  We address the problem of image denoising in additive white noise without
placing restrictive assumptions on its statistical distribution. In the recent
literature, specific noise distributions have been considered and
correspondingly, optimal denoising techniques have been developed. One of the
successful approaches for denoising relies on the notion of unbiased risk
estimation, which enables one to obtain a useful substitute for the mean-square
error. For the case of additive white Gaussian noise contamination, the risk
estimation procedure relies on Stein's lemma. Sophisticated wavelet-based
denoising techniques, which are essentially nonlinear, have been developed with
the help of the lemma. We show that, for linear, shift-invariant denoisers, it
is possible to obtain unbiased risk estimates of the mean-square error without
using Stein's lemma. An interesting consequence of this development is that the
unbiased risk estimator becomes agnostic to the statistical distribution of the
noise. As a proof of principle, we show how the new methodology can be used to
optimize the parameters of a simple Gaussian smoother. By locally adapting the
parameters of the Gaussian smoother, we obtain a shift-variant smoother, which
has a denoising performance (quantified by the improvement in peak
signal-to-noise ratio (PSNR)) that is competitive to far more sophisticated
methods reported in the literature. The proposed solution exhibits considerable
parallelism, which we exploit in a Graphics Processing Unit (GPU)
implementation.
