Independent Positive Semidefinite Tensor Analysis in Blind Source Separation

Independent vector analysis followed by HMM-based feature enhancement for robust speech recognition

This paper addresses the determined convolutive blind source separation (BSS) problem. The state-of-the-art independent low-rank matrix analysis (ILRMA), unifying independent component analysis (ICA) and nonnegative matrix factorization, has the disadvantage of ignoring inter-frame and inter-frequency spectral correlation of source signals. We here propose a new BSS method that estimates a linear transformation for spectral decorrelation and performs ILRMA in the transformed domain. A newly introduced optimization problem is an extension of that for ICA based on maximum likelihood. For this problem, we provide a necessary and sufficient condition for the existence of optimal solutions, and develop algorithms based on block coordinate descent methods with closed-form solutions. Experimental results show the improved separation performance of the proposed method compared to ILRMA.

This article describes a computationally-efficient blind source separation (BSS) method based on the independence, low-rankness, and directivity of the sources. A typical approach to BSS is unsupervised learning of a probabilistic model that consists of a source model representing the time-frequency structure of source images and a spatial model representing their inter-channel covariance structure. Building upon the low-rank source model based on nonnegative matrix factorization (NMF), which has been considered to be effective for inter-frequency source alignment, multichannel NMF (MNMF) assumes source images to follow multivariate complex Gaussian distributions with unconstrained full-rank spatial covariance matrices (SCMs). An effective way of reducing the computational cost and initialization sensitivity of MNMF is to restrict the degree of freedom of SCMs. While a variant of MNMF called independent low-rank matrix analysis (ILRMA) severely restricts SCMs to rank-1 matrices under an idealized condition that only directional and less-echoic sources exist, we restrict SCMs to jointly-diagonalizable yet full-rank matrices in a frequency-wise manner, resulting in FastMNMF1. To help inter-frequency source alignment, we then propose FastMNMF2 that shares the directional feature of each source over all frequency bins. To explicitly consider the directivity or diffuseness of each source, we also propose rank-constrained FastMNMF that enables us to individually specify the ranks of SCMs. Our experiments showed the superiority of FastMNMF over MNMF and ILRMA in speech separation and the effectiveness of the rank constraint in speech enhancement.

The independent vector analysis (IVA) algorithm employs a multivariate source prior to retain the dependency between different frequency bins of each source and thereby avoids the permutation problem that is inherent to blind source separation (BSS). In this paper, a multivariate Student's t distribution is adopted as the source prior, which because of its heavy tail nature can better model the large amplitude information in the frequency bins. Therefore it can improve the separation performance and the convergence speed of the IVA and fast version of the IVA (FastIVA) algorithms as compared with the IVA algorithm based on another multivariate super Gaussian source prior. Separation performance with real binaural room impulse responses (BRIRs) is evaluated by detailed simulation studies when using the different source priors, and the experimental results confirm that the IVA and the FastIVA with the proposed multivariate Student's t source prior can consistently achieve improved and faster separation performance.

Fast fixed-point independent vector analysis (FastIVA) is an improved independent vector analysis (IVA) method, which can achieve faster and better separation performance than original IVA. As an example IVA method, it is designed to solve the permutation problem in frequency domain independent component analysis by retaining the higher order statistical dependency between frequencies during learning. However, the performance of all IVA methods is limited due to the dimensionality of the parameter space commonly encountered in practical frequency-domain source separation problems and the spherical symmetry assumed with the source model. In this article, a particular permutation problem encountered in using the FastIVA algorithm is highlighted, namely the block permutation problem. Therefore a new audio video based fast fixed-point independent vector analysis algorithm is proposed, which uses video information to provide a smart initialization for the optimization problem. The method cannot only avoid the ill convergence resulting from the block permutation problem but also improve the separation performance even in noisy and high reverberant environments. Different multisource datasets including the real audio video corpus AV16.3 are used to verify the proposed method. For the evaluation of the separation performance on real room recordings, a new pitch based evaluation criterion is also proposed.

A novel method is proposed to improve the performance of independent vector analysis (IVA) for blind signal separation of acoustic mixtures. IVA is a frequency-domain approach that successfully resolves the well-known permutation problem by applying a spherical dependency model to all pairs of frequency bins. The dependency model of IVA is equivalent to a single clique in an undirected graph; a clique in graph theory is defined as a subset of vertices in which any pair of vertices is connected by an undirected edge. Therefore, IVA imposes the same amount of statistical dependency on every pair of frequency bins, which may not match the characteristics of real-world signals. The proposed method allows variable amounts of statistical dependencies according to the correlation coefficients observed in real acoustic signals and, hence, enables more accurate modeling of statistical dependencies. A number of cliques constitutes the new dependency graph so that neighboring frequency bins are assigned to the same clique, while distant bins are assigned to different cliques. The permutation ambiguity is resolved by overlapped frequency bins between neighboring cliques. For speech signals, we observed especially strong correlations across neighboring frequency bins and a decrease in these correlations with an increase in the distance between bins. The clique sizes are either fixed, or determined by the reciprocal of the mel-frequency scale to impose a wider dependency on low-frequency components. Experimental results showed improved performances over conventional IVA. The signal-to-interference ratio improved from 15.5 to 18.8 dB on average for seven different source locations. When we varied the clique sizes according to the observed correlations, the stability of the proposed method increased with a large number of cliques.

