Seismic Data Reconstruction and Denoising by Enhanced Hankel Low-Rank Matrix Estimation

Abstract

Seismic data reconstruction and denoising play a fundamental role in most seismic data processing algorithms which are often designed for regularly sampled and reliable data. By using the fact that the (block) Hankel matrix formulated from clean seismic data is low-rank if it corresponds to a few linear events, the low-rank based approach has been successfully used for seismic data reconstruction and denoising. In this paper, we simultaneously exploit the Hankel and low-rank structures within the (block) Hankel matrices of the clear and complete seismic data and formulate the problem of seismic data reconstruction and denoising as a Hankel low-rank reconstruction problem. The additional Hankel structure can further improve the performance for reconstruction and denoising. We then propose an iterative algorithm for solving the corresponding Hankel low-rank reconstruction problem. The algorithm is based on the alternating direction method of multipliers (ADMM) and has closed-form solutions for each update. Experiments on both synthetical and real seismic data demonstrate the superior performance of the proposed algorithm compared with conventional low-rank based methods for simultaneous seismic data reconstruction and denoising.