We present a new method for image denoising based on singularity analysis. The image is characterized via its multifractal spectrum, which mode yields the most frequent H�lder exponent. Using 2-microlocal analysis, we define an operator that shifts the spectrum so that the transformed image has almost sure H�lder exponent a little above 2. This manipulation leads to a smooth image while preserving the relative strength of the singularities (as for instance edges or textures) in the signal. Experimental results on Radar images are presented.