## 2 Related Work  
Seismic data acquisition, essential for oil and gas exploration, often faces the challenge of noise interference. The most common form of seismic noise is random noise, which can penetrate the entire time domain and significantly distort real seismic data. Over the years, numerous noise suppression techniques have been developed to mitigate such interference and enhance seismic data quality.  
Traditional methods, such as transform-domain-based approaches and sparse transforms, have been widely used for seismic denoising. Some early work by [PERSON] [1] introduced a random noise suppression technique, which was further refined with methods like empirical mode decomposition (EMD) [4], wavelet transforms [2], and curvelet transforms [3]. These techniques have demonstrated their ability to suppress random noise, but they often struggle with more complex, non-stationary noise types.  
More recent advancements in seismic denoising have leveraged machine learning and deep learning (DL) techniques. Several studies have explored the use of DL for seismic signal restoration. For example, [PERSON] et al. [32] proposed a U-Net deep neural network for seismic data denoising, achieving significant improvements in noise removal. Similarly, [PERSON] et al. [33] introduced a deep residual seismic denoising model, which surpassed traditional shallow neural networks in learning seismic features and reducing noise. Other work, such as that by [PERSON] et al. [34], utilized CNNs with dual residual structures to improve feature extraction and denoising performance. [PERSON] et al. [42] used the self-attention mechanism in the moving window to effectively suppress random seismic noise based on the Swin Transformer model in 2D seismic data denoising, thus improving the signal-to-noise ratio.  
Despite the success of these methods, many existing approaches still focus predominantly on the time-domain features of seismic signals, neglecting frequency-domain information. This oversight often leads to suboptimal performance, particularly when dealing with seismic data characterized by low signal-to-noise ratios (SNRs). To address this, recent research has emphasized the importance of multi-scale feature extraction and the incorporation of frequency-domain information. For example, [PERSON] et al. [26] developed an unsupervised learning method for seismic image denoising using convolutional neural networks, while [PERSON] et al. [40] proposed a Fourier-domain adaptation technique to enhance the performance of seismic models on real data. [PERSON] et al. [43] used the Swin Transformer and a multi-scale channel attention enhancement U-Net to improve seismic denoising, addressing complex noise in synthetic and in situ seismic data. [PERSON] et al. [44] used an adaptive time-frequency denoising method to solve source-related seismic noise, dynamically optimizing the threshold curve to effectively suppress high-amplitude noise and improve signal recovery.  
This paper builds upon these advancements by proposing a novel feedback information distillation network (FID-N) that operates in the NSCT domain. This method aims to effectively suppress seismic noise, especially in low-SNR conditions, by utilizing a two-path information distillation block in a recurrent manner. The feedback mechanism in the FID-N allows for iterative denoising, leveraging the strengths of each stage to improve the data quality progressively.