Independent Low-Rank Matrix Analysis with Decorrelation Learning

The issue of convolutive blind source separation (BSS) is addressed in this paper. Independent low-rank matrix analysis (ILRMA), unifying frequency-domain independent component analysis (FDICA) and nonnegative matrix factorization (NMF), is a method that has recently proposed to model low-rank structure of source spectra by using NMF in addition to independence between sources used in FDICA and independent vector analysis (IVA). Although ILRMA has been shown to provide better separation performance than FDICA and IVA, the frequency components of each source are assumed to be independent in ILRMA due to NMF modeling of source spectra, which may degrade its performance when the short-term Fourier transform (STFT) is unable to decorrelate the frequency components for each source. This paper therefore presents a new BSS method that unifies IVA and positive semidefinite tensor factorization (PSDTF). PSDTF models not only power spectra in the same way NMF does but also models the correlations between frequency bins in each source. The proposed method can be viewed as a multichannel extension of PSDTF and exploits both the independence between sources and the inter-frequency correlations as a clue for separating mixtures. Experimental results indicate the improved performance of our approach.

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.

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.

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.

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.

Recently, blind source separation (BSS) methods have gained significant attention in the area of signal processing. Independent component analysis (ICA) and second-order blind identification (SOBI) are two popular BSS methods that have been applied to modal identification of mechanical and structural systems. Published results by several researchers have shown that ICA performs satisfactorily for systems with very low levels of structural damping, for example, for damping ratios of the order of 1% critical. For practical structural applications with higher levels of damping, methods based on SOBI have shown significant improvement over ICA methods. However, traditional SOBI methods suffer when nonstationary sources are present, such as those that occur during earthquakes and other transient excitations. In this paper, a new technique based on SOBI, called the modified cross-correlation method, is proposed to address these shortcomings. The conditions in which the problem of structural system identification can be posed as a BSS problem is also discussed. The results of simulation described in terms of identified natural frequencies, mode shapes, and damping ratios are presented for the cases of synthetic wind and recorded earthquake excitations. The results of identification show that the proposed method achieves better performance over traditional ICA and SOBI methods. Both experimental and large-scale structural simulation results are included to demonstrate the applicability of the newly proposed method to structural identification problems.

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.

In this article, we propose a new blind speech extraction (BSE) method that robustly extracts a directional speech from background diffuse noise by combining independent low-rank matrix analysis (ILRMA) and efficient rank-constrained spatial covariance matrix (SCM) estimation. To achieve more accurate BSE than ILRMA, which assumes each source to be a point source (rank-1 spatial model), the proposed method restores the lost spatial basis for the full-rank SCM of diffuse noise. We adopt the multivariate complex generalized Gaussian distribution (GGD) as the statistical generative model to express various types of observed signal. To estimate the model parameters for an arbitrary shape parameter of the multivariate GGD, we derive a new inequality for rank-constrained SCMs. Also, we propose new acceleration methods to accomplish much faster extraction than conventional blind source separation methods. In BSE experiments using simulated and real recorded data, we confirm that the proposed method achieves more accurate and faster speech extraction than conventional methods.

The problem of blind source separation (BSS) has been intensively studied by the signal processing community. The first solutions to deal with BSS were proposed in the 1980's and are founded on the concept of independent component analysis (ICA). More recently, aiming at tackling some limitations of ICA-based methods, much attention has been paid to alternative BSS approaches. In this tutorial, in addition to providing a brief review of the classical BSS framework, we present two research trends in this area, namely source separation over Galois fields and sparse component analysis. For both subjects, we provide an overview of the main criteria, highlighting scenarios that can benefit from these more recent BSS paradigms.

Chapter 1 - Introduction

For the problem of blind source separation (BSS) with the sparsity properties of the high frequency wavelet transform coefficients, the paper proposed a new method based on compressed sensing (CS) and K-means clustering algorithm. Compared with the traditional methods of blind source separation, simulation results demonstrated that the proposed method improves the quality of the recovered signal significantly, and improves the speed of separating and reconstruction obviously.

Nonnegative Matrix Factorization (NMF) has proven to be a useful tool for the analysis of nonnegative multivariate data. However, it is known not to lead to unique results when applied to nonnegative Blind Source Separation (BSS) problems. In this paper we present first results of an extension to the NMF algorithm which solves the BSS problem when the underlying sources are sufficiently sparse. As the proposed target function is discontinuous and possesses many local minima, we use a genetic algorithm for its minimization. Application to a microarray data set will be considered also.

The problem of blind source separation (BSS) for multiple-input multiple-output (MIMO) autoregressive (AR) mixtures is addressed in this paper. A new time-domain method for system identification and BSS is proposed based on the Gaussian mixture model (GMM) for sources distribution. The algorithm is based on the generalized expectation-maximization (GEM) method for joint estimation of the AR model parameters and the GMM parameters of the sources. The method is tested via simulations of synthetic and real audio signals. The results show that the proposed algorithm outperforms the well-known multidimensional linear predictive coding (LPC), and it achieves higher signal-to-interference ratio (SIR) in the BSS problem.

Fast fixed-point independent vector analysis algorithms for convolutive blind source separation

We address the problem of Blind Source Separation (BSS) of superimposed signals in situations where one signal has constant or slowly varying intensities at some consecutive locations and at the corresponding locations the other signal has highly varying intensities. Independent Component Analysis (ICA) is a major technique for Blind Source Separation and the existing ICA algorithms fail to estimate the original intensities in the stated situation. We combine the advantages of existing sparse methods and Kernel ICA in our technique, by proposing wavelet packet based sparse decomposition of signals prior to the application of Kernel ICA. Simulations and experimental results illustrate the effectiveness and accuracy of the proposed approach. The approach is general in the way that it can be tailored and applied to a wide range of BSS problems concerning one-dimensional signals and images (two-dimensional signals).