Image Denoising in the Wavelet Transform Domain Based on Stein´s Principle

In this tutorial paper, we are interested in image denoising in the wavelet domain. The objective is to describe in a unifying framework the most relevant methods which exploit Stein´s principle to build estimators for images embedded in Gaussian noise. The appealing advantage of Stein´s Unbiased Risk Estimate (SURE) is that it does not require a priori knowledge about the statistics of the unknown data, while yielding an estimate of the quadratic risk only depending on the statistics of the observed data. Hence, it avoids the difficult problem of the estimation of the hyperparameters of some prior distribution, which classically needs to be addressed in Bayesian methods. We begin by formulating the noise reduction problem as a problem involving the minimization of criteria derived from Stein´s principle. Then, we focus on the main methods operating on linear expansions of the observed image. Both cases of non redundant and overcomplete representations are addressed. Besides, a special attention is paid to multispectral images for which there is much gain to expect in exploiting the cross-channel correlations in the denoising procedure.