Seismic data denoising via double sparsity dictionary and fast iterative shrinkage-thresholding algorithm

Seismic data denoising acts as one of the important roles in seismic data processing. Double sparse dictionary can provide the two-level sparsity for model, which has higher anti-noise ability than single sparsity transform denoising. In this paper, we developed a seismic data denoising workflow based on the double sparse transform and fast iterative shrinkage-thresholding algorithm (FISTA). We firstly represent data by contourlet transform and obtain a primary coefficient dictionary via FISTA. Then we obtain the learned dictionary through the data-driven tight frame (DDTF) and update the learned dictionary via FISTA. Finally, the new contourlet coefficients are reconstructed by DDTF dictionary and updated dictionary coefficients. Moreover, the hard thresholding and inverse contourlet transform are applied in new contourlet coefficients. Consequently, it achieves denoising. The synthetic data and field data experiments illustrated that compared with fixed-base transform, the proposed method obtains sparse representation of seismic data adaptively, and it performances well in the complexity seismic data. Compared with dictionary learning, the proposed method has less computational time-consuming. What is more, the proposed method overcomes the disadvantage that dictionary learning often produces artifacts due to no prior-constraint structural information in seismic data denoising.