Coherent Noise Attenuation by Kurtosis-Guided Adaptive Dictionary Learning Based on Variational Sparse Representation

In seismic data denoising, coherent noise is usually challenging to remove because it has similar features with signal. Therefore, attenuating coherent noise is of great importance for seismic data. To obtain a good denoising result, it is necessary to fully consider the features of coherent noise and choose the appropriate denoising methods. Here, we propose a kurtosis-guided adaptive dictionary learning (KGADL) algorithm based on the variational sparse representation model. First, the variational sparse representation is to construct initial dictionary that depends on the seismic data, so that it can accurately contain the features of the seismic data, so as to improve the accuracy of sparse representation. Then, we use the K-singular value decomposition (K-SVD) algorithm to update the dictionary and introduce kurtosis to measure each atom after updating. Atoms with high kurtosis values usually exhibit strong irregularities and are considered noise, while atoms with low kurtosis values have more feature of valid waves and are considered signal. The atoms with low kurtosis values characterizing valid signal are retained to get the special dictionary that adapts to the complexity of the input seismic data, and this dictionary is used to suppress the coherent noise in seismic data. Finally, the denoising performance of the proposed method is illustrated by examples of both synthetic and field seismic data.