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We propose a novel speech enhancement technique based on the hypothesized Wiener filter (HWF) methodology. The proposed HWF algorithm selects a filter for enhancing the input noisy signal by first 'hypothesizing' a set of filters and then choosing the most appropriate one for the actual filtering. We show that the proposed HWF can intrinsically offer superior performance to conventional Wiener filtering (CWF) algorithms, which typically perform a selection of a filter based only on the noisy input signal which results in a sub-optimal choice of the filter. We present results showing the advantages of HWF based speech enhancement over CWF, particularly with respect to the baseline performances achievable by HWF and with respect to the type of clean frames used, namely, codebooks vs a large number of clean frames. We show the consistently better performance of HWF based speech enhancement (over CWF) in terms of spectral distortion at various input SNR levels.