A new paper is added to the collection of reproducible documents: Double sparsity dictionary for seismic noise attenuation

A key step in sparsifying signals is the choice of a sparsity-promoting dictionary. There are two basic approaches to design such a dictionary: the analytic approach and the learning-based approach. While the analytic approach enjoys the advantage of high efficiency, it lacks adaptivity to various data patterns. On the other hand, the learning-based approach can adaptively sparsify different datasets but has a heavier computational complexity and involves no prior-constraint pattern information for particular data. We propose a double sparsity dictionary (DSD) for seismic data in order to combine the benefits of both approaches. We provide two models to learn the DSD: the synthesis model and the analysis model. The synthesis model learns DSD in the data domain, and the analysis model learns DSD in the model domain. We give an example of the analysis model and propose to use the seislet transform and data-driven tight frame (DDTF) as the base transform and adaptive dictionary respectively in the DSD framework. DDTF obtains an extra structure regularization by learning dictionaries, while the seislet transform obtains a compensation for the transformation error caused by slope dependency. The proposed DSD aims to provide a sparser representation than the individual transform and dictionary and therefore can help achieve better performance in denoising applications. Although for the purpose of compression, the proposed DSD is less sparse than the seislet transform, it outperforms both seislet and DDTF in distinguishing signal and noise. Two simulated synthetic examples and three field data examples confirm a better denoising performance of the proposed approach.