# Time-Frequency Domain Seismic Signal Denoising Based on Generative Adversarial Networks
## 2 Method
### Discriminator Network Structure  
For generative adversarial networks (GANs), the quality of the generator's output relies heavily on the performance of the discriminator, making the optimization of the discriminator crucial. In this work, we build upon GANs and divide the discriminator into a feature extraction module and a discrimination module. Taking two-channel time-frequency spectra as input, the feature extraction module adaptively extracts time-frequency spectral features and computes the perceptual loss, which measures the high-level feature differences between the generator's output and the real signal. The discrimination module evaluates the denoising performance of the generator. Perceptual loss has been applied in seismic image denoising tasks, where SeisGAN [29] and MSRD-GAN [30] both adopted a supervised approach, extracting perceptual features through a pre-trained VGG network [31] and combining pixel-level loss, perceptual loss, and adversarial loss to compute the generator loss according to Equation (3). \[\ell_{\text{G}}=\ell_{\text{MSE}}+\alpha\ell_{\text{VGG}}+\beta\ell_{\text{ ADV}} \tag{3}\]  
Compared to using only pixel loss, the inclusion of perceptual loss results in denoised data with more detailed information. The perceptual loss compares the convolutional features of the generated image and the real image, enabling the capture of more image details. In tasks such as image super-resolution and style transfer, pre-trained VGG networks are commonly used to extract perceptual features. However, using the VGG network to extract perceptual features for seismic signals and their time-frequency representations has certain limitations:  
(1) The VGG network was trained on the ILSVRC-2012 [32] dataset, which contains 1000 different categories of natural images, including animals, vehicles, natural landscapes,and buildings. The features of these images differ significantly from those of seismic time-frequency spectra, limiting the effectiveness of using the VGG network to extract features from seismic time-frequency spectra. (2) The VGG network takes RGB three-channel image data as input, while seismic signals represented in the time-frequency domain after a short-time Fourier transform (STFT) have two channels: real and imaginary parts. Therefore, before using the VGG network to extract features from seismic time-frequency spectra, the data need to be padded with zeros or other means to form a three-channel input. However, these padded channels do not contain any useful information, leading to a waste of computational resources. In this paper, the discriminator is divided into two components: a feature extraction module and a discrimination module. Taking two-channel time-frequency spectra as input, the feature extraction module adaptively extracts features from the time-frequency spectra, while the discrimination module evaluates the denoising performance of the generator  
The feature extraction module employs a three-step strategy for feature extraction: First, it extracts shallow features through a densely connected structure; second, it applies pooling operations of different kernel sizes to the shallow features and then upsamples the resulting feature maps using the PixShuffle [33] layer, concatenating them to form a multi-scale feature representation; finally, it introduces a channel attention mechanism to assign different weights to different channels of the multi-scale feature maps, thereby enhancing the overall expressive capability of the feature extraction module. In Figure 4, the feature extraction module extracts a feature map of size \(32\times 16\times 200\) through dense connections, downsamples the feature map through max pooling, and upsamples it through the PixShuffle layer. After concatenating the obtained features, we extract high-level features through LighWeight Convolutional Block Attention Module (LCBAM).