Low-rank approximation has emerged as a promising technique for recovering five-dimensional (5D) seismic data, yet the quest for higher accuracy and stronger rank robustness remains a critical pursuit. We introduce a low-rank approximation method by leveraging the complete graph tensor network (CGTN) decomposition and the learnable transform (LT), referred to as the LRA-LTCGTN method, to simultaneously denoise and reconstruct 5D seismic data. In the LRA-LTCGTN framework, the LT is employed to project the frequency tensor of the original 5D data onto a small-scale latent space. Subsequently, the CGTN decomposition is executed on this latent space. We adopt the proximal alternating minimization algorithm to optimize each variable. Both 5D synthetic data and field data examples indicate that the LRA-LTCGTN method exhibits notable advantages and superior efficiency compared to the damped rank-reduction (DRR), parallel matrix factorization (PMF), and LRA-CGTN methods. Moreover, a sensitivity analysis underscores the remarkably stronger robustness of the LRA-LTCGTN method in terms of rank without any optimization procedure with respect to rank, compared to the LRA-CGTN method.

低阶近似已成为恢复五维 (5D) 地震数据的一种有前景的技术，但追求更高的精度和更强的阶鲁棒性仍然是一个关键的追求。我们通过利用完整图张量网络 (CGTN) 分解和可学习变换 (LT) 引入一种低秩近似方法（称为 LRA-LTCGTN 方法），以同时对 5D 地震数据进行去噪和重建。在LRA-LTCGTN框架中，LT用于将原始5D数据的频率张量投影到小尺度潜在空间上。随后，在这个潜在空间上执行 CGTN 分解。我们采用近端交替最小化算法来优化每个变量。 5D 合成数据和现场数据示例表明，与阻尼秩降低 (DRR)、并行矩阵分解 (PMF) 和 LRA-CGTN 方法相比，LRA-LTCGTN 方法表现出显着的优势和卓越的效率。此外，敏感性分析强调了与 LRA-CGTN 方法相比，LRA-LTCGTN 方法在排名方面具有明显更强的鲁棒性，无需任何排名优化程序。