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

To testify the effectiveness of NACA and AIA-DF, the detection experiments based on different underwater sonar images are presented. The proposed non-local spatial information denoising method based on the golden ratio in this paper is used for removing noise in the underwater sonar images. On that basis, the proposed NACA is used for underwater sonar image detection. Meanwhile, the proposed NACA is compared with QSFLA-NSM [7], ACA-IQPSO [22], QSFLA [26,27], CPSO [20], and QPSO [28]. Except that the number of clustering centres is adaptively set according to AIA-DF in NACA, the number of clustering centres is 3 in other intelligent optimization algorithms. The population size is 20, the sub-populations size is 5 in proposed NACA, QSFLA-NSM, and QSFLA, the size of the belief space is 8 in NACA, ACA-IQPSO, and CPSO, the global maximum number of iterations is 10, the local maximum number of iterations is 2 in NACA, QSFLA-NSM, and QSFLA. The experiment environment is using Matlab R2012b with a 2.7 GHz Core processor and 8 GB of RAM.

To demonstrate the effectiveness of NACA, Figure 11 shows the detection results of the underwater sonar image shown in Figure 9a.

As is described in Figure 11, the regions of object-highlight and shadow are more accurately detected by NACA in Figure 11a. It is found that many noise points cannot be removed in Figure 11b,d. In Figure 11e,f, the detection results have poor integrity in the regions of object-highlight and shadow, respectively. It will cause serious difficulty to the subsequent underwater sonar image recognition. Therefore, compared with the detection results of QSFLA-NSM, ACA-IQPSO, QSFLA-NSM, QSFLA, CPSO, and QPSO, the proposed NACA can effectively remove the noise and accurately complete underwater sonar image detection.

Subsequently, the quantitative analysis of the detection results in Figure 12 is performed. The values of fitness function [25] after each iteration in the detection process of NACA and contrast algorithms is shown in Table 2.

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

As can be seen from Table 2 and Figure 12, the best fitness values of the proposed NACA is the largest after each iteration. Only NACA converges after four iterations. The results show that the proposed NACA has a better search ability and a faster convergence speed (the speed corresponds to the number of iterations). Meanwhile, the fitness function values after the first iteration are close to the fitness function values after 10 iterations in Figure 12. This means that AIA-DF can obtain better initial clustering centres in the proposed NACA. Through qualitative analysis and quantitative analysis of the underwater sonar detection results, the effectiveness of the proposed NACA is verified.

To further verify the effectiveness of the proposed NACA, Figure 13 shows the detection results of the underwater sonar image.

**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.

The values of fitness function [25] after each iteration in the detection process of NACA and contrast algorithms are shown Table 3. Figure 14 shows the chart of the best fitness function values in Table 3.

**Table 3.** The values of fitness function after each iteration in the detection process.


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

As can be seen in Figure 13, NACA more accurately completes the detection of different regions in Figure 13c. Figure 13d,f show over detection in the shadow region. The detection result fails to effectively remove the noise in Figure 13e,g,h. At the same time, the best fitness values of NACA are also the largest after each iteration in Table 3 and Figure 14. Comparing with other algorithms, the detection results demonstrate that NACA has the better search ability and a faster convergence speed (the speed corresponds to the number of iterations) based on the better initialization results that were obtained by AIA-DF in the paper. Therefore, through qualitative and quantitative analysis, the proposed NACA can effectively remove the noise and better complete the process of underwater sonar image detection.

To demonstrate the effectiveness of AIA-DF, Figure 15 shows the detection result after the first iteration in the detection process of Figure 11. The fitness function value after iteration is shown in the first line of Table 2.

**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.

As can be seen in Figure 15, only NACA can accurately detect the region of the object highlight region and shadow. It also effectively removes the noise in the underwater sonar image in Figure 15a. These results show that AIA-DF can find more accurate clustering centres. In addition, it can be seen from Figures 15a and 11a that the detection result after the first iteration is almost identical with the final detection result. The experimental results demonstrate that AIA-DF contributes to improving convergence speed (the speed corresponds to the number of iterations), accuracy, and search ability in the proposed NACA. Through qualitative analysis and quantitative analysis of the underwater sonar image detection results after the first iteration, the effectiveness of AIA-DF is proved.

