Curvelet domain denoising based on kurtosis characteristics

摘要

Curvelet transform can be effective in eliminating seismic noise by properly setting a threshold to the curvelet coefficients. However, when the signal-to-noise ratio (SNR) of data is low, it is difficult to select a suitable threshold to remove data noise, because the curvelet coefficients are similar between signals and noise. In this paper, we propose to incorporate the kurtosis statistic representing non-Gaussian characteristics of signals into an adaptive threshold-setting scheme. Curvelet transform decomposes noisy seismic data into curvelets with different scales and directions. The kurtosis estimated from the coefficient matrix at each scale and direction is then used to weight the threshold. Therefore, the threshold difference between signals and noise is enlarged and signals will be better preserved in seismic reconstruction. Synthetic and real data examples demonstrate that curvelet selection based on the kurtosis statistic removes data noise effectively, and thus is a credible method for denoising and signal preserving of seismic data with low SNR.