Retrieving the leaked signals from noise using a fast dictionary-learning method

Abstract

Most traditional seismic denoising algorithms will cause damage to useful signals, which are visible from the removed noise profiles and are known as signal leakage. The local signal-and-noise orthogonalization method is an effective method for retrieving the leaked signals from the removed noise. Retrieving leaked signals while rejecting noise is compromised by the smoothing radius parameter in the local orthogonalization method. It is not convenient to adjust the smoothing radius because it is a global parameter, whereas the seismic data are highly variable locally. To retrieve the leaked signals adaptively, we have adopted a new dictionary-learning (DL) method. Because of the patch-based nature of the DL method, it can adapt to the local features of seismic data. We train a dictionary of atoms that represent the features of the useful signals from the initially denoised data. Based on the learned features, we retrieve the weak leaked signals from the noise via a sparse coding step. Considering the large computational cost when training a dictionary from high-dimensional seismic data, we leverage a fast dictionary updating algorithm, in which the singular value decomposition is replaced via the algebraic mean to update the dictionary atom. We test the performance of our method on several synthetic and field data examples, and we compare it with that from the state-of-the-art local orthogonalization method.