Seismic Signal Matching and Complex Noise Suppression by Zernike Moments and Trilateral Weighted Sparse Coding

Noise in field seismic data is usually complicated. Most signal-to-noise (S/N) ratio enhancement methods are designed for some specific noise type and they will become less effective when dealing with complex noise. In this article, we propose to use a trilateral weighted sparse coding (TWSC) scheme within the block matching framework for complex noise attenuation. Block matching-based approaches take the repetitive nature of effective signals into account which facilitates the S/N ratio enhancement. Block matching requires the identification of similar signal patches through a data set. This becomes more challenging for low-quality data. Thus, the signal matching criterion is of great importance. The Euclidean distance is the most widely used criterion for similarity measurement in block matching. It becomes a bottleneck for matching low-quality data or for data with rotations. To overcome this obstacle, we modify the Euclidean distance criterion by computing distances using Zernike moments which are rotation invariant and add noise robustness. This in turn benefits the subsequent filtering stage by TWSC, which uses two weight matrices to characterize the complex noise properties, and a third matrix to characterize the sparsity priors of signal. The improved sparse coding model is solved by the alternating direction method of multipliers. Tests on synthetic and several field data sets show that the proposed strategy achieves better performance in dealing with complex noise.