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This paper presents a single-microphone approach to the enhancement of noisy reverberant speech via inverse filtering and spectral processing. An efficient algorithm is used to blindly estimate the inverse filter of the Room Impulse Response (RIR). This filter is used to attenuate the early reverberation. A simple technique to blindly determine the filter length is presented. A two-step spectral subtraction method is proposed to efficiently reduce the effects of background noise and the residual reverberation on the equalized impulse response. In general, the equalized impulse response has two detrimental effects, late impulses and pre-echoes. For the late impulses, an efficient spectral subtraction algorithm is developed which introduces only minor musical noise. Then a new algorithm is introduced which reduces the remaining pre-echo effects. The performance of this two-stage method is examined in different reverberant conditions including real environments. It is also evaluated with white Gaussian and recorded babble noise. The results obtained demonstrate that the proposed blind method is superior in terms of reducing early and late reverberation effects and noise compared to well known single-microphone techniques in the literature.