An effective image restoration using Kullback-Leibler divergence minimization

Image restoration is a significant inverse problem in image processing community. We present an iterative alternating minimization of Kullback Leibler divergence (KLD) for an optimized image denoising. It is obtained by modeling the original image and the additive noise as multivariate Gaussian processes with unknown covariance matrices in wavelet domain. The original image and noise parameters are estimated by minimizing KLD between a model family of probability distributions defined using the linear image degradation model and a desired family of probability distributions constrained to be concentrated on the observed noisy image. The wavelet coefficients are modeled using the class of Gaussian Scale Mixture (GSM), which represents the heavy-tailed statistical distribution, suitable for natural images. The algorithm provides closed form expressions for the parameters updates and converge only in few iterations. The efficiency of proposed method is demonstrated through numerical simulations, both visually and in terms of signal to noise ratio.