Compressed sensing with log-sum heuristic recover for seismic denoising

Abstract

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.