  This paper is devoted to adaptive signal denoising in the context of Graph
Signal Processing (GSP) using Spectral Graph Wavelet Transform (SGWT). This
issue is addressed \emph{via} a data-driven thresholding process in the
transformed domain by optimizing the parameters in the sense of the Mean Square
Error (MSE) using the Stein's Unbiased Risk Estimator (SURE). The SGWT
considered is built upon a partition of unity making the transform
semi-orthogonal so that the optimization can be performed in the transformed
domain. However, since the SGWT is over-complete, the divergence term in the
SURE needs to be computed in the context of correlated noise. Two thresholding
strategies called coordinatewise and block thresholding process are
investigated. For each of them, the SURE is derived for a whole family of
elementary thresholding functions among which the soft threshold and the
James-Stein threshold. This multi-scales analysis shows better performance than
the most recent methods from the literature. That is illustrated numerically
for a series of signals on different graphs.
