## 3 The Proposed Method  
### Mscae  
Based on the AE introduced in Section 2.1, the structure of the convolutional autoencoder is obtained by replacing the matrix operations in it with convolutional operations. Usually, features are extracted using convolutional kernels of the same size in the convolutional autoencoder. The literature [18] verified the effectiveness of the multi-scale convolutional network. Compared to traditional CNN, the use of parallel convolutional paths with different convolutional kernel sizes enables multi-scale learning, allowing the model to extract features from different time scales, ensuring the integrity of the representations and making full use of both global and local information. In this paper, we adopt the idea of multi-scale convolution to construct MSCAE to extract a more robust HI based on the full utilization of global and local degradation information, and the automatic extraction of HI can be realized. The structure of the proposed MSCAE is shown in Figure 3.  
As shown in Figure 3, the proposed MSCAE uses three convolutional paths for feature extraction of the input data. It is worth noting that the three convolutional paths use one-dimensional convolution with different convolutional kernel sizes, aiming to make full use of the global and local information of the input data for more effective feature extraction. In the encoding stage, three pathways perform parallel convolution and pooling operations on the input data. Suppose \(E_{n,m}^{i}\) denotes the \(n\)-th channel of convolutional layer data in the \(m\)-th encode block in the \(i\)-th(\(i=1,2,3\)) pathway and \(N_{m}^{e}\) is the number of convolutional layer channels in the \(m\)-th encode block. Then, the one-dimensional convolution operation can be expressed as:  
\[Z_{k,m+1}^{i,e}=f_{r}\left(\sum_{n=1}^{N_{m}^{e}}E_{n,m}^{i}*w_{k,m}^{i,e}+b_{ m}^{i,e}\right) \tag{10}\]  
where \(*\) is the one-dimensional convolution operation. \(w_{k,n,m}^{i,e}\) denotes the weight of the \(k\)-th convolutional kernel of the convolutional layer in the \(m\)-th encode block. \(b_{m}^{i,e}\) is bias. \(f_{r}\) adopts the ReLU activation function. \(Z_{k,m+1}^{i,e}\) denotes the \(k\)-th channel data of the convolutional layer operation result in the \(m\)-th encode block of the \(i\)-th pathway. After performing a convolution operation, a downsampling operation is performed on the convolution result using maximum pooling to reduce the size of the data. The pool  
Figure 2: The structure of LSTM. ing result \(I_{k,m+1}^{i}\) for the \(k\)-th channel data of the pooling layer in the \(m\)-th encoding block of the \(i\)-th pathway can be expressed as:  
\[E_{k,m+1}^{i}=P\Big{(}Z_{k,m+1}^{i,e},p_{m},s_{m}\Big{)} \tag{11}\]  
where \(P\) denotes the maximum pooling operation, \(p_{m}\) is the size of the pooling window in the \(m\)-th convolution block, and \(s_{m}\) is the stride. After the input data are extracted by \(L\) encoding blocks of features, the Flatten layer is used to turn the high-level representations into one-dimensional data, which is input to the fully connected block for HI extraction. It is worth noting that the fully connected block of MSCAE proposed in this paper uses only one fully connected layer in both encoding and decoding parts, and the number of hidden neurons is the same. Then, the extracted HI can be expressed as:  
\[\hat{y}=\sigma\Big{(}W_{fe}X_{e}+b_{fe}\Big{)} \tag{12}\]  
where \(\hat{y}\) denotes the extracted HI, \(W_{fe}\) and \(b_{fe}\) denote the encoded partial weight and bias, respectively, and \(\sigma\) denotes the Sigmoid activation function. In the decoding stage, there are also three parallel paths.