Retrieving useful signals from highly corrupted erratic noise using robust residual dictionary learning

Abstract

Seismic denoising will inevitably cause signal leakage, which is seen as coherent signal energy in the removed noise profile. Most traditional methods either ignore the signal leakage while maintaining clean denoised data or adjust parameters to decrease the signal leakage while causing more residual noise in the denoised data. The local signal-and-noise orthogonalization method can help retrieve the leaked signals without bringing significant residual noise. However, when seismic data contain erratic noise, the local orthogonalization method does not work properly because of the unstable inversion when solving the local orthogonalization weight due to the large-amplitude erratic noise. We propose a robust dictionary learning and sparse coding algorithm to retrieve the leaked signals. In this robust method, we substitute the L2-norm regularized sparse coding model with a Huber-norm sparse coding model, which is solved iteratively via a robust algorithm. The dictionary atoms used to retrieve the leaked signals are first learned from the initial estimate of signals and then updated during the robust iterations. Synthetic and field data examples containing erratic noise are used to demonstrate the effectiveness of the proposed method.