Compressed sensing with log-sum heuristic recover for seismic denoising

• Published in: Frontiers in Earth Science
• Main Authors: Fengyuan Sun, Qiang Zhang, Zhipeng Wang, Wei Hou
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2024-01-01
• Subjects: compressed sensing; log-sum heuristic recovery; seismic denoising; lp norm; the log-sum heuristic recovery (LHR)
• Online Access: https://www.frontiersin.org/articles/10.3389/feart.2023.1285622/full

The compressed sensing (CS) method, commonly utilized for restructuring sparse signals, has been extensively used to attenuate the random noise in seismic data. An important basis of CS-based methods is the sparsity of sparse coefficients. In this method, the sparse coefficient vector is acquired by minimizing the l1 norm as a substitute for the l0 norm. Many efforts have been made to minimize the lp norm (0 < p < 1) to obtain a more desirable sparse coefficient representation. Despite the improved performance that is achieved by minimizing the lp norm with 0 < p < 1, the related sparse coefficient vector is still suboptimal since the parameter p is greater than 0 rather than infinitely approaching 0 p→0+. Therefore, the CS method with the limit p→0+ is proposed to enhance the sparse performance and thus generate better denoised results in this paper. Our proposed method is referred to as the CS-LHR method because the solving process for minimizing p→0+ is the log-sum heuristic recovery (LHR). Furthermore, to improve the computational efficiency, we incorporate the majorization-minimization (MM) algorithm in this CS-LHR method. Experimental results of synthetic and real seismic records demonstrate the remarkable performance of CS-LHR in random noise suppression.