A complex diffusion driven approach for removing data-dependent multiplicative noise

Abstract

In this paper we propose a second-order non-linear PDE based on the complex diffusion function. The proposed method exhibits better restoration capability of ramp edges in comparison to other second-order methods discussed in the literature. The proposed model is designed for Gamma distributed multiplicative noise which commonly appears in Ultra Sound (US) and Synthetic Aperture Radar (SAR) images. The fidelity/reactive term augmented to the complex diffusive term is derived based on the Bayesian maximum a posteriori probability (MAP) estimator as detailed in Aubert and Ajol ([10]). The regularization parameter is selected based on the noise variance of the image and thus this adaptive method helps in restoring the images at various noise variances without manually fixing the parameter. The results shown in terms of both visual and qualitative measures demonstrate the capability of the model to restore images from their degraded observations. © Springer-Verlag 2013.