Low-frequency seismic random noise attenuation based on EPLL-TV under double prior constraints

The expected patch log likelihood (EPLL) method utilizes the learned Gaussian mixture model (GMM) as a prior for white Gaussian noise removal, so that every patch from noisy data is likely under the prior and the global morphology is remained along with denoising. For suppressing the low-frequency seismic random noise having similar waveforms to the signals, we propose an Expected Patch Log Likelihood-Total Variation (EPLL-TV) algorithm, which is constrained by the EPLL prior and the total variation (TV) prior. In the denoising process, the TV prior introduces the structural features of the current data and restrains the random noise by enhancing the gradient sparsity of seismic data. Hence, the EPLL-TV algorithm is able to choose the Gaussian component which is closest to the features of signals from pre-learned general prior of EPLL, although the features in the patch are severely disturbed by the low-frequency noise. Then the seismic events with complex structures can be accurately restored by the chosen Gaussian component, which provides more reliable structures for denoising via the TV prior. We use the alternating direction method of multipliers (ADMM) to solve the proposed optimization model with double constraints and reconstruct the data in Fourier domain to reduce computational complexity. The results of the synthetic and field seismic data demonstrate that the proposed EPLL-TV method is superior to the other methods mentioned in our paper in terms of recovering the seismic events with complex structures and suppressing the low-frequency seismic random noise which has similar waveforms to the signals.