Due to speckle phenomenon, some form of filtering must be applied to SAR data prior to performing any polarimet- ric analysis. Beyond the simple multilooking operation (i.e., moving average), several methods have been designed specifically for PolSAR filtering. The specifics of speckle noise and the correlations between polarimetric channels make PolSAR filtering more challenging than usual image restoration problems. Despite their striking performance, existing image denoising algorithms, mostly designed for additive white Gaussian noise, cannot be directly applied to PolSAR data. We bridge this gap with MuLoG by providing a general scheme that stabilizes the variance of the po- larimetric channels and that can embed almost any Gaussian denoiser. We describe MuLoG approach and illustrate its performance on airborne PolSAR data using a very recent Gaussian denoiser based on a convolutional neural network.