In this paper, we propose a new algorithm that efficiently separates a directional source and diffuse background noise based on independent low-rank matrix analysis (ILRMA). ILRMA is one of the state-of-the-art techniques of blind source separation (BSS) and is based on a rank-1 spatial model. Although such a model does not hold for diffuse noise, ILRMA can accurately estimate the spatial parameters of the directional source. Motivated by this fact, we utilize these estimates to restore the lost spatial basis of diffuse noise, which can be considered as an efficient full-rank spatial covariance estimation. BSS experiments show the efficacy of the proposed method in terms of the computational cost and separation performance.

The most standard blind source separation (BSS) methods address the situation when a set of signals are available, e.g. from measurements, and all of them are linear memoryless combinations, with unknown coefficient values, of the same limited set of unknown source signals. BSS methods aim at estimating these unknown source signals and/or coefficients. This generic problem is e.g. faced in the field of Earth observation (where it is also called “unsupervised unmixing”), when considering the commonly used (over)simplified model of hyperspectral images. Each pixel of such an image has an associated reflectance spectrum derived from measurements, which is defined by the fraction of sunlight power reflected by the corresponding Earth surface at each wavelength. Each source signal is then the single reflectance spectrum associated with one of the classes of pure materials which are present in the region of Earth corresponding to the overall considered hyperspectral image. Besides, the associated coefficients define the surfaces on Earth covered with each of these pure materials in each sub-region corresponding to one pixel of the considered image. However, real hyperspectral data e.g. obtained in urban areas have a much more complex structure than the above basic model: each class of pure materials (e.g. roof tiles, trees or asphalt) has so-called spectral or intra-class variability, i.e. it yields a somewhat different spectral component in each pixel of the image. In this complex framework, this chapter shows that Principal Component Analysis (PCA) and its proposed extension are of high interest at three stages of our investigation. First, PCA allows us to analyze the above-mentioned spectral variability of real high-dimensional hyperspectral data and to propose an extended data model which is suited to these complex data. We then develop a versatile extension of BSS methods based on Nonnegative Matrix Factorization, which adds the capability to handle arbitrary forms of intra-class variability by transposing PCA concepts to this original version of the BSS tramework. Finally, PCA again proves to be very well suited to analyzing the high-dimensional data obtained as the result of the proposed BSS method.

We propose a blind source separation method that yields high-quality speech with low distortion. Time-frequency (TF) masking can effectively reduce interference, but it produces nonlinear distortion. By contrast, linear filtering using a separation matrix such as independent vector analysis (IVA) can avoid nonlinear distortion, but the separation performance is reduced under reverberant conditions. The tandem connectionist approach combines several separation methods and it has been used frequently to compensate for the disadvantages of these methods. In this study, we propose associative memory model (AMM)-based linear filtering and a tandem connectionist framework, which applies TF masking followed by linear filtering. By using AMM trained with speech spectra to optimize the separation matrix, the proposed linear filtering method considers the properties of speech that are not considered explicitly in IVA, such as the harmonic components of spectra. TF masking is applied in the proposed tandem connectionist framework to reduce unwanted components that hinder the optimization of the separation matrix, and it is approximated by using a linear separation matrix to reduce nonlinear distortion. The results obtained in simultaneous speech separation experiments demonstrate that although the proposed linear filtering method can increase the signal-to-distortion ratio (SDR) and signal-to-interference ratio (SIR) compared with IVA, the proposed tandem connectionist framework can obtain greater increases in SDR and SIR, and it reduces the phoneme error rate more than the proposed linear filtering method.

Conventional Blind Source Separation (BSS) techniques are computationally complex. This is due to the calculation of the demixing matrix for the entire signal or due to the frequent update of the demixing matrix at every time frame index, making them impractical to use in many real-time applications. In this paper, a robust, neural network based two-microphone sound source localization method is used as a criterion to enhance the efficiency of the Independent Vector Analysis (IVA), a BSS method. IVA is used to separate speech and noise sources which are convolutedly mixed. The practical usability of the proposed method is proved by implementing it on a smartphone to separate speech and noise in real-world scenarios for hearing-aid applications. The experimental results with objective and subjective tests reveal the usefulness of the developed method for real-world applications.

