SEISMIC DATA DENOISING USING DOUBLE SPARSITY DICTIONARY AND ALTERNATING DIRECTION METHOD OF MULTIPLIERS

摘要

Recently, the dictionary learning plays a more and more important role in seismic data denoising. Compared with the fixed-basis transform (e.g., Fourier transform, wavelet transform, curvelet transform, contourlet transform and shearlet transform), the denoising of dictionary learning is better because of adaptive sparse representation of seismic data. However, dictionary learning often produces artifacts due to no prior-constraint structural information. In this paper, we propose a new denoising approach, which has double sparsity and combines the advantage of fixed-basis transform and dictionary learning. The whole work-flow of the new denoising approach is as follows. Firstly, we can obtain sparse coefficients of seismic data via shearlet transform. Secondly, sparse coefficients are divided into some suitable size blocks which are regarded as training sets. Thirdly, the alternating direction method of multipliers (ADMM) is used in sparse coding to update dictionary coefficients. Then, the data-driven tight frame (DDTF) is used in dictionary updating to update dictionary atoms. Again, the ADMM is used to resolve the convex optimization problem, and we reshape output blocks to obtain new sparse coefficients. Finally, the hard-thresholding and inverse shearlet transform are applied to new sparse coefficients to achieve denoising. The synthetic data and field data experiments show that the new denoising approach obtain better result than fixed-basis transform and dictionary learning. In conclusion, the new denoising approach can attenuate artifacts and improve the quality of seismic data denoising.