  Wavelet denoising is a classical and effective approach for reducing noise in
images and signals. Suggested in 1994, this approach is carried out by
rectifying the coefficients of a noisy image in the transform domain, using a
set of scalar shrinkage function (SFs). A plethora of papers deals with the
optimal shape of the SFs and the transform used, where it is known that
applying the SFs in redundant bases provides improved results. This paper
provides a complete picture of the interrelations between the transform used,
the optimal shrinkage functions, and the domains in which they are optimized.
In particular, we show that for subband optimization, where each SF is
optimized independently for a particular band, optimizing the SFs in the
spatial domain is always better than or equal to optimizing the SFs in the
transform domain. For redundant bases, we provide the expected denoising gain
we may achieve, relative to the unitary basis, as a function of the redundancy
rate.
