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This paper proposes a speech enhancement algorithm to improve the speech intelligibility by suppressing both reverberation and background noise. The algorithm adopts a non-causal single-channel minimum variance distortionless response (MVDR) filter to exploit an additional information that is included in the noisy-reverberant signals in subsequent frames. The noisy-reverberant signals are decomposed into the parts of the desired signal and the interference that is not correlated to the desired signal. Then, the filter equation is derived based on the MVDR criterion to minimize the residual interference without bringing speech distortion. The estimation of the correlation parameter, which plays an important role to determine the overall performance of the system, is mathematically derived based on the general statistical reverberation model. Furthermore, the practical implementation methods to estimate sub-parameters required to estimate the correlation parameter are developed. The efficiency of the proposed enhancement algorithm is verified by performance evaluation. From the results, the proposed algorithm achieves significant performance improvement in all studied conditions and shows the superiority especially for the severely noisy and strongly reverberant environment.