Adaptive Dictionary Learning for Blind Seismic Data Denoising

Abstract

The data-driven tight frame (DDTF) method is a dictionary learning method which has been used widely in the adaptive sparse representation and the seismic random noise attenuation. In the DDTF method, the thresholding operator setting plays a significant role on balancing the noise removal and preservation of detail information with high frequency. The hard thresholding operator is closely related to the noise variance; however, the noise variance is unknown and unstable which varies spatially. In this letter, we propose a spatially adaptive DDTF (SA-DDTF) method to find an optimal thresholding parameter without knowing the noise variance. The thresholding is determined by the coherence between the dictionary and the reconstruction residual. Furthermore, the thresholding is chosen adaptively for each patch of the seismic data. In case of the synthetic seismic data denoising, we obtain the reconstructed seismic data with a higher signal-to-noise ratio value. Furthermore, compared with the existing random noise reduction methods, the SA-DDTF method performs much better on the amplitude preservation of weak signal when attenuating the blind random noise for field data.