A Joint Framework for Seismic Signal Denoising Using Total Generalized Variation and Shearlet Transform

Seismic exploration is a remote-sensing tool applied in a great many projects for engineering and resource-exploration purposes. Random noise suppression is one of the key steps in seismic-signal processing, especially those with important details and features. The threshold-shrinkage method based on Shearlet transform has been effectively applied in seismic-signal denoising. However, the method usually introduces the boundary effect, which influences the imaging quality. The denoising method of total generalized variation (TGV) is easy to produce 'oil painting' effect, but it can effectively suppress the boundary effect. This paper proposes a denoising method based on Shearlet threshold-shrinkage and TGV for making full use of their characteristics, which can recover both edges and fine details much better than the existing regularization methods. First, we use the Shearlet threshold-shrinkage result as the input of TGV to obtain the primary denoising result and the residual profile. Second, we use the interactive iteration of Shearlet threshold-shrinkage and TGV to extract the signals efficiently from the residual profile and perform the effective signals stack continuously. During the processing, the adaptive-weight factor is combined for estimating the optimal denoising result. Last, the final estimated denoising result is obtained when the stopping criterion is met or the maximum number of iterations is reached. The synthetic and field results show that the proposed method can effectively suppress random noise. In addition, it can also remove the boundary effect and 'oil painting' effect, which further improves the signal-to-noise ratio (SNR).