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The paper addresses a robust wavelet-based speech enhancement for automatic speech recognition in reverberant and noisy conditions. We propose a novel scheme in improving the speech, late reflection, and noise power estimates from the observed contaminated signal. The improved estimates are used to calculate the Wiener gain in filtering the late reflections and additive noise. In the proposed scheme, optimization of the wavelet family and its parameters is conducted using an acoustic model (AM). In the offline mode, the optimal wavelet family is selected separately for the speech, late reflections, and background noise based on the AM likelihood. Then, the parameters of the selected wavelet family are optimized specifically for each signal subspace. As a result we can use a wavelet sensitive to the speech, late reflection, and the additive noise, which can independently and accurately estimate these signals directly from an observed contaminated signal. For speech recognition, the most suitable wavelet is identified from the pre-stored wavelets, and wavelet-domain filtering is conducted to the noisy and reverberant speech signal. Experimental evaluations using real reverberant data demonstrate the effectiveness and robustness of the proposed method.