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In this paper, we propose a spectral difference approach for noise power estimation in speech enhancement. The noise power estimate is given by recursively averaging past spectral power values using a smoothing parameter based on the current observation. The smoothing parameter in time and frequency is adjusted by the spectral difference between consecutive frames that can efficiently characterize noise variation. Specifically, we propose an effective technique based on a sigmoid-type function in order to adaptively determine the smoothing parameter based on the spectral difference. Compared to a conventional method, the proposed noise estimate is computationally efficient and able to effectively follow noise changes under various noise conditions.