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 3-D seismic data processing, we propose a novel data-driven tight frame (DDTF) dictionary learning method with an overcomplete dictionary constructed by discrete cosine transform (DCT) for 3-D seismic data denoising. The advantage of the DDTF algorithm is that only one singular value decomposition (SVD) is required to update the entire dictionary, to accelerate the computational efficiency of 3-D seismic data denoising. First, the seismic data is divided into patches to form matrix samples, and DCT is selected according to preset parameters to initialize the dictionary. Then, the initial dictionary is trained by the 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 methods, such as the damped rank-reduction (DRR) method in 3-D seismic data denoising, and the denoising performance is better than the traditional DDTF method, which is conducive to the application of field data.