This paper addresses a challenging single-channel speech enhancement problem in real-world environment where speech signal is corrupted by high level background noise. While most state-of-the-art algorithms tries to estimate noise spectral power and filter it from the observed one to obtain enhanced speech, the paper discloses another approach inspired from audio source separation technique. In the considered method, generic spectral characteristics of speech and noise are first learned from various training signals by non-negative matrix factorization (NMF). They are then used to guide the similar factorization of the observed power spectrogram into speech part and noise part. Additionally, we propose to combine two existing group sparsity-inducing penalties in the optimization process and adapt the corresponding algorithm for parameter estimation based on mul-tiplicative update (MU) rule. Experiment results over different settings confirm the effectiveness of the proposed approach .