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

To demonstrate the superiority in the search ability of the new update strategy in NACA, in the benchmark functions, Sphere function and Griewank function are used to test the position distribution of particles in this paper. Sphere function is unimodal and only has one global optimal solution. Griewank function is multimodal and has many local optimal solutions, however only has one global optimal solution. Figure 16 shows the distribution of particle positions in the new update strategy and old update strategy [22]. The relevant parameters are as follows: the dimension of the solution space is 2, the size of the belief space is 30, the size of the subspaces is 5, the global maximum number of iterations is 10, and the local maximum number of iterations is 2.

**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.

It can be seen in Figure 16 that compared with the old update strategy, the distribution of particle positions in the new update strategy are more dispersed. The new update strategy is easier to obtain the global optimal solution and has a stronger search ability in this paper.

In order to further verify the effectiveness of the new update strategy in its search ability, the fitness function values are calculated by Sphere function and Griewank function in the new update strategy and old update strategy, and the result of the fitness function values are shown in Figure 17. The relevant parameters are as follows: the dimension of the solution space is 30, the size of the belief space is 10, the size of the subspaces is 2, the global maximum number of iterations is 100, and the local maximum number of iterations is 10.

As can be seen in Figure 17, the fitness function values of the old update strategy are always greater than that of the new update strategy in each iteration. Compared with the old update strategy, the new update strategy is more likely to jump out of the local optimization. The experiment results further demonstrate that the search ability of the new update strategy is better than the old update strategy.

**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.

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

To prove the adaptability of the proposed denoising method and NACA, Figure 18 shows the detection results of the structured seabed which is an object in sand ripples. Figure 19 shows the detection results of the starboard original sonar image with a ship. Figure 20 shows the detection results of a floating object. The experiment environment uses Matlab R2012b with a 2.7 GHz Core processor and 8 GB of RAM.

**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.

It can be seen from the detection results in Figure 18b, Figure 19b, and Figure 20b that the proposed denoising method can remove noise effectively in polytype underwater sonar images. The boundary information of the different regions is accurately detected in Figure 18c, Figure 19c, and Figure 20c. Moreover, the iteration times of the algorithm are only two times, which further proves the adaptability of the AIA-DF in this paper. Therefore, the adaptability of the proposed method has been effectively proved.

#### **5. Conclusions**

This paper proposed an adaptive approach to denoise and detect the underwater sonar image. The problem of the inappropriate filtering degree parameter means that it seriously affects the denoising performance in underwater sonar images, which is solved by the proposed adaptive non-local spatial information denoising method based on the golden ratio in the paper. NACA is proposed in this paper. Firstly, in the population space, AIA-DF is adopted to obtain good initial clustering centres by calculating the potential entropy of the data field from the underwater sonar images dataset. In the belief space, a new update strategy is adopted to update cultural individuals according to the idea of QSFLA. The new update strategy further improves the search ability of NACA.

We apply the proposed method to the different underwater sonar images. The experimental results demonstrate that the proposed denoising method can effectively remove noise and reduce the difficulty of the following underwater sonar image recognition. Compared to the comparison algorithms, the proposed NACA has more advantages in its search ability and convergence speed (the speed corresponds to the number of iterations). AIA-DF can better locate initial clustering centres and enhance convergence efficiency of NACA which contributes to accurately complete underwater sonar image detection and convergence to the global optimal solution within small epochs. This paper provides an effective and important method for underwater sonar image detection. It has much academic and practical importance.

**Author Contributions:** Conceptualization, X.W., J.Y., and Q.L.; Methodology, X.H. and W.H.; Software, W.H.; Investigation, X.H. and W.H.; Resources, X.W.; Writing—original draft preparation, Q.L. and W.H.; Writing—review and editing, X.W., Q.L., J.Y., and X.H.; Visualization, X.H.; Supervision, X.W. and J.Y.; Project administration, X.W.; Funding acquisition, X.W.

**Funding:** This research was supported in part by the National Natural Science Foundation of China grant number 41876110, the Fundamental Research Funds for the Central Universities of China grant number HEUCF180601, the Heilongjiang Province Outstanding Youth Science Fund of China grant number JC2017017, and in part by the Fok Ying-Tong Education Foundation of China grant number 151007.

**Conflicts of Interest:** The authors declare no conflict of interest.
