Mixture of gaussians based robust sparse representation for erratic noise suppression

Random noise suppression is always a crucial procedure of seismic processing. Conventional sparsity-based methods with least-squares based likelihood have demonstrated their usefulness in Gaussian random noise suppression. However, they are not robust to the erratic noise which possesses high-amplitude feature and follows non-Gaussian distribution. To solve this issue, we present a mixture of Gaussians based robust sparse representation model (noted as TREASURE), for erratic noise suppression. In which, the noise is modeled as a specific mixture of Gaussians (MoG) distribution and the basic idea is that the MoG distribution is a universal approximator for any continuous distribution. In addition, the sparse prior is combined with such noise modeling to present robust and sparse representations. In particular, we present an efficient algorithm to estimate the parameters in TREASURE via expectation maximization (EM) and Linearized-Bregman (LB) algorithms. Experimental results of both synthetic and field data sets show the better performance in comparison to conventional method.