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

Source Separation using Regularized NMF with MMSE Estimates under GMM Priors with Online Learning for The Uncertainties