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Recently, a two-phase scheme for removing salt-and-pepper impulse noise has been proposed [R.H. Chan et al], In the first phase, an adaptive median filter is used to identify pixels which are likely to be contaminated by noise (noise candidates). In the second phase, the image is restored by minimizing a specialized regularization functional that applies only to those selected noise candidates. As an extension of this work, we propose an efficient method to accomplish the second phase. The speed of our method can be double as that of the method proposed in [R.H. Chan et al] for images contaminated by 30% salt-and-pepper noise and is faster for higher noise level.