Underdetermined mixing matrix estimation by exploiting sparsity of sources

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.

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.

To effectively separate underdetermined convolutive mixtures, an accurate and robust underdetermined convolutive blind source separation (BSS) method in the time–frequency domain based on single source points (SSPs) is proposed. Firstly, convolutive BSS in the time domain is transformed into instantaneous BSS in the time–frequency domain by short-time Fourier transform (STFT). Secondly, hierarchical clustering is carried out after the extraction and identification of SSPs by using sparse coding technology. Thirdly, source separation in the frequency domain is obtained based on Lp norm minimization and then alignments are permutated and scales are compensated. Finally, inverse STFT is adopted to reconstruct the separated signals in the time domain. Furthermore, numerical case studies and experimental case studies on a cylindrical test bed are carried out to validate the effectiveness of the proposed method. Generally, this paper provides an accurate and robust underdetermined convolutive BSS technique for mixing matrix estimation, source identification and contribution evaluation, which can provide significant evidence for vibration and noise monitoring and control.

This paper considers complex-valued mixing matrix estimation in underdetermined blind source separation. An effective estimation algorithm based on both single-source-point (SSP) detection and modified dynamic data field clustering is proposed. First, array-processing-based time–frequency SSP detection is applied to improve signal sparsity, therein utilizing the real and imaginary components of the observed signals in the time–frequency domain. The algorithm can be applied to the estimation of complex-valued mixing matrix based on L-shaped arrays and uniform circular arrays. Then, to overcome the limitation that the clustering performance of traditional algorithms is affected by noise, data cleansing detection is introduced to reselect the SSPs with high potential energy as representative objects to achieve preliminary data classification. Finally, a dynamic data field clustering algorithm is adopted to move and merge the representative objects until all column vectors of the mixing matrix are estimated. Simulation results show that the proposed method can effectively estimate complex-valued mixing matrices with high accuracy, especially in real-world noncooperative cases without prior knowledge.

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.

This paper discusses underdetermined blind source separation (BSS) using a compressed sensing (CS) approach, which contains two stages. In the first stage we exploit a modified K-means method to estimate the unknown mixing matrix. The second stage is to separate the sources from the mixed signals using the estimated mixing matrix from the first stage. In the second stage a two-layer sparsity model is used. The two-layer sparsity model assumes that the low frequency components of speech signals are sparse on K-SVD dictionary and the high frequency components are sparse on discrete cosine transformation (DCT) dictionary. This model, taking advantage of two dictionaries, can produce effective separation performance even if the sources are not sparse in time-frequency (TF) domain.

We propose an algorithm that exploits the benefits of sparse filtering and directional clustering when estimating under-determined mixing matrix from mixtures of sufficiently sparse sources. To express the direction of each sample by only a few vectors in which one vector is more dominant than the remaining ones, we propose to minimize the power mean of the magnitude-squared cosine distances between the estimated mixing matrix and the data. For the special case of estimating determined mixing matrix, we derive a stability condition for methods based on the magnitude-squared cosine metric. Our stability condition shows that the proposed approach, K-hyperlines, and sparse filtering can recover the invertible mixing matrix when the sources are i.i.d. super-Gaussian. Simulations using both synthetic data and recorded speech mixtures show that the proposed algorithm outperforms existing algorithms with lower computational complexity.

In this paper, we propose a novel method for the detection of road accidents by analyzing audio streams for road surveillance application. In the last decade, due to the increase in a number of people and transportation vehicles, traffic accidents have become one of a major public issue worldwide. The vast number of injuries and death due to road traffic accident reveals the story of a global crisis of road safety. A total of 52,160 road traffic accidents (RTA), 1130 injuries and 85 fatalities were registered during the year 2000, in the state of Qatar. An increase in the number of transportation vehicles around cities has risen the need for more security and safety in public environments. The most obvious reason for a person's death during accidents is the absence or prolong response time of the first aid facility, which is due to the delay in the information of the accident being reached to the police, hospital or ambulance team. In the last couple of years, several surveillance systems have been proposed based on image and video processing for automatically detecting road accidents and car crashes to ensure a quick response by emergency teams. However, in some situations such as adverse weather conditions or cluttered environments, the visual information is not sufficient enough, whereas analyzing the audio tracks can significantly improve the overall reliability of surveillance systems. In this paper we propose a novel method that automatically identifies hazardous situations such as tire skidding and car crashes in presence of background noises, by analyzing the audio streams. Previous studies show that methods for the detection, estimation, and classification of nonstationary signals can be enhanced by utilizing the time-frequency (TF) characteristics of such signals. The TF-based techniques have been proved to outperform classical techniques based on either time or frequency domains, in analyzing real-life nonstationary signals. Time-frequency distributions (TFDs) give additional information about signals that cannot be extracted from either the time domain or frequency domain representations, i.e. the instantaneous frequency of the components of a signal. In order to utilize this extra information provided by TF domain representation, the proposed approach extracts TF image features from quadratic time-frequency distributions (QTFDs), for the detection of audio anomalies. The extended modified-B distribution (EMBD) is utilized to transform a 1-dimensional audio signal into 2-dimensional TF representation which is interpreted as an image. The image descriptors based features are then extracted from the TF representation to classify visually the audio signals into background or abnormal activity patterns in the TF domain. The proposed features are based on Haralick's texture features extracted from the TF representation of audio signals considered and processed as a textured image. These features are used to characterize and hence classify audio signals into M classes. This research study demonstrates that a TF image pattern recognition approach offers significant advantages over standard signal classification methods that utilize either t-domain only or f-domain only features. The proposed method has been experimentally validated on a large open source database of sounds, including several kinds of background noise. The events to be recognized are superimposed on different background sounds of roads and traffic jam. The obtained results are compared with a recent study, utilizing the same large and complex data set of audio signals, and the same experimental setup. The overall classification results confirm the superior performance of the proposed approach with accuracy improvement up to 6%.

