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This paper addresses the problem of speech dereverberation considering a noisy and slowly time-varying environment. The proposed multimicrophone speech dereverberation model utilizes the estimated acoustic impulse responses (AIRs) to dereverberate the speech as well as improve the signal-to-noise ratio without a priori information about the AIRs, location of the source and microphones, or statistical properties of the speech/noise, which are some common assumptions in the related literature. The received noisy signals are filtered through an eigenfilter which improves the power of the speech signal as compared to that of the additive noise. The eigenfilter is efficiently computed avoiding the tedious Cholesky decomposition, solely from the estimates of the AIRs. The design of the eigenfilter also incorporates a frequency domain constraint that improves the quality of the speech signal, resists spectral nulls in addition to improving the signal-to-noise ratio (SNR). A zero-forcing equalizer (ZFE) is used to dereverberate the speech signal by eliminating the distortion caused by the AIRs as well as the eigenfilter. The ZFE is implemented in block-adaptive form which makes the proposed technique suitable for speech dereverberation in a time-varying condition. The simulation results verify the superior performance of the proposed method as compared to the state-of-the-art dereverberation techniques in terms of log-likelihood ratio (LLR), segSNR, weighted spectral slope (WSS), and perceptual evaluation of speech quality (PESQ).