Statistical denoising of signals in the S-transform domain

In this paper, the denoising of stochastic noise in the S-transform (ST) and generalized S-transform (GST) domains is discussed. First, the mean power spectrum (MPS) of white noise is derived in the ST and GST domains. The results show that the MPS varies linearly with the frequency in the ST and GST domains (with a Gaussian window). Second, the local power spectrum (LPS) of red noise is studied by employing the Monte Carlo method in the two domains. The results suggest that the LPS of Gaussian red noise can be transformed into a chi-square distribution with two degrees of freedom. On the basis of the difference between the LPS distribution of signals and noise, a denoising method is presented through hypothesis testing. The effectiveness of the method is confirmed by testing synthetic seismic data and a chirp signal.