Nonnegative Matrix Factorization with Orthogonal Activations for Supervised Speech Enhancement

Nonnegative matrix factorization (NMF) decomposes a matrix into basis and activation matrices. Imposing constraints on the factorization can improve the performance of supervised speech enhancement based on NMF. Constraints such as signal sparsity, spectral smoothness, and temporal continuity ensure enhanced speech signals are more accurate and intelligible. We propose constraining NMF by minimizing the squared Euclidean norm and incorporating orthogonality constraints into the activation matrix. Unlike the conventional method, our approach avoids the need for post-processing normalization, which can disrupt the orthogonality of the activation matrix. We present and assess two distinct orthogonality criteria designed to maintain the nonnegativity of the activation matrix while ensuring orthogonality. Each criterion is integrated into the multiplicative update rules, resulting in efficient supervised speech enhancement. Experimental results are conducted on a dataset of noisy speech signals contaminated with various types of noise at different levels. Our findings indicate that constrained NMF with the proposed orthogonality criteria significantly outperforms unconstrained NMF and a conventional orthogonally constrained NMF approach, which can introduce artifacts and reduce the clarity of enhanced speech.