Fast Dictionary Learning Based on Data-Driven Tight Frame for 3-D Seismic Data Denoising

Seismic denoising is a fundamental and critical task in seismic data processing. Aiming at solving the computational complexity of in 3D seismic data processing, we propose a novel data-driven tight frame (DDTF) dictionary learning method with over-complete dictionary constructed by discrete cosine transform for 3D seismic data denoising. The advantage of the DDTF algorithm is that only one singular value decomposition is required to update the entire dictionary, so as to accelerate the computational efficiency of 3D seismic data denoising. First, the seismic data is divided into patches to form matrix samples, and discrete cosine transform is selected according to preset parameters to initialize the dictionary. Then, the initial dictionary is trained by DDTF algorithm to update the dictionary. After that, the updated dictionary is used to denoise the block samples of seismic data. Finally, the proposed method is tested with synthetic data and field data. The results show that this method can significantly reduce the computational burden of state-of-the-art method, such as damped rank-reduction (DRR) method in 3D seismic data denoising, and the denoising performance is better than traditional DDTF method, which is conducive to the application of field data.