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This paper investigates a non-negative matrix factorization (NMF)- based approach to the semi-supervised single-channel speech enhancement problem where only non-stationary additive noise signals are given. The proposed method relies on sinusoidal model of speech production which is integrated inside NMF framework using linear constraints on dictionary atoms. This method is further developed to regularize harmonic amplitudes. Simple multiplicative algorithms are presented. The experimental evaluation was made on TIMIT corpus mixed with various types of noise. It has been shown that the proposed method outperforms some of the state-of-the-art noise suppression techniques in terms of signal-to-noise ratio.