How much can a Gaussian smoother denoise?

Abstract

Recently, a suite of increasingly sophisticated methods have been developed to suppress additive noise from images. Most of these methods take advantage of sparsity of the underlying signal in a specific transform domain to achieve good visual or quantitative results. These methods apply relatively complex statistical modelling techniques to bifurcate the noise from the signal. In this paper, we demonstrate that a spatially adaptive Gaussian smoother could be a very effective solution to the image denoising problem. To derive the optimal parameter estimates for the Gaussian smoothening kernel, we derive and deploy a surrogate of the mean-squared error (MSE) risk similar to the Stein's estimator for Gaussian distributed noise. However, unlike the Stein's estimator or its counterparts for other noise distributions, the proposed generic risk estimator (GenRE) uses only first- and second-order moments of the noise distribution and is agnostic to the exact form of the noise distribution. By locally adapting the parameters of the Gaussian smoother, we obtain a denoising function that has a denoising performance (quantified by the peak signal-to-noise ratio (PSNR)) that is competitive to far more sophisticated methods reported in the literature. To avail the parallelism offered by the proposed method, we also provide a graphics processing unit (GPU) based implementation.