# Seismic Random Noise Attenuation via Low-Rank Tensor Network
## 5 Conclusions  
This paper introduces a novel approach for seismic denoising by integrating low-rank tensor approximation (LRTA) with deep learning (DL). By transforming the manually selected parameters of conventional LRTA into learnable parameters of a DL network, our proposed low-rank tensor network (LRTNet) enables the automatic acquisition of optimal values from training data, significantly reducing the parameter sensitivity of traditional LRTA methods. The embedded LRTA mechanism not only enhances the interpretability of the network, but also ensures that the method remains grounded in physical principles, bridging the gap between data-driven and model-driven approaches.  
Experimental evaluations on both synthetic and real field datasets demonstrate that LRTNet outperforms traditional methods, such as Pyseistr and TNN-SSTV, in suppressing random noise while preserving critical stratigraphic structures and fault discontinuities. On synthetic data, LRTNet achieves an average signal-to-noise ratio (SNR) improvement of 45.0% and 53.6% over Pyseistr and TNN-SSTV, respectively. Real data tests further confirm its practical applicability, showing consistent enhancements in noise suppression without compromising geological features.  
Despite its promising performance, LRTNet has limitations that warrant further investigation. These include signal leakage, computational efficiency challenges due to the sequential nature of the ADMM framework, and the gap between synthetic and real data domains. Future work will focus on addressing these limitations through techniques such as domain adaptation, parallelization of the ADMM framework, and the development of more refined evaluation metrics. Additionally, exploring the integration of LRTNet with other physics-aware DL architectures could further enhance its performance and applicability.  
In summary, LRTNet represents a significant advancement in seismic data processing, offering a robust, physics-aware solution for noise attenuation. Its ability to combine the interpretability of LRTA with the adaptive learning capabilities of DL positions it as a valuable tool for both academic research and industrial applications.  
Conceptualization, T.Z.; methodology, T.Z.; software, L.O. and T.C.; validation, T.Z. and L.O.; formal analysis, L.O.; investigation, L.O. and T.C.; resources, T.Z.; data curation, T.C.; writing--original draft preparation, T.Z. and L.O.; writing--review and editing, T.Z.; visualization, T.C.; supervision, T.Z.; project administration, T.Z.; funding acquisition, T.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Chengdu Key Research and Development Support Program \"Jie Bang Gua Shuai\" Project under grant number 2023-JB00-00012-GX.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original data presented in the study are all openly available. The synthetic 3D dataset for fault detection can be found in FaultSeg: [[https://github.com/xinwucwp/faultSeg](https://github.com/xinwucwp/faultSeg)]([https://github.com/xinwucwp/faultSeg](https://github.com/xinwucwp/faultSeg)) (accessed on 15 January 2024). F3-2020 is available on Seg Wiki: [[https://wiki.seg.org/wiki/F3_Netherlands](https://wiki.seg.org/wiki/F3_Netherlands)]([https://wiki.seg.org/wiki/F3_Netherlands](https://wiki.seg.org/wiki/F3_Netherlands)) (accessed on 3 March 2024). Penobscot is available on Seg Wiki: [[https://wiki.seg.org/wiki/Penobscot_3D](https://wiki.seg.org/wiki/Penobscot_3D)]([https://wiki.seg.org/wiki/Penobscot_3D](https://wiki.seg.org/wiki/Penobscot_3D)) (accessed on 18 March 2024).  
**Acknowledgments:** We appreciate all the contributors of FaultSeg for releasing the synthetic 3D fault dataset. We also want to thank all the contributors who collected and released the two real field datasets we used.  
**Conflicts of Interest:** The authors declare no conflicts of interest.