Convolutive Blind Source Separation Methods

In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks

Overcomplete Blind Source Separation by Combining ICA and Binary Time-Frequency Masking

A limitation in many source separation tasks is that the number of source signals has to be known in advance. Further, in order to achieve good performance, the number of sources cannot exceed the number of sensors. In many real-world applications these limitations are too strict. We propose a novel method for over-complete blind source separation. Two powerful source separation techniques have been combined, independent component analysis and binary time-frequency masking. Hereby, it is possible to iteratively extract each speech signal from the mixture. By using merely two microphones we can separate up to six mixed speech signals under anechoic conditions. The number of source signals is not assumed to be known in advance. It is also possible to maintain the extracted signals as stereo signal

Mixture of beamformers for speech separation and extraction

In many audio applications, the signal of interest is corrupted by acoustic background noise, interference, and reverberation. The presence of these contaminations can significantly degrade the quality and intelligibility of the audio signal. This makes it important to develop signal processing methods that can separate the competing sources and extract a source of interest. The estimated signals may then be either directly listened to, transmitted, or further processed, giving rise to a wide range of applications such as hearing aids, noise-cancelling headphones, human-computer interaction, surveillance, and hands-free telephony. Many of the existing approaches to speech separation/extraction relied on beamforming techniques. These techniques approach the problem from a spatial point of view; a microphone array is used to form a spatial filter which can extract a signal from a specific direction and reduce the contamination of signals from other directions. However, when there are fewer microphones than sources (the underdetermined case), perfect attenuation of all interferers becomes impossible and only partial interference attenuation is possible. In this thesis, we present a framework which extends the use of beamforming techniques to underdetermined speech mixtures. We describe frequency domain non-linear mixture of beamformers that can extract a speech source from a known direction. Our approach models the data in each frequency bin via Gaussian mixture distributions, which can be learned using the expectation maximization algorithm. The model learning is performed using the observed mixture signals only, and no prior training is required. The signal estimator comprises of a set of minimum mean square error (MMSE), minimum variance distortionless response (MVDR), or minimum power distortionless response (MPDR) beamformers. In order to estimate the signal, all beamformers are concurrently applied to the observed signal, and the weighted sum of the beamformers’ outputs is used as the signal estimator, where the weights are the estimated posterior probabilities of the Gaussian mixture states. These weights are specific to each timefrequency point. The resulting non-linear beamformers do not need to know or estimate the number of sources, and can be applied to microphone arrays with two or more microphones with arbitrary array configuration. We test and evaluate the described methods on underdetermined speech mixtures. Experimental results for the non-linear beamformers in underdetermined mixtures with room reverberation confirm their capability to successfully extract speech sources

Informed algorithms for sound source separation in enclosed reverberant environments

While humans can separate a sound of interest amidst a cacophony of contending sounds in an echoic environment, machine-based methods lag behind in solving this task. This thesis thus aims at improving performance of audio separation algorithms when they are informed i.e. have access to source location information. These locations are assumed to be known a priori in this work, for example by video processing. Initially, a multi-microphone array based method combined with binary time-frequency masking is proposed. A robust least squares frequency invariant data independent beamformer designed with the location information is utilized to estimate the sources. To further enhance the estimated sources, binary time-frequency masking based post-processing is used but cepstral domain smoothing is required to mitigate musical noise. To tackle the under-determined case and further improve separation performance at higher reverberation times, a two-microphone based method which is inspired by human auditory processing and generates soft time-frequency masks is described. In this approach interaural level difference, interaural phase difference and mixing vectors are probabilistically modeled in the time-frequency domain and the model parameters are learned through the expectation-maximization (EM) algorithm. A direction vector is estimated for each source, using the location information, which is used as the mean parameter of the mixing vector model. Soft time-frequency masks are used to reconstruct the sources. A spatial covariance model is then integrated into the probabilistic model framework that encodes the spatial characteristics of the enclosure and further improves the separation performance in challenging scenarios i.e. when sources are in close proximity and when the level of reverberation is high. Finally, new dereverberation based pre-processing is proposed based on the cascade of three dereverberation stages where each enhances the twomicrophone reverberant mixture. The dereverberation stages are based on amplitude spectral subtraction, where the late reverberation is estimated and suppressed. The combination of such dereverberation based pre-processing and use of soft mask separation yields the best separation performance. All methods are evaluated with real and synthetic mixtures formed for example from speech signals from the TIMIT database and measured room impulse responses

