Three-dimensional seismic data reconstruction via partial sum of tensor nuclear norm minimisation

Rank-reduction (RR) has become a hotspot in seismic data reconstruction research in recent years. Traditional RR methods generally use the nuclear norm as a convex proxy for rank, but these methods overly penalise large singular values, leading to reconstruction results that deviate from the optimal solution. In this paper, we propose a tensor robust principal component analysis (TRPCA) model with minimisation of the partial sum of tensor nuclear norm (PSTNN) for three-dimensional (3D) reconstruction of seismic data. PSTNN minimises only the partial singular values and can approximate the rank function more accurately. TRPCA can accurately recover the 3D tensor corrupted by sparse errors, improving the accuracy of seismic data reconstruction. The experimental results of the simulated data and real data show that the reconstruction effect of the proposed method on the 3D seismic data is better than the compared methods.