  We propose a new method to enforce priors on the solution of the nonnegative
matrix factorization (NMF). The proposed algorithm can be used for denoising or
single-channel source separation (SCSS) applications. The NMF solution is
guided to follow the Minimum Mean Square Error (MMSE) estimates under Gaussian
mixture prior models (GMM) for the source signal. In SCSS applications, the
spectra of the observed mixed signal are decomposed as a weighted linear
combination of trained basis vectors for each source using NMF. In this work,
the NMF decomposition weight matrices are treated as a distorted image by a
distortion operator, which is learned directly from the observed signals. The
MMSE estimate of the weights matrix under GMM prior and log-normal distribution
for the distortion is then found to improve the NMF decomposition results. The
MMSE estimate is embedded within the optimization objective to form a novel
regularized NMF cost function. The corresponding update rules for the new
objectives are derived in this paper. Experimental results show that, the
proposed regularized NMF algorithm improves the source separation performance
compared with using NMF without prior or with other prior models.
