## 3 Implementation of Proposed Method
### Single Feature Extraction Network  
#### 3.2.1 Depthwise Separable Convolution  
The standard convolution operation has the effect of filtering features based on the convolutional kernels and combining features to produce a new representation. The filtering and combination steps can be split into two steps via the use of factorized convolutions called depthwise separable convolutions for substantial reduction in computational cost. Depthwise separable convolution proposed by [PERSON] in [22] are made up of two layers: depthwise convolutions and pointwise convolutions. Depthwise convolutions are applied on each input channel, and pointwise convolutions are then used to create a linear combination of the output of the depthwise layer.  
As shown in Figure 3a, a standard convolutional layer takes as input a \(D_{F}\times D_{F}\times M\) feature map \(F\) and produces a \(D_{F}\times D_{F}\times N\) feature map G where \(D_{F}\) is the width and height of the input feature map, \(M\) is the number of input channels, \(D_{G}\) is the width and height of the output feature map, and \(N\) is the number of the output channel. The standard convolutional layer is parameterized by convolution kernel K of size \(D_{K}\times D_{K}\times M\times N\), where \(D_{K}\) is the size of the kernel, \(M\) is the number of input channels, and \(N\) is the number of output channels. Standard convolutions have the computational cost of:  
\[D_{K}\cdot D_{K}\cdot M\cdot N\cdot D_{F}\cdot D_{F}, \tag{3}\]  
Figure 2: Synthetic aperture sonar image object segmentation results. (**a**) Original sonar image. (**b**) The highlight area of the object. (**c**) The shadow area of the object.  
where the computational cost depends multiplicatively on the number of input channels \(M\), the number of output channels \(N\), the kernel size \(D_{K}\times D_{K}\), and the feature map size \(D_{F}\times D_{F}\). Depthwise separable convolution decomposes a standard convolution into a depthwise convolution and a pointwise convolution [22]. It can break the interaction between the number of output channels and the size of the kernel [23; 24; 25].  
Depthwise convolution in Figure 3b has a computational cost of:  
\[D_{K}\cdot D_{K}\cdot M\cdot D_{F}\cdot D_{F}, \tag{4}\]  
It only filters input channels, it does not combine them to create new features. So, the pointwise convolution computes a linear combination of the output of depthwise convolution via 1 \(\times\) 1 convolution and generates new features [11], as seen in Figure 3c. Pointwise convolution has a computational cost of:  
\[M\cdot N\cdot D_{F}\cdot D_{F}, \tag{5}\]  
Therefore, the cost of depthwise separable convolutions can be described as:  
\[D_{K}\cdot D_{K}\cdot M\cdot D_{F}\cdot D_{F}+M\cdot N\cdot D_{F}\cdot D_{F}, \tag{6}\]  
which is the sum of the depthwise and pointwise convolutions. By expressing convolution as the process of filtering and combining, we obtain a reduction in the computation of:  
\[(D_{K}\cdot D_{K}\cdot M\cdot D_{F}+M\cdot N\cdot D_{F}\cdot D_{F})/(D_{K} \cdot D_{K}\cdot M\cdot N\cdot D_{F}\cdot D_{F})=1/N+1/D_{K}^{2}, \tag{7}\]  
When 3 \(\times\) 3 depthwise separable convolutions are used, the computation can be reduced to one-ninth of the standard convolutions. Compared with standard convolution, using depthwise separable convolution can save computing resources better, reduce classification time, and improve classification performance.