We present a heuristic algorithm for the choice of the wedgelet regularization parameter for the purpose of denoising in the case where the noise variance σ<sup>2</sup> is not known. Numerical experiments comparing wavelet thresholding with wedgelet denoising, and with the related schemes <i>quadtree approximation</i> and <i>platelet approximation</i>, allow to assess the respective strengths of the different approaches. For small values of σ<sup>2</sup>, wavelets are clearly superior to wedgelets, and they are better at restoring textured regions. For large σ<sup>2</sup>, or for images of a predominantly geometric nature, wedgelets yield consistently better results. Moreover, the tests reveal that the heuristic algorithm is quite effective in choosing the regularization parameter.