Non-convex compressed sensing with frequency mask for seismic data reconstruction and denoising

• Published in: Geophysical Prospecting Vol. 62; no. 6; pp. 1389 - 1405
• Main Author: Gholami, Ali
• Format: Journal Article
• Language: English
• Published: Houten Blackwell Publishing Ltd 01.11.2014; Wiley Subscription Services, Inc
• Subjects: Compressed sensing; Ground roll; Interpolation; Inverse problem; Noise; Oil exploration; Oil reserves; Parameter estimation; Seismic; Signal processing; Sparsity
• ISSN: 0016-8025; 1365-2478
• DOI: 10.1111/1365-2478.12146

ABSTRACT Compressed Sensing has recently proved itself as a successful tool to help address the challenges of acquisition and processing seismic data sets. Compressed sensing shows that the information contained in sparse signals can be recovered accurately from a small number of linear measurements using a sparsity‐promoting regularization. This paper investigates two aspects of compressed sensing in seismic exploration: (i) using a general non‐convex regularizer instead of the conventional one‐norm minimization for sparsity promotion and (ii) using a frequency mask to additionally subsample the acquired traces in the frequency‐space (f−x) domain. The proposed non‐convex regularizer has better sparse recovery performance compared with one‐norm minimization and the additional frequency mask allows us to incorporate a priori information about the events contained in the wavefields into the reconstruction. For example, (i) seismic data are band‐limited; therefore one can use only a partial set of frequency coefficients in the range of reflections band, where the signal‐to‐noise ratio is high and spatial aliasing is low, to reconstruct the original wavefield, and (ii) low‐frequency characteristics of the coherent ground rolls allow direct elimination of them during reconstruction by disregarding the corresponding frequency coefficients (usually bellow 10 Hz) via a frequency mask. The results of this paper show that some challenges of reconstruction and denoising in seismic exploration can be addressed under a unified formulation. It is illustrated numerically that the compressed sensing performance for seismic data interpolation is improved significantly when an additional coherent subsampling is performed in the f−x domain compared with the t−x domain case. Numerical experiments from both simulated and real field data are included to illustrate the effectiveness of the presented method.