Seismic Random Noise Attenuation via Low-Rank Tensor Network

Seismic data are easily contaminated by random noise, impairing subsequent geological interpretation tasks. Existing denoising methods like low-rank approximation (LRA) and deep learning (DL) show promising denoising capabilities but still have limitations; for instance, LRA performance is parameter-sensitive, and DL networks lack interpretation. As an alternative, this paper introduces the low-rank tensor network (LRTNet), an innovative approach that integrates low-rank tensor approximation (LRTA) with DL. Our method involves constructing a noise attenuation model that leverages LRTA, total variation (TV) regularization, and weighted tensor nuclear norm minimization (WTNNM). By applying the alternating direction method of multipliers (ADMM), we solve the model and transform the iterative schemes into a DL framework, where each iteration corresponds to a network layer. The key learnable parameters, including weights and thresholds, are optimized using labeled data to enhance performance. Quantitative evaluations on synthetic data reveal that LRTNet achieves an average signal-to-noise ratio (SNR) of 9.37 dB on the validation set, outperforming Pyseistr (6.46 dB) and TNN-SSTV (6.10 dB) by 45.0% and 53.6%, respectively. Furthermore, tests on real field datasets demonstrate consistent enhancements in noise suppression while preserving critical stratigraphic structures and fault discontinuities. The embedded LRTA mechanism not only improves network interpretability, but also reduces parameter sensitivity compared to conventional LRA methods. These findings position LRTNet as a robust, physics-aware solution for seismic data restoration.