Rank-reduction approaches assume that seismic data in the frequency-space domain is of low-rank after a specific pre-transformation. 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 project onto the convex set (POCS) framework can be used for noise attenuation and data reconstruction simultaneously. Multichannel singular spectrum analysis (MSSA) is a classic 3D 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 3D 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.

Seismic data interpolation is a highly ill-posed problem. Therefore, designing an appropriate regulating method, aiming to reduce multi-solutions, is of utmost importance. Sparse and low-rank priors or constraints, which consider certain kinds of redundant data structures from different viewpoints, are widely used to constrain recovered seismic data to achieve a better fit. Considering that additional information enables us to obtain more accurate reconstructions, we formulated a seismic data interpolation model with irregular missing traces as a joint sparse and low-rank matrix approximation problem. The result is a solution that fits the given data, while simultaneously being sparse and low-rank. Subsequently, an efficient alternating algorithm is developed to solve the proposed objective function. Our proposed model called joint sparse and low-rank priors (JSLRP) model performs better on synthetic and field 3-D seismic data when compared to the classic low-rank methods, such as multichannel singular spectrum analysis (MSSA) and damped MSSA.