Modeling and Denoising Wigner-Ville Distribution

Due to the bilinear nature of Wigner-Ville and other time-frequency distributions, they produce poor results in the presence of additive noise. Though smoothed versions of the Wigner-Ville distribution (WVD) such as smoothed pseudo Wigner-Ville distribution (SPWVD) can suppress the noise effect, they still contain considerable noise. In this paper, we introduce a novel noise suppression method for WVD and its smoothed version, SPWVD, based on non-linear, non-Gaussian modeling of these distributions. We demonstrate that these distributions have significantly non-Gaussian statistics that are appropriately described by two-dimensional generalized autoregressive conditional heteroscedasticity (GARCH) model. Then, we apply a maximum a-posteriori (MAP) estimator for estimating the clean distributions based on GARCH modeling. Furthermore, we apply denoised distributions for estimating the instantaneous frequency (IF) of signals such as radar´s Doppler frequency. Experimental results demonstrate the efficiency of proposed method in denoising WVD and SPWVD and also in IF estimation.