Once image motion is accurately estimated, we can utilize those motion estimates for image sharpening and we can remove motion blurs. First, this paper presents a variational motion de-blurring method using a spatially variant model of motion blurs. The standard variational method is not proper for the motion de-blurring, because it is sensitive to model errors, and occurrence of errors are inevitable in motion estimation. To improve the robustness against the model errors, we employ a nonlinear robust estimation function for measuring energy to be minimized. Secondly, we experimentally compare the variational method with our previously presented PDE-based method that does not need any accurate blur model.