Independent vector analysis (IVA) is a special form of independent component analysis (ICA), which has demonstrated its prominent performance in solving convolutive blind source separation (BSS) problems in the frequency domain. Most IVA algorithms are based on optimizing certain contrast functions, where the main difficulty of these approaches lies in finding a reliable and fast estimation of the unknown distribution of sources. Despite the rich availability of efficient tensorial approaches to the standard ICA problem, these methods have not been explored considerably for IVA. In this article, we propose a matrix joint diagonalization approach to solve the complex IVA problem. The new factorization neither relies on a whitening process, nor does it require an estimate of the joint probability distribution of the dependent signal groups. The latter is in contrast to most IVA approaches up to date. The underlying geometry of the problem is investigated together with a critical point analysis of the resulting cost function. A conjugate gradient algorithm on the appropriate manifold setting is developed.

Integrating information from multiple biological layers is a key approach to unraveling the complexities of the human brain, with its multiple overlapping structural and functional subsystems operating at widely different temporal and spatial scales. Moreover, it has true potential to positively impact mental health patients through early diagnosis and individualized treatment. This chapter lays out a succession of approaches to synergistic fusion of multimodal brain imaging data, with a special focus on blind source separation (BSS) and deep learning (DL) methods. Firstly, a broad unified description of the BSS field is introduced, serving as a theoretical backbone for the chapter. Complementary to that, a detailed case study of three different applications of joint independent component analysis (jICA) provides both a reference guide on data fusion and a bridge into more advanced BSS methods. Various advanced BSS methods such as multiset canonical correlation analysis (mCCA), multi-way partial least squares (N-PLS), independent vector analysis (IVA) and Parallel ICA are then reviewed and discussed in terms of their strengths and limitations. Finally, DL methods are introduced, focusing on three important applications: classification utilizing strategies for multimodal data augmentation, embedding of learned representations in order to reveal disease severity spectra, and multimodal tissue segmentation.

A new independent component analysis (ICA) formulation called independent vector analysis (IVA) was proposed in order to solve the permutation problem in convolutive blind source separation (BSS). Instead of running ICA in each frequency bin separately and correcting the disorder with an additional algorithmic scheme afterwards, IVA exploited the dependency among the frequency components of a source and dealt with them as a multivariate source by modeling it with sparse and spherically, or radially, symmetric joint probability density functions (pdfs). In this paper, we compare the speech separation performances of IVA by using a group of l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> -norm-invariant sparse pdfs where the value of and the sparseness can be controlled. Also, we derive an IVA algorithm from a nonparametric perspective with the constraint of spherical symmetry and high dimensionality. Simulation results confirm the efficiency of assuming sparseness and spherical symmetry for the speech model in the frequency domain.

Rescue robots have been developed for search and rescue operations in times of large-scale disasters. Such a robot is used to search for survivors in disaster sites by capturing their voices with its microphone array. However, since the robot has many vibration motors, ego noise is mixed with voices, and it is difficult to differentiate the ego noise from a call for help from a disaster survivor. In our previous works, an ego noise reduction technique that combines a method of blind source separation called independent low-rank matrix analysis and postprocessing for noise cancellation was proposed. In the practical use of this robot, to determine the precise location of survivors, the direction of the observed voice should be estimated after the ego noise reduction process. To achieve this objective, in this study, a new hose-shaped rescue robot with microphone arrays was developed. Moreover, we adapt postfilter called MOSIE to our previous noise reduction method to listen to stereo sound because this robot can record stereo sound. By performing in a simulated disaster site, we confirm that the operator can perceive the direction of a survivor's location by applying a speech enhancement technique combining independent low-rank matrix analysis, noise cancellation, and postfiltering to the observed multichannel noisy signals.

Independent vector analysis (IVA) minimizes an objective function to estimate separation filters that separate mixture signals into individual source signals. Unfortunately, IVA often suffers from the well-known block permutation problem. To mitigate that problem, the use of geometry knowledge has been studied, but two crucial issues remain: the necessity of non-differential processes outside the minimization and of high-level geometrical clues such as the directions of arrival (DOAs) of the source signals. This paper thus presents a novel IVA method whose objective function has a differentiable max-directivity beamforming normalization (MDBN) term. This term uses geometry knowledge from only a low-level geometrical clue (the positions of the microphone array) via the traditional beamforming (BF) concept that each separation filter should have a maximum gain for each specific DOA across all frequency bins. Thus, our overall objective function can be minimized by gradient descent, and the MDBN term encourages the separation filters to focus on specific directions, which implicitly estimates the most reasonable DOAs of the source signals at each iteration. Therefore, our method uses geometry knowledge while avoiding the above two issues and estimates good separation filters mitigating the permutation problem. Several experiments show that our method outperforms the conventional BF and IVA methods.