Seismic data denoising under the morphological component analysis framework by dictionary learning

Traditional denoising methods based on fixed transforms are not suited for exploiting their complicated characteristics and attenuating noise due to their lack of adaptability. Recently, a novel method called morphological component analysis (MCA) was proposed to separate different geometrical components by amalgamating several irrelevance transforms. For studying the local singular and smooth linear components characteristics of seismic data, we propose a novel method that excels particularly in attenuating random and coherent noise while preserving effective signals. The proposed method, which combines MCA, dictionary learning (DL), and deep noise reduction consists of three steps: first, we separate the local singular and smooth linear components from the seismic signal using MCA. Second, we apply a DL method on these two components to suppress noise and obtain the denoised signal and noise. In the final step, we apply the DL method to the noise to obtain a little of the seismic signal. Afterwards, we integrate the two seismic signals to obtain the final denoised seismic signal. Numerical results indicate that the proposed method can effectively suppress the undesired noise, maximally preserve the information of geologic bodies and structures, and improve the signal-to-noise ratio (S/N) of the data. We also demonstrate the superior performance of this approach by comparing with other novel dictionaries such as discrete cosine transforms (DCTs), undecimated discrete wavelet transforms (UDWTs), or curvelet transforms. This algorithm provides new ideas for data processing to advance quality and S/N of seismic data.