Estimation of non-Gaussian noise parameters in the wavelet domain using the moment-generating function

Abstract

We discuss methods for modeling and removal of noise in astronomical images. For its favorable properties, we exploit the undecimated wavelet representation and apply noise suppression in this domain. Usually, the noise analysis of the studied imaging system is carried out in the spatial domain. However, noise in astronomical data is non-Gaussian, and thus the noise model parameters need to be estimated directly in the wavelet domain. We derive equations for estimating the sample moments for non-Gaussian noise in the wavelet domain. We consider that the sample moments in the spatial domain are known from the noise analysis and that the model parameters are estimated by using the method of moments.