In this paper we propose a combined method for removing impulse noise. In the first phase, we use an efficient detector, called the Statistics of Ordered Difference Detector (SODD) to identify pixels which are likely to be corrupted by impulse noise. The proposed SODD can yield very high noise detection accuracy at high noise density. This noise detection phase is crucial for the following noise removal. In the second phase, only these noise candidates are restored using the variational method. Edges and noise free pixels of images filtered by our combined method are preserved. Simulation results indicate that the proposed method is significantly better than those using other impulse noise reduction filters.