In this study, we aim to improve the performance of audio source separation for monaural mixture signals. For monaural audio source separation, semisupervised nonnegative matrix factorization (SNMF) can achieve higher separation performance by employing small supervised signals. In particular, penalized SNMF (PSNMF) with orthogonality penalty is an effective method. PSNMF forces two basis matrices for target and nontarget sources to be orthogonal to each other and improves the separation accuracy. However, the conventional orthogonality penalty is based on an inner product and does not affect the estimation of the basis matrix properly because of the scale indeterminacy between the basis and activation matrices in NMF. To cope with this problem, a new PSNMF with cosine similarity between the basis matrices is proposed. The experimental comparison shows the efficacy of the proposed cosine similarity penalty in supervised audio source separation.

An online nonnegative matrix factorization (NMF) algorithm based on recursive least squares (RLS) is described in a matrix form, and a simplified algorithm for a low-complexity calculation is developed for frame-by-frame online audio source separation system. First, the online NMF algorithm based on the RLS method is described as solving the NMF problem recursively. Next, a simplified algorithm is developed to approximate the RLS-based online NMF algorithm with low complexity. The proposed algorithm is evaluated in terms of audio source separation, and the results show that the performance of the proposed algorithms are superior to that of the conventional online NMF algorithm with significantly reduced complexity.

The Hilbert transformation together with empirical mode decomposition (EMD) produces Hilbert spectrum (HS) which is a fine-resolution time-frequency representation of any nonlinear and non-stationary signal. The EMD decomposes the mixture signal into some oscillatory components each one is called intrinsic mode function (IMF). Some modification of the conventional EMD is proposed here. The instantaneous frequency of every real valued IMF component is computed with Hilbert transformation. The HS is constructed by arranging the instantaneous frequency spectra of IMF components. The HS of the mixture signal is decomposed into subspaces corresponding to the component sources. The decomposition is performed by applying independent component analysis (ICA) and Kulback-Leibler divergence based K-means clustering on the selected number of bases derived from HS of the mixture. The time domain source signals are assembled by applying some post processing on the subspaces. We have produced experimental results using the proposed separation technique.