Strong random noise attenuation by shearlet transform and time-frequency peak filtering

Abstract

Directional wavelet transforms combined with coefficient thresholding are very competitive in denoising seismic signals. However, these techniques struggle when the coefficients of signal and noise have comparable magnitudes. To better address this problem, we have developed an improvement to this method by applying time-frequency peak filtering (TFPF) to the directional wavelet coefficients. TFPF consists of computing the instantaneous frequency of a frequency-modulated analytic signal. The use of a longer or shorter smoothing window helps to emphasize either signal or remove random noise. In our method, we use the shearlet transform as a directional wavelet transform and estimate signal dips based on the cumulative energy in each decomposition direction. TFPF is then applied to the fine-scale wavelet coefficients to enhance signal and remove high-frequency noise. Coefficient thresholding is applied to all other scales. Experimental results demonstrate that our algorithm can effectively eliminate strong random noise and preserve events of interest.