5D Seismic Data Reconstruction and De-noising Using the Parallel Matrix Factorization Method (An SVD-free Technique)

The fully sampled noise-free seismic data can be embedded into a low rank tensor. Missing traces and random noise increase the rank of the tensor, thereby permitting multidimensional pre-stack seismic data reconstruction to be treated as a tensor completion problem. While researchers have proposed a number of methods to solve the tensor completion problem, most of the methods utilize SVD to reduce the rank of the tensor and reconstruct the missing traces. The computational cost of SVD makes these algorithms unattractive for large batch processes. In this paper, we extend the matrix factorization method proposed for matrix completion to tensor completion. We investigate and apply an SVD free approach known as parallel matrix factorization (PMF) to solve 5D seismic data reconstruction. The main computational cost of PMF is attributed to solving for the pseudo inverse of a small matrix, which represents a substantial reduction in computational cost in comparison to SVD based algorithms. Finally, synthetic data sets and a field data set are used to examine the performance of PMF method.