Complex Gaussian Scale Mixtures of Complex Wavelet Coefficients

In this paper, we propose the complex Gaussian scale mixture (CGSM) to model the complex wavelet coefficients as an extension of the Gaussian scale mixture (GSM), which is for real-valued random variables to the complex case. Along with some related propositions and miscellaneous results, we present the probability density functions of the magnitude and phase of the complex random variable. Specifically, we present the closed forms of the probability density function (pdf) of the magnitude for the case of complex generalized Gaussian distribution and the phase pdf for the general case. Subsequently, the pdf of the relative phase is derived. The CGSM is then applied to image denoising using the Bayes least-square estimator in several complex transform domains. The experimental results show that using the CGSM of complex wavelet coefficients visually improves the quality of denoised images from the real case.