Three-Dimensional Seismic Data Reconstruction Based on Fully Connected Tensor Network Decomposition

Rank-reduction approaches assume that seismic data in the frequency-space domain is of low-rank after a specific pretransformation. The presence of noise or missing traces will increase the rank; therefore, seismic data can be denoised and recovered via rank-reduction techniques. The iterative weighted projection onto convex sets (POCS) framework can be used for noise attenuation and data reconstruction simultaneously. Multichannel singular spectrum analysis (MSSA) is a classic 3-D seismic data reconstruction algorithm that rearranges the temporal frequency slices of the data with missing traces into a block Hankel matrix and then uses randomized singular value decomposition (RSVD) to interpolate slices. To further improve the efficiency and precision of 3-D seismic data reconstruction, we introduce the fully connected tensor network (FCTN) decomposition over the Hankel tensor of the frequency slices. We show that our novel rank-reduction method estimates fewer parameters than MSSA, yielding more accurate and robust results. Moreover, FCTN decomposes a fourth-order tensor into four factor contractions, which breaks the limitations that traditional tensor decomposition methods, such as CANDECOMP/PARAFAC (CP) and Tucker decomposition, cannot establish the connections between different factors and are less effective at characterizing relationships. The newly proposed approach does not require singular value decomposition (SVD), leading to an overall reduction in computational complexity. Synthetic and field examples are used to compare the performance of our method with MSSA, and our numerical results reveal the better performance of the proposed FCTN decomposition method for seismic data with large gaps or a high missing ratio.