Novel robust filtering algorithms applicable to signal and image processing are introduced. They use the robust techniques of rank and M estimators. The proposed robust rank M filters enhance the quality of radar images providing effective speckle suppression, impulse noise removal, preservation of edges and details. The properties of these algorithms are demonstrated by simulated images and real data. It is shown that the proposed filters provide good visual quality of processed images and have some advantages (in the MSE sense) in comparison to the known ones when the noise level is high.