# Time-Frequency Domain Seismic Signal Denoising Based on Generative Adversarial Networks
## 2 Method
### Generator Network Structure  
The generator is based on the U-Net architecture and can be seen as composed of three parts: an encoder, a decoder, and skip connections. As shown in Figure 2, the encoder takes the STFT time-frequency spectrum as input and produces downsampled feature maps. The decoder part upsamples and convolves the feature maps. Finally, via convolutions and outputs of two masked signals ranging from \((0,1)\), these two masked signals are multiplied with the real and imaginary parts of the input time-frequency spectrum, respectively, yielding the time-frequency spectrum of the effective signal. Figure 1: The overall structure of the proposed method. Figure 2: Structure of generator network. As shown in Figure 2, the generator follows the U-Net architecture, taking the real and imaginary parts of the STFT spectrum as input. The input data are processed through \(3\times 3\) convolutional kernels with instance normalization (IN) and ReLU activation function. The encoder part eventually represents the input as a \(256\times 4\times 51\) feature vector. Then, we use RSBU to further extract the feature (RSBU is the Residual Shrinkage Building Unit depicted in Figure 3). In the decoder part, bilinear interpolation and \(3\times 3\) convolutional kernels are used to generate the corresponding high-dimensional non-linear mapping. In the last layer, we use \(1\times 1\) convolution and Sigmoid to produce the mask ranging from 0 to 1. Compared to the standard U-Net, the generator incorporates improvements in the normalization, downsampling, and upsampling processes, making it more suitable for the task of seismic signal denoising. U-Net employs batch normalization (BN) for normalization. BN introduces noise to individual samples by computing the mean and variance across multiple samples, thereby diminishing the independence between different data points for tasks that require high output detail [19; 20]. In contrast, instance normalization (IN) removes the summation across the batch dimension, and the proposed method utilizes IN to independently compute the mean and variance for each channel. IN has been widely applied to tasks that require high output detail, such as generative adversarial networks (GANs) and image super-resolution [21; 22; 23], and it can better preserve the time-frequency spectral details of seismic signals [24]. U-Net performs downsampling through max-pooling layers, but [PERSON] et al. [25] demonstrated through experiments that using convolutions with larger strides instead of pooling for dimensionality reduction can improve the accuracy of image recognition tasks. In this work, we employ convolutions with a stride of 2 for downsampling. U-Net achieves upsampling through transposed convolutions, which involve padding the input feature map elements and the surrounding areas and then convolving the padded feature map. However, due to the padding between feature map elements, the outputs of transposed convolutions exhibit uneven overlaps, leading to the checkerboard artifact that causes a grid-like pattern of alternating light and dark pixels in the final output image [26]. To avoid this issue, we employ bilinear interpolation and the convolution kernels to generate the output. Figure 3: Structure of Residual Shrinkage Building Unit (RSBU). tion for upsampling, which does not produce checkerboard artifacts and is computationally simpler and more efficient. In deep neural networks, gradients may gradually diminish (vanishing gradient) or amplify (exploding gradient) during the backpropagation process, resulting in ineffective optimization of the parameters in the shallow layers. Residual Networks (ResNets) [27] alleviate the vanishing and exploding gradient problems by introducing a skip connection between the input and output. This allows the loss to be backpropagated not only through the convolutional layers but also directly through the identity mapping function.