Robust variational Bayesian clustering for underdetermined speech separation

The main focus of this thesis is the enhancement of the statistical framework employed for underdetermined T-F masking blind separation of speech. While humans are capable of extracting a speech signal of interest in the presence of other interference and noise; actual speech recognition systems and hearing aids cannot match this psychoacoustic ability. They perform well in noise and reverberant free environments but suffer in realistic environments. Time-frequency masking algorithms based on computational auditory scene analysis attempt to separate multiple sound sources from only two reverberant stereo mixtures. They essentially rely on the sparsity that binaural cues exhibit in the time-frequency domain to generate masks which extract individual sources from their corresponding spectrogram points to solve the problem of underdetermined convolutive speech separation. Statistically, this can be interpreted as a classical clustering problem. Due to analytical simplicity, a finite mixture of Gaussian distributions is commonly used in T-F masking algorithms for modelling interaural cues. Such a model is however sensitive to outliers, therefore, a robust probabilistic model based on the Student's t-distribution is first proposed to improve the robustness of the statistical framework. This heavy tailed distribution, as compared to the Gaussian distribution, can potentially better capture outlier values and thereby lead to more accurate probabilistic masks for source separation. This non-Gaussian approach is applied to the state-of the-art MESSL algorithm and comparative studies are undertaken to confirm the improved separation quality. A Bayesian clustering framework that can better model uncertainties in reverberant environments is then exploited to replace the conventional expectation-maximization (EM) algorithm within a maximum likelihood estimation (MLE) framework. A variational Bayesian (VB) approach is then applied to the MESSL algorithm to cluster interaural phase differences thereby avoiding the drawbacks of MLE; specifically the probable presence of singularities and experimental results confirm an improvement in the separation performance. Finally, the joint modelling of the interaural phase and level differences and the integration of their non-Gaussian modelling within a variational Bayesian framework, is proposed. This approach combines the advantages of the robust estimation provided by the Student's t-distribution and the robust clustering inherent in the Bayesian approach. In other words, this general framework avoids the difficulties associated with MLE and makes use of the heavy tailed Student's t-distribution to improve the estimation of the soft probabilistic masks at various reverberation times particularly for sources in close proximity. Through an extensive set of simulation studies which compares the proposed approach with other T-F masking algorithms under different scenarios, a significant improvement in terms of objective and subjective performance measures is achieved

Dictionary Learning for Sparse Representations With Applications to Blind Source Separation.

During the past decade, sparse representation has attracted much attention in the signal processing community. It aims to represent a signal as a linear combination of a small number of elementary signals called atoms. These atoms constitute a dictionary so that a signal can be expressed by the multiplication of the dictionary and a sparse coefficients vector. This leads to two main challenges that are studied in the literature, i.e. sparse coding (find the coding coefficients based on a given dictionary) and dictionary design (find an appropriate dictionary to fit the data). Dictionary design is the focus of this thesis. Traditionally, the signals can be decomposed by the predefined mathematical transform, such as discrete cosine transform (DCT), which forms the so-called analytical approach. In recent years, learning-based methods have been introduced to adapt the dictionary from a set of training data, leading to the technique of dictionary learning. Although this may involve a higher computational complexity, learned dictionaries have the potential to offer improved performance as compared with predefined dictionaries. Dictionary learning algorithm is often achieved by iteratively executing two operations: sparse approximation and dictionary update. We focus on the dictionary update step, where the dictionary is optimized with a given sparsity pattern. A novel framework is proposed to generalize benchmark mechanisms such as the method of optimal directions (MOD) and K-SVD where an arbitrary set of codewords and the corresponding sparse coefficients are simultaneously updated, hence the term simultaneous codeword optimization (SimCO). Moreover, its extended formulation ‘regularized SimCO’ mitigates the major bottleneck of dictionary update caused by the singular points. First and second order optimization procedures are designed to solve the primitive and regularized SimCO. In addition, a tree-structured multi-level representation of dictionary based on clustering is used to speed up the optimization process in the sparse coding stage. This novel dictionary learning algorithm is also applied for solving the underdetermined blind speech separation problem, leading to a multi-stage method, where the separation problem is reformulated as a sparse coding problem, with the dictionary being learned by an adaptive algorithm. Using mutual coherence and sparsity index, the performance of a variety of dictionaries for underdetermined speech separation is compared and analyzed, such as the dictionaries learned from speech mixtures and ground truth speech sources, as well as those predefined by mathematical transforms. Finally, we propose a new method for joint dictionary learning and source separation. Different from the multistage method, the proposed method can simultaneously estimate the mixing matrix, the dictionary and the sources in an alternating and blind manner. The advantages of all the proposed methods are demonstrated over the state-of-the-art methods using extensive numerical tests

A Study on Linear Blind Source Separation using Associative Memory Model

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