\mathit{\eta}$ |
---|---|---|---|

1 | 0.030 | 0.050 | 0.539 |

2 | 0.040 | 0.200 | 0.609 |

3 | 0.015 | 0.030 | 0.689 |

4 | 0.020 | 0.035 | 0.624 |

5 | 0.010 | 0.050 | 0.634 |

6 | 0.010 | 0.040 | 0.584 |

7 | 0.005 | 0.040 | 0.617 |

8 | 0.010 | 0.035 | 0.681 |

9 | 0.005 | 0.030 | 0.532 |

10 | 0.010 | 0.040 | 0.575 |

11 | 0.002 | 0.005 | 0.567 |

12 | 0.030 | 0.100 | 0.604 |

13 | 0.005 | 0.040 | 0.676 |

14 | 0.010 | 0.060 | 0.636 |

15 | 0.005 | 0.015 | 0.650 |

16 | 0.005 | 0.020 | 0.649 |

17 | 0.010 | 0.025 | 0.605 |

18 | 0.020 | 0.035 | 0.571 |

19 | 0.005 | 0.070 | 0.556 |

20 | 0.030 | 0.050 | 0.539 |

Iterative Times | NACA | QSFLA-NSM | ACA-IQPSO | QSFLA | CPSO | QPSO |
---|---|---|---|---|---|---|

1 | 3.024 | 2.188 | 2.028 | 1.969 | 1.737 | 1.724 |

2 | 3.024 | 2.495 | 2.320 | 2.554 | 2.100 | 2.024 |

3 | 3.024 | 2.695 | 2.520 | 2.554 | 2.236 | 2.083 |

4 | 3.024 | 2.695 | 2.520 | 2.554 | 2.315 | 2.083 |

5 | 3.024 | 2.695 | 2.520 | 2.554 | 2.417 | 2.241 |

6 | 3.087 | 2.695 | 2.806 | 2.554 | 2.417 | 2.241 |

7 | 3.087 | 2.695 | 2.806 | 2.554 | 2.421 | 2.241 |

8 | 3.087 | 2.862 | 2.806 | 2.727 | 2.475 | 2.410 |

9 | 3.087 | 2.862 | 2.806 | 2.727 | 2.475 | 2.410 |

10 | 3.087 | 2.862 | 2.806 | 2.727 | 2.475 | 2.410 |

Iterative Times | NACA | QSFLA-NSM | ACA-IQPSO | QSFLA | CPSO | QPSO |
---|---|---|---|---|---|---|

1 | 2.365 | 2.184 | 2.003 | 1.956 | 1.794 | 2.066 |

2 | 2.477 | 2.184 | 2.003 | 2.080 | 1.951 | 2.066 |

3 | 2.477 | 2.212 | 2.003 | 2.080 | 2.103 | 2.170 |

4 | 2.477 | 2.212 | 2.133 | 2.312 | 2.103 | 2.170 |

5 | 2.532 | 2.212 | 2.133 | 2.337 | 2.162 | 2.170 |

6 | 2.532 | 2.426 | 2.133 | 2.337 | 2.226 | 2.170 |

7 | 2.532 | 2.426 | 2.273 | 2.337 | 2.226 | 2.184 |

8 | 2.532 | 2.426 | 2.273 | 2.337 | 2.253 | 2.209 |

9 | 2.532 | 2.426 | 2.273 | 2.337 | 2.253 | 2.209 |

10 | 2.532 | 2.426 | 2.273 | 2.337 | 2.253 | 2.209 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, X.; Li, Q.; Yin, J.; Han, X.; Hao, W.
An Adaptive Denoising and Detection Approach for Underwater Sonar Image. *Remote Sens.* **2019**, *11*, 396.
https://doi.org/10.3390/rs11040396

**AMA Style**

Wang X, Li Q, Yin J, Han X, Hao W.
An Adaptive Denoising and Detection Approach for Underwater Sonar Image. *Remote Sensing*. 2019; 11(4):396.
https://doi.org/10.3390/rs11040396

**Chicago/Turabian Style**

Wang, Xingmei, Qiming Li, Jingwei Yin, Xiao Han, and Wenqian Hao.
2019. "An Adaptive Denoising and Detection Approach for Underwater Sonar Image" *Remote Sensing* 11, no. 4: 396.
https://doi.org/10.3390/rs11040396