Graph signal processing focuses on extending the theory and methodologies of standard signal processing to signals defined on the vertices of a graph. Increasingly popular because of the flexibility of the underlying structure, this research area can be applied in many contexts (such as telecommunications networks, social networks, organic chemistry, or neurology). In this talk, we consider the case of signal denoising on graphs. The proposed methodology consists in applying a data-driven thresholding procedure in a well-chosen transformed domain, in which the signal is presumed sparsely represented. The threshold calibration is obtained by minimizing Stein’s unbiased risk estimate adapted to the chosen transformation. We provide an evaluation of the empirical performance of the method as well as a comparison with penalized estimators (such as graph trend filtering). Finally, we will discuss some perspectives and potential applications.