A method and system denoises a mixed signal. A constrained non-negative matrix factorization (NMF) is applied to the mixed signal. The NMF is constrained by a denoising model, in which the denoising model includes training basis matrices of a training acoustic signal and a training noise signal, and statistics of weights of the training basis matrices. The applying produces weight of a basis matrix of the acoustic signal of the mixed signal. A product of the weights of the basis matrix of the acoustic signal and the training basis matrices of the training acoustic signal and the training noise signal is taken to reconstruct the acoustic signal. The mixed signal can be speech and noise.