In this paper, we propose a double sparsity dictionary (DSD) for seismic data in order to combine the benefits of both analytic and learning-based sparsity-promoting transforms. We provide two models to learn the DSD: the synthesis model and the analysis model. The synthesis model learns DSD in the image domain, and the analysis model learns DSD in the model domain. As a tutorial, we give an example of the analysis model and propose to use the seislet transform and data-drive tight frame (DDTF) as the base transform and adaptive dictionary in the DSD framework. DDTF obtains an extra structure regularization when learning dictionaries, while the seislet transform obtains a compensation of the transformation error caused by slope dependency. The given DSD can provide a sparser representation than the individual transform and dictionary and therefore can help achieve better performance in denoising applications. Field data example confirms a superior denoising performance of the proposed approach.


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