Robust multi-dimensional reconstruction via Group Sparsity with Radon operators

Abstract

Seismic data processing, specifically tasks like denoising and interpolation, often hinges on sparse solutions of linear systems. Group sparsity plays an essential role in this context by enhancing sparse inversion. It introduces more refined constraints, which preserve the inherent relationships within seismic data. To this end, we propose a robust Orthogonal Matching Pursuit algorithm, combined with Radon operators in the frequency-slowness f- p domain, to tackle the strong group-sparsity problem. This approach is vital for interpolating seismic data and attenuating erratic noise simultaneously. Our algorithm takes advantage of group sparsity by selecting the dominant slowness group in each iteration and fitting Radon coefficients with a robust ℓ1-ℓ1 norm by the alternating direction method of multipliers (ADMM) solver. Its ability to resist erratic noise, along with its superior performance in applications such as simultaneous source deblending and reconstruction of noisy onshore datasets, underscores the importance of group sparsity. Both synthetic and real comparative analyses further demonstrate that strong group sparsity inversion consistently outperforms corresponding traditional methods without the group sparsity constraint. These comparisons emphasize the necessity of integrating group sparsity in these applications, thereby showing its indispensable role in optimizing seismic data processing.