Non-Parametric Simultaneous Reconstruction and Denoising via Sparse and Low-Rank Regularization

Abstract

Spatial irregular sampling and random noise are two important factors that restrict the accuracy of seismic imaging. Seismic wavefield reconstruction and denoising based on sparse representation are two popular antidotes to these two inevitable issues, respectively. This article presents a non-parametric simultaneous reconstruction and denoising via sparse and low-rank regularization that dealt with the prestack gathers efficiently and automatically. The proposed method makes no additional prior assumptions on original data other than that the seismic signal is compressible. The key parameters estimation adopts a data-driven framework without person-dependent intervention. The basic idea of the approach is to combine the two related algorithms. Thus, the sparse decomposition needs to be performed only once. We first extract the solution matrix via Fourier dictionary and then perform the reconstruction and denoising successively in the sparse domain. Obtaining a perfect interpolation result requires that the seismic data satisfy the Shannon–Nyquist sampling theorem. However, data with steep-dip events or gaps, which cannot be adequate for the procedure, are a challenge that must be faced. This work proposes to deal with the common-offset gathers, which is characterized by flat, even approximate horizontal events, to handle the under-sampling obstacle. Another excellent property of the common-offset gathers is the simple and periodic repetitive texture structure, which can be represented sparsely and accurately by the Fourier dictionary. Thus, the computational complexity of the sparse representation is reduced. Both synthetic and practical applications indicate that our algorithm is efficient and effective.