Image de-noising is a traditional task related to linear and non-linear 2D filtering methods. The artificial neural network (ANN) can be also used as a kind of a sophisticated non-linear filter on local pixel neighborhood (3x3). The disadvantage of linear systems and neural networks is their sensitivity to impulse (isolated) noise. That is why the median and the other rank based filters are better in this case. The opposite situation is in the case of Gaussian noise when the mean filtering has higher value of signal / noise ratio (SNR) than the median filter. The first aim of our paper is to define k-robustness of local de-noising. Then it is easy to build up a new class of k-robust de-noising systems consisting of input frame, robust preprocessing, ANN and robust postprocessing. Implementation details related to signal processing and learning are also included. The third aim of our paper is to learn 1-robust and 2-robust systems to have maximum possible SNR for Gaussian noise on real MR image of human brain.