Single-Mixture Audio Source Separation by Subspace Decomposition of Hilbert Spectrum

A novel technique is developed to separate the audio sources from a single mixture. The method is based on decomposing the Hilbert spectrum (HS) of the mixed signal into independent source subspaces. Hilbert transform combined with empirical mode decomposition (EMD) constitutes HS, which is a fine-resolution time-frequency representation of a nonstationary signal. The EMD represents any time-domain signal as the sum of a finite set of oscillatory components called intrinsic mode functions (IMFs). After computing the spectral projections between the mixed signal and the individual IMF components, the projection vectors are used to derive a set of spectral independent bases by applying principal component analysis (PCA) and independent component analysis (ICA). A k-means clustering algorithm based on Kulback-Leibler divergence (KLd) is introduced to group the independent basis vectors into the number of component sources inside the mixture. The HS of the mixed signal is projected onto the space spanned by each group of basis vectors yielding the independent source subspaces. The time-domain source signals are reconstructed by applying the inverse transformation. Experimental results show that the proposed algorithm performs separation of speech and interfering sound from a single mixture