Sparse Non-negative Matrix Factorization (SNMF) and Deep Neural Networks (DNN) have emerged individually as two efficient machine learning techniques for single-channel speech enhancement. Nevertheless, there are only few works investigating the combination of SNMF and DNN for speech enhancement and robust Automatic Speech Recognition (ASR). In this paper, we present a novel combination of speech enhancement components based-on SNMF and DNN into a full-stack system. We refine the cost function of the DNN to back-propagate the reconstruction error of the enhanced speech. Our proposal is compared with several state-of-the-art speech enhancement systems. Evaluations are conducted on the data of CHiME-3 challenge which consists of real noisy speech recordings captured under challenging noisy conditions. Our system yields significant improvements for both objective quality speech enhancement measurements with relative gain of 30%, and a 10% relative Word Error Rate reduction for ASR compared to the best baselines.
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