Underdetermined convolutive blind source separation in the time–frequency domain based on single source points and experimental validation

Blind source separation (BSS) in time-frequency (TF) domain is a versatile framework to recover sources from the recorded mixture signals in a reverberant environment. In general, a two-stage strategy is one of the popular BSS frameworks for the underdetermined BSS case (the number of mixtures is less than the number of sources), which is a tough problem due to the mixing matrix is not invertible. In this paper, we propose a new two-stage scheme combining density-based clustering and sparse reconstruction to estimate mixing matrix and sources, respectively. At the first stage, we transform the mixing matrix estimation as an eigenvector clustering problem based on a particular local dominant assumption. The eigenvectors are first exploited from the rank-one structure of local covariance matrices of mixture TF vectors. These eigenvectors are then clustered and adjusted to give estimated mixing matrix by cooperating density-based clustering and weight clustering. At the second stage, we transform the source reconstruction as a ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> norm (0 <; p ≤ 1) minimization by an iterative Lagrange multiplier method. With a proper initialization, the obtained solution is a global minimum for any p in (0, 1] with convergence guarantee. The proposed approach is demonstrated to be superior to the state-of-the-art baseline methods in various underdetermined experiments.

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time-frequency domain with the STFT, which describes the local characteristic of the signal from the time-frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.

This paper considers the mixing matrix estimation in the underdetermined blind source separation. An effective estimation algorithm based on local directional density detection (LDDD) and dynamic data field clustering (DDFC) is proposed. First, argument-based time-frequency single source points detection is employed to improve signal sparsity. To overcome the limitation of traditional clustering algorithms, which depend on the preset of initial clustering centers and the number of sources, the LDDD is introduced to choose the single source points with high potential energy as representative objects to form data preliminary classification. Then DDFC algorithm is adopted to move and merge the representative objects until all column vectors of mixing matrix are estimated. Simulation results show that the proposed method can effectively estimate mixing matrix with high accuracy, especially in the real non-cooperative cases where the number of sources is unknown.

Underdetermined blind source separation is to recover the source signals from the observed signals without prior knowledge of the mixing channel. In signal processing, it is an open problem attracted the attention of more and more researchers. In this paper, we presents a fast and effective time-frequency algorithm to separate speech source signals in the underdetermined mixture case. In the proposed algorithm, the time-domain mixture signals are transformed to the frequency-domain by using short-time Fourier transform (STFT). Then the mixing matrix is estimated using K-means clustering, and frequency-domain sources are separated by solving a low-dimensional linear programming problem based on the estimated mixing matrix. Finally, the time-domain source signals are obtained using inverse STFT. The proposed algorithm has two advantages, one is to save time consumption, the other is to obtain better separation performance. Experimental results based on two mixtures of four speech sources demonstrate the feasibility and superiority of the proposed algorithm.

In this paper, a single source points (SSPs) detection method based on local dominance is devised for mixing matrix estimation in underdetermined blind source separation (UBSS). In the proposed detector, time-frequency (TF) points of mixed signals are firstly divided into different groups, and the local covariance matrix of each group is calculated. Taking advantage of the local dominance property, the groups with rank-one local covariance matrices are then identified as single source groups, i.e., the TF points of mixed signals in single source groups are regarded as SSPs. Finally, the obtained SSPs are clustered by the hierarchical clustering algorithm to achieve mixing matrix estimation. Simulations with real audio sources show that the proposed method yields competitive robustness, efficiency and effectiveness, in comparison with the traditional methods.

Narrow-band interference (NBI) is a critical issue for synthetic aperture radar (SAR), in which the imaging quality can be degraded severely. To suppress NBI effectively, a novel interference suppression algorithm using robust principal component analysis (RPCA) based signal separation in time-frequency domain is proposed. The RPCA algorithm is introduced for signal separation in the time-frequency domain for the first time. The fundamental assumption of RPCA is that a matrix can be modeled as a combination of a low-rank matrix and a sparse counterpart. In terms of the SAR echo, the short time Fourier transformation (STFT) matrix of mixed signals (i.e., useful SAR signals and NBIs) well fits the assumption of RPCA. Based on this property, radar echoes are first transformed into the time-frequency domain by STFT to form an STFT matrix. Then, the RPCA algorithm is used to decompose the STFT matrix into a low-rank matrix (i.e., NBIs) and a sparse matrix (i.e., useful signals). Finally, the NBIs can be reconstructed and subtracted from the echoes to realize the interference suppression. The experimental results of simulated and measured data demonstrate that the proposed algorithm not only can suppress interference effectively, but also preserve the useful information as much as possible.

apport de recherche ISSN 0249-6399 ISRN INRIA/RR--7116--FR+ENGinria-00435807, version 2- 14 Dec 2009Under-determined reverberant audio source separation using a full-rank spatial covariance model

Multi-bearing defect detection with trackside acoustic signal based on a pseudo time–frequency analysis and Dopplerlet filter

An algorithm for mixing matrix estimation in instantaneous blind source separation

Underdetermined mixing matrix estimation by exploiting sparsity of sources

Mine microseismic signal denoising is a basic and crucial link in microseismic data processing, which influences the accuracy and reliability of the monitoring system, and is of great significance with regard to safety during mining. Therefore, this study introduces a deep learning method to improve the mapping function and sparsity of signals in the time-frequency domain and constructs a denoising framework based on a deep convolutional autoencoder to address the denoising problem of mine microseismic signals. First, all noisy microseismic signals are normalized to ensure the nonlinear expression ability of the constructed denoising framework. Then, the normalized signals are transformed into the time-frequency domain using the short-time Fourier transform (STFT), and the real and imaginary parts of time-frequency coefficients serve as the input of the deep convolutional autoencoder to output the masks of the effective and noise signals. Next, these masks are applied to the time-frequency coefficients of the noisy microseismic signals, and the time-frequency coefficients of the potentially effective and noise signals are estimated. Finally, inverse STFT is used to transform these time-frequency coefficients to the time domain to obtain the final denoised effective and noise signals. The constructed framework automatically learns rich features from synthetic data to separate the effective and noise signals, thereby achieving the purpose of fast and automatic denoising. The experimental results show that compared with the wavelet threshold and ensemble empirical mode decomposition, the denoising framework considerably improves the signal-to-noise ratio of mine microseismic signals with less waveform distortion. Moreover, it can achieve a better denoising effect efficiently even in the case of a low SNR, which has obvious advantages. The constructed denoising framework is suitable for microseismic monitoring signals of various mine dynamic disasters and provides strong technical support for intelligent monitoring and early warning concerning production risks in mines.

Supervised single channel dual domains speech enhancement using sparse non-negative matrix factorization

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.

Convolutive blind source separation and adaptive beamforming have similar goals and similar system structure. Both attempt to extract selected source signals from observed sensor mixtures by a filter array. However, time and frequency information are utilized in convolutive blind source separation while spatial information of source signals or sensor array is used in adaptive beamforming. In this paper, we start with a brief introduction of blind source separation and adaptive beamforming. Next, we review approaches combining spatial information used in beamforming with time/frequency processing used in convolutive blind source separation. We also present a new proposed combination approach and simulation results.

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.