Speckle reduction is a long-standing topic in SAR data pro- cessing. Continuous progress made in the field of image denoising fuels the development of methods dedicated to speckle in SAR images. Adaptation of a denoising technique to the specific statistical nature of speckle presents variable levels of difficulty. It is well known that the logarithm trans- form maps the intrinsically multiplicative speckle into an additive and stationary component, thereby paving the way to the application of general-purpose image denoising meth- ods to SAR intensity images. Multi-channel SAR images such as obtained in interferometric (InSAR) or polarimetric (PolSAR) configurations are much more challenging. This paper describes MuLoG, a generic approach for mapping a multi-channel SAR image into real-valued images with an additive speckle component that has a variance approxi- mately constant. With this approach, general-purpose image denoising algorithms can be readily applied to restore InSAR or PolSAR data. In particular, we show how recent denois- ing methods based on deep convolutional neural networks lead to state-of-the art results when embedded with MuLoG framework.