Complex Nonnegative Matrix Factorization Research Articles

Efficient Noisy Sound-Event Mixture Classification Using Adaptive-Sparse Complex-Valued Matrix Factorization and OvsO SVM.

This paper proposes a solution for events classification from a sole noisy mixture that consist of two major steps: a sound-event separation and a sound-event classification. The traditional complex nonnegative matrix factorization (CMF) is extended by cooperation with the optimal adaptive L1 sparsity to decompose a noisy single-channel mixture. The proposed adaptive L1 sparsity CMF algorithm encodes the spectra pattern and estimates the phase of the original signals in time-frequency representation. Their features enhance the temporal decomposition process efficiently. The support vector machine (SVM) based one versus one (OvsO) strategy was applied with a mean supervector to categorize the demixed sound into the matching sound-event class. The first step of the multi-class MSVM method is to segment the separated signal into blocks by sliding demixed signals, then encoding the three features of each block. Mel frequency cepstral coefficients, short-time energy, and short-time zero-crossing rate are learned with multi sound-event classes by the SVM based OvsO method. The mean supervector is encoded from the obtained features. The proposed method has been evaluated with both separation and classification scenarios using real-world single recorded signals and compared with the state-of-the-art separation method. Experimental results confirmed that the proposed method outperformed the state-of-the-art methods.

Complex ISNMF: A Phase-Aware Model for Monaural Audio Source Separation

This paper introduces a phase-aware probabilistic model for audio source separation. Classical source models in the short-time Fourier transform domain use circularly-symmetric Gaussian or Poisson random variables. This is equivalent to assuming that the phase of each source is uniformly distributed, which is not suitable for exploiting the underlying structure of the phase. Drawing on preliminary works, we introduce here a Bayesian anisotropic Gaussian source model in which the phase is no longer uniform. Such a model permits us to favor a phase value that originates from a signal model through a Markov chain prior structure. The variance of the latent variables are structured with nonnegative matrix factorization (NMF). The resulting model is called complex Itakura–Saito NMF (ISNMF) since it generalizes the ISNMF model to the case of nonisotropic variables. It combines the advantages of ISNMF, which uses a distortion measure adapted to audio and yields a set of estimates which preserve the overall energy of the mixture, and of complex NMF, which enables one to account for some phase constraints. We derive a generalized expectation-maximization algorithm to estimate the model parameters. Experiments conducted on a musical source separation task in a semiinformed setting show that the proposed approach outperforms state-of-the-art phase-aware separation techniques.

Acoustic Denoising using Dictionary Learning with Spectral and Temporal Regularization.

We present a method for speech enhancement of data collected in extremely noisy environments, such as those obtained during magnetic resonance imaging (MRI) scans. We propose an algorithm based on dictionary learning to perform this enhancement. We use complex nonnegative matrix factorization with intra-source additivity (CMF-WISA) to learn dictionaries of the noise and speech+noise portions of the data and use these to factor the noisy spectrum into estimated speech and noise components. We augment the CMF-WISA cost function with spectral and temporal regularization terms to improve the noise modeling. Based on both objective and subjective assessments, we find that our algorithm significantly outperforms traditional techniques such as Least Mean Squares (LMS) filtering, while not requiring prior knowledge or specific assumptions such as periodicity of the noise waveforms that current state-of-the-art algorithms require.

Audio signal separation through complex tensor factorization: Utilizing modulation frequency and phase information

I propose a complex-valued tensor factorization algorithm for audio-source separation to exploit not only amplitude but phase information of audio signals in the modulation frequency (MF) domain. The proposed algorithm is extended from complex non-negative matrix factorization, which is capable of decomposing an arbitrary complex matrix such as the complex spectrum in the acoustic frequency domain. The proposed method enables us to factorize an arbitrary complex tensor of order 3. The detailed performance of the proposed algorithm for single-channel source separation is investigated through numerical experiments. I examine the quantitative contributions of the MF domain and phase information examined by additionally presenting three tensor factorization algorithms and using five objective indices for source separation.

Complex non-negative matrix factorization: Phase-aware sparse representation of audio spectrograms

Non-negative matrix factorization (NMF) has attracted a lot of attention after being proposed as a powerful approach for audio source separation. Factorizing the magnitude spectrogram of a mixture signal into the product of two non-negative matrices can be interpreted as approximating the observed spectra at each time frame as a linear sum of basis spectra scaled by time-varying amplitudes. One drawback of this approach is that the additivity of magnitude spectra is assumed, which holds only approximately. To address this drawback, we introduce a novel framework called the “Complex NMF,” which makes it possible to realize NMF-like signal decompositions in the complex spectrogram domain. We further develop a time-domain extension of this approach, which is noteworthy in that it allows for several extensions that were not possible with the conventional NMF framework.

Single-channel blind separation using L₁-sparse complex non-negative matrix factorization for acoustic signals.

An innovative method of single-channel blind source separation is proposed. The proposed method is a complex-valued non-negative matrix factorization with probabilistically optimal L1-norm sparsity. This preserves the phase information of the source signals and enforces the inherent structures of the temporal codes to be optimally sparse, thus resulting in more meaningful parts factorization. An efficient algorithm with closed-form expression to compute the parameters of the model including the sparsity has been developed. Real-time acoustic mixtures recorded from a single-channel are used to verify the effectiveness of the proposed method.