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We have proposed a novel approach to compressing seismic data in order to perform transform-domain thresholding-based random noise attenuation. By considering the benefits of both analytic and learning-based sparsity-promoting transforms, we propose a DSD framework for compensating for the weaknesses of both approaches and sparsifying seismic data for random noise attenuation. We propose two models to construct the DSD framework. One model is based on learning in the data domain, and is called the synthesis-based DSD; the other model is based on learning in the model domain, and is called the analysis-based DSD. We select the seislet transform as the analytic-basis transform and DDTF as the learning-based sparse dictionary to construct a cascaded DSD framework based on the analysis-based DSD. Synthetic and field data examples with simulated random noise and one field data example with real noise demonstrate a superior performance of the proposed DSD in application to random noise attenuation of seismic reflection data.