# A Denoising Method for Seismic Data Based on SVD and Deep Learning
## 2 Method
### Denoising Method Based on SVD and Deep Learning
#### 2.2.2 Deeply Separable Convolution in MobileNetV2 Networks  
Deeply separable convolution is a crucial part of the MobileNet network and its ability to operate efficiently. Deeply separable convolution is divided into two parts, the depthwise and pointwise convolutions. Depthwise convolution is the process of extracting features from an image using a single convolution channel to produce an output feature map that maintains the same channel as the input feature map. Pointwise convolution refers to the up-and down-dimensioning of the feature map by 1 \(\times\) 1 convolution. The network can achieve the same results as standard convolution with fewer parameters and operations by replacing standard convolution with these two components [23].  
The number of parameters and operations in the deeply separable convolution is \(\frac{1}{N}+\frac{1}{H_{i}^{2}}\) times the number of parameters of the standard convolution, where the number of convolution kernels is N, and the size of the convolution kernel is \(H_{i}\). The \(H_{i}\) in the MobileNetV2 network is 3, so the network has eight to nine times less computation than the standard convolution, reducing the number of operations to a large extent [23].  
The MobileNetV2 network structure is shown in Table 2 and Figure 3, with 17 bottleneck layers, 1 standard convolutional layer (Conv), and 2 pointwise convolution layers (Pw Conv), for a total of 54 trainable parameter layers. Figure 4 shows a bottleneck layer containing two pointwise convolutional layers and one depthwise convolutional layer (Dw Conv). When the bottleneck layer step size is 1, the training images are first up-dimensioned by 1 \(\times\) 1 convolution, and then depthwise convolution is performed to extract features. Finally, the input and output are summed up by linear pointwise convolution, forming the residual structure. When the bottleneck layer step size is 2, the shortcut structure is not added because the input size does not match the output, and the rest is consistency. The linear bottleneck and inverted residuals used in the MobileNetV2 structure optimize the network, resulting in deeper layers, smaller models, and faster runs [23].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Batch Size** & **Run Time (h)** & **ImageNet Accuracy (\%)** \\ \hline restnet50 & 8 & 8.77 & 99.91 \\ MobileNetV2 & 16 & 3.25 & 99.94 \\ \hline \hline \end{tabular}
\end{table}
Table 1: MobileNet comparison to popular models.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Input** & **Network Layer** & **Expansion Multiplier** & **Output Channels** & **Number Repetitions** & **Stride** \\ \hline
224\({}^{2}\)\(\times\) 3 & conv2d & - & 32 & 1 & 2 \\
112\({}^{2}\)\(\times\) 32 & bottleneck & 6 & 16 & 1 & 1 \\
112\({}^{2}\)\(\times\) 16 & bottleneck & 6 & 24 & 2 & 2 \\
56\({}^{2}\)\(\times\) 24 & bottleneck & 6 & 32 & 3 & 2 \\
28\({}^{2}\)\(\times\) 32 & bottleneck & 6 & 64 & 4 & 2 \\
14\({}^{2}\)\(\times\) 64 & bottleneck & 6 & 96 & 3 & 1 \\
14\({}^{2}\)\(\times\) 96 & bottleneck & 6 & 160 & 3 & 2 \\
7\({}^{2}\)\(\times\) 160 & bottleneck & 6 & 320 & 1 & 1 \\
7\({}^{2}\)\(\times\) 320 & conv2d 1 \(\times\) 1 & - & 1280 & 1 & 1 \\
7\({}^{2}\)\(\times\) 1280 & avgpool 7 \(\times\) 7 & - & - & 1 & - \\
1 \(\times\) 1 \(\times\) 1280 & conv2d 1 \(\times\) 1 & - & k & - & \\ \hline \hline \end{tabular} Note: Table 2 is referenced from [23].  
\end{table}
Table 2: MobileNetV2 network architecture.  
Figure 3: MobileNetV2 network architecture.