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A new, efficient speech enhancement algorithm (SEA) is developed in this paper. In this low-complexity SEA, a noisy speech signal is first decorrelated and then the clean speech components are estimated from the decorrelated noisy speech samples. The distributions of clean speech and noise signals are assumed to be Laplacian and Gaussian, respectively. The clean speech components are estimated either by maximum likelihood (ML) or minimum-mean-square-error (MMSE) estimators. These estimators require some statistical parameters derived from speech and noise. These parameters are adaptively extracted by the ML approach during the active speech or silence intervals, respectively. In addition, a voice activity detector (VAD) that uses the same statistical model is employed to detect whether the speech is active or not. The simulation results show that our SEA approach performs as well as a recent high efficiency SEA that employs the Wiener filter. The computational complexity of this algorithm is very low compared with existing SEAs with low computational complexity.