3.2.2. New Update Strategy

In the belief space, to complete the update process by using the new update strategy in terms of QSFLA-NSM. In the first place, cultural individuals are divided into the multiple subpopulations and sorted from large to small according to the fitness function value [25]. Each subpopulation executes the local search strategy. In the second place, with the subpopulation complete local search strategy, all subpopulations are mixed for global information exchange. Then, the belief space is divided into subpopulations again. Local search and global information exchange will alternate until the number of iterations is satisfied

Local search completes the update of the worst cultural individual in each subpopulation. The first step of the local search [5] is expressed as:

$$newY\_{w}(t+1) = \begin{cases} \begin{array}{l} P(t) + \beta \cdot |S\_{b}(t) - Y\_{w}(t)| \cdot \ln\left(\frac{1}{\mu\_{1}}\right) \\\ P(t) - \beta \cdot |S\_{b}(t) - Y\_{w}(t)| \cdot \ln\left(\frac{1}{\mu\_{1}}\right) \end{array} \tag{20}$$

where *t* is the current local iterative times, *μ*<sup>1</sup> is a random number in [0,1], *P*(*t*) is the local attractor, and *β* is the contraction–expansion coefficient. *Sb* is the situational knowledge of the subpopulation on behalf of the local best cultural individual. *Yw* is the local worst cultural individual.

Comparing the fitness function values of *newYw* and *Yw*, if the fitness function value of *newYw* is larger, *Yw* is replaced by *newYw*. Whereas, *Sg* which represents the global best individual, will replace *Sb* in Equation (20). *newYw* is calculated by Equation (20) again. If the fitness function value of *newYw* is still less than *Yw*, it will randomly generate an individual from the solution space and replace *Yw*. When the upper limit of the local iteration number is reached, the local search is over.

#### **4. Experiments and Discussion**

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

The underwater sonar images include the object-highlight region, sea-bottom-reverberation region, and shadow region. However, because of the complexity of the underwater environment, the underwater sonar image is easily affected by the reverberation effect, strong speckle noise, fuzzy edge, and weak texture information. This means that the underwater sonar images contain a lot of noise.

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

To prove the superiority of the proposed denoising method, Figure 9 shows the denoising results based on Figure 1a of the proposed denoising method and the previous denoising method [7]. The experiment environment is using Matlab R2012b with a 2.7 GHz Core processor and 8 GB of RAM.

**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.

As can be seen from Figure 9b,d, compared with the previous thresholds *hmin* = 0.01, the adaptive thresholds *Ahmin* = 0.019 can remove more fairly small filtering degree parameters and effectively remove image noise points. Meanwhile, the threshold *Ahmax* = 0.032 is smaller than *hmax* = 0.05 which can remove more fairly large filtering degree parameters. It contributes to keeping the underwater sonar image details better when the image noise points are removed.

A relatively simple and effective the fuzzy c-means (FCM) [10] is used to further qualitatively verify the effectiveness of the denoising method proposed in this paper. Figure 10 shows the detection results of FCM based on the thresholds in Figure 9b,d.

As can be seen from Figure 10a,b, compared with the previous threshold *hmin*, *Ahmin* removes smaller parameters in a larger range. Therefore, it can effectively improve the performance of sonar images. Meanwhile, as shown in Figure 10c,d, compared with the previous threshold *hmax*, *Ahmax* can more accurately define the boundaries of relatively large *h*, which benefits preserving detail information in sonar images. The noise can be effectively removed on the basis of preserving image details by the proposed denoising method which contributes to the remainder of the image processing.

**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.
