Outlier Denoising Using a Novel Statistics-Based Mask Strategy for Compressive Sensing

Denoising is always an important step in seismic processing, in order to produce high-quality data for subsequent imaging and inversion. Different types of noise can be suppressed using targeted denoising methods. For outlier noise with singular amplitudes, many classical denoising methods suffer from signal leakage. To mitigate this issue, we developed a statistics-based mask method and incorporated it into the compressive sensing (CS) framework, in order to remove outlier noise. A statistical analysis for seismic data amplitudes was first used to identify the locations of traces containing outlier noise. Then, the outlier trace locations were compared with a mask matrix generated by jitter sampling, and we replaced the sampled traces of the jitter mask that had the outlier noise with their nearby unsampled traces. The optimized sampling matrix enabled us to effectively identify and remove outliers. This optimized mask strategy converts an outlier denoising problem into a data reconstruction problem. Finally, a sparsely constrained inverse problem was solved using a soft-threshold iteration solver to recover signals at the null locations. The feasibility and adaptability of the proposed method were demonstrated through numerical experiments for synthetic and field data. The results showed that the proposed method outperformed the conventional f-x deconvolution and median filter method, and could accurately suppress outlier noise and recover missed expected signals.