Statistical modeling and denoising Wigner–Ville distribution

Studying the properties of the Wigner–Ville distribution (wvd) and its smoothed versions such as smoothed pseudo-WVD (spwvd), we demonstrate that they have significantly non-Gaussian statistics. Also, we investigate the presence of two-dimensional heteroscedasticity in them for different signals based on employing Lagrange multiplier (LM) procedure. Therefore, we employ a heteroscedastic model called two-dimensional generalized autoregressive conditional heteroscedastic (2-D garch) for statistical modeling of these distributions. This modeling captures the characteristics of WVD and SPWVD, such as heavy tailed marginal distribution, and the dependencies among them. Since the performance of WVD and its smoothed versions degrade in the presence of additive noise, we design a novel Bayesian estimator for estimating the clean distributions based on garch modeling. Also, estimating the instantaneous frequency (if) curves of signals in presence of noise based on WVD and its smoothed versions is an interesting topic in the radar domain. So, we apply the denoised distributions for estimating the if. Experimental results demonstrate the efficiency of proposed method in denoising wvd and SPWVD and also performance improvement for if estimation in utilizing the denoised distributions.