Abstract
In this study, a new technique in source separation using Two-Dimensional Nonnegative Matrix Factorization (NMF2D) with the Beta-divergence is proposed. The Time-Frequency (TF) profile of each source is modeled as two-dimensional convolution of the temporal code and the spectral basis. In addition, adaptive sparsity constraint was imposed to reduce the ambiguity and provide uniqueness to the solution. The proposed model used Beta-divergence as a cost function and updated by maximizing the joint probability of the mixing spectral basis and temporal codes using the multiplicative update rules. Experimental tests have been conducted in audio application to blindly separate the source in musical mixture. Results have shown the effectiveness of the algorithm in separating the audio sources from single channel mixture.
Highlights
Nonnegative Matrix Factorization (NMF) (Lee and Seung, 1999) has become one of the promising and exciting techniques in signal processing
To further improve the algorithm, this study proposed a sparseness constraint to be imposed in the cost function to reduce the ambiguity the ambiguity associated with the estimation of the spectral basis and temporal codes
Two-dimensional nonnegative matrix factorization: In derivation of nonnegative matrix factorization framework, firstly, we considered a source model of Y which is defined as a follows: coefficients used by each source signal, we can restore each of the original signals with most of the interference from the unwanted signals removed
Summary
Nonnegative Matrix Factorization (NMF) (Lee and Seung, 1999) has become one of the promising and exciting techniques in signal processing. One of the most useful property of NMF is that the nonnegative constraint by itself enforcing the sparse representation of the data This representation makes the encoded data easy to be estimated because data was encoded by using only a few active components. In NMF2D, the Time-Frequency (TF) profile of each source is modeled as two-dimensional convolution of the temporal code and the spectral basis. This significantly reduces the number of components per source needed in the decomposition. To further improve the algorithm, this study proposed a sparseness constraint to be imposed in the cost function to reduce the ambiguity the ambiguity associated with the estimation of the spectral basis and temporal codes
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