Two‐dimensional dictionary learning for suppressing random seismic noise

Dictionary learning is a successful method for random seismic noise attenuation that has been proven by some scholars. Dictionary learning–based techniques aim to learn a set of common bases called dictionaries from given noised seismic data. Then, the denoising process will be performed by assuming a sparse representation on each small local patch of the seismic data over the learned dictionary. The local patches that are extracted from the seismic section are essentially two‐dimensional matrices. However, for the sake of simplicity, almost all of the existing dictionary learning methods just convert each two‐dimensional patch into a one‐dimensional vector. In doing this, the geometric structure information of the raw data will be revealed, leading to low capability in the reconstruction of seismic structures, such as faults and dip events. In this paper, we propose a two‐dimensional dictionary learning method for the seismic denoising problem. Unlike other dictionary learning–based methods, the proposed method represents the two‐dimensional patches directly to avoid the conversion process, and thus reserves the important structure information for a better reconstruction. Our method first learns a two‐dimensional dictionary from the noisy seismic patches. Then, we use the two‐dimensional dictionary to sparsely represent all of the noisy two‐dimensional patches to obtain clean patches. Finally, the clean patches are patched back to generate a denoised seismic section. The proposed method is compared with the other three denoising methods, including FX‐decon, curvelet and one‐dimensional learning method. The results demonstrate that our method has better denoising performance in terms of signal‐to‐noise ratio, fault and amplitude preservation.