High-Dimensional Seismic Data Reconstruction Based on Linear Radon Transform–Constrained Tensor CANDECOM/PARAFAC Decomposition

Random noise and missing seismic traces are common in field seismic data, which seriously affects the subsequent seismic processing flow. The complete noise-free high-dimensional seismic dataset in the frequency–space (f-x) domain under the local linear assumption are regarded as a low-rank tensor, and each high dimensional seismic dataset containing only one linear event is a rank-1 tensor. The tensor CANDECOM/PARAFAC decomposition (CPD) method estimates complete noise-free seismic signals by characterizing high-dimensional seismic signals as the sum of several rank-1 tensors. In order to improve the stability and effect of the tensor CPD algorithm, this paper proposes a linear Radon transform–constrained tensor CPD method (RCPD) by using the sparsity of factor matrix in the Radon domain after high-dimensional seismic signal tensor CPD and uses alternating direction multiplier method (ADMM) to solve the established optimization problem. This proposed method is an essential realization of the high-dimensional linear Radon transform, and the results of synthetic and field data reconstruction prove the effectiveness of the proposed method.