Time-frequency (TF) analysis (TFA) to nonstationary signals can reveal the nonlinearly changing instantaneous frequencies (IFs) of signals; it is, therefore, widely used for rotating machinery fault diagnosis under time-varying speed conditions. However, the traditional TFA methods may only reveal the outline of IFs due to the extra TF diffusion caused by limited TF resolution, hindering the fault diagnosis of rotating machinery. To enhance the readability of the time-frequency representation (TFR) of the signals with IF trajectories linearly time-varying, linear chirplet transform has been proved effective. To effectively tackle the signal with nonlinearly changing IFs, a string of chirp-rates is preferred, where the final TFR is obtained by superposition of each corresponding sub-TFR at each TF point. However, the extra cross-term interferences resulted from a string of chirp-rates cannot be neglected on TFRs. Aiming at alleviating the cross-terms from the TFR, matching and reassignment based TF enhancement strategy is proposed, where only the appropriate chirp-rate and its corresponding TFR slice is retained at each time instant. The appropriate chirp-rate is adaptively selected by the index—spectral kurtosis. To further increase the readability of the resulting TFR, a reassignment technique synchrosqueezing transform is integrated with the proposed matching strategy. By iteratively employing reassignments, TFR with the enhanced energy and sharp IF ridges can be generated. The effectiveness of the proposed method is validated by both simulated and experimental analyses. It is shown that the proposed method is effective in processing time-varying signals and can provide more accurate IF estimation, which paves the way for rotating machinery fault diagnosis under nonstationary speed conditions.

Synchro spline-kernelled chirplet extracting transform: A useful tool for characterizing time-varying features under noisy environments and applications to bearing fault diagnosis

Wind turbines usually operate in harsh environments and in working conditions of variable speed, which easily causes their key components such as gearboxes to fail. The gearbox vibration signal of a wind turbine has nonstationary characteristics, and the existing time-frequency (TF) analysis (TFA) methods have some problems such as insufficient concentration of TF energy. In order to obtain a more apparent and more congregated time-frequency representation (TFR), this paper proposes a new TFA method, namely adaptive multiple second-order synchrosqueezing wavelet transform (AMWSST2). Firstly, a short-time window is innovatively introduced on the foundation of classical continuous wavelet transform, and the window width is adaptively optimized by using the center frequency and scale factor. After that, a smoothing process is carried out between different segments to eliminate the discontinuity and thus adaptive wavelet transform is generated. Then, on the basis of the theoretical framework of synchrosqueezing transform and accurate instantaneous frequency estimation by the utilization of second-order local demodulation operator, adaptive second-order synchrosqueezing wavelet transform (AWSST2) is formed. Considering that the quality of actual TFA is greatly disturbed by noise components, through performing multiple synchrosqueezing operations, the congregation of TFR energy is further improved, and finally, the AMWSST2 algorithm studied in this paper is proposed. Since synchrosqueezing operations are performed only in the frequency direction, this method AMWSST2 allows the signal to be perfectly reconstructed. For the verification of its effectiveness, this paper applies it to the processing of the vibration signal of the gearbox of a 750 kW wind turbine.

This paper presents a robust blind separation method of sparse sources named robust sparse blind source separation (r-SBSS). Allowing for the morphological diversity of the source, we first assume that one source can be divide into two parts, namely global component and local component. Furthermore, a novel optimization model is built upon the low-rank matrix recovery and the sparse modeling of both the sources and the outliers with different regularized constraints. We also provide the corresponding optimization algorithm, which allows combining both low-rank double dictionary learning and low-rank representation strategy to realize source separation and mixing matrix estimation respectively. In the proposed method, the dictionary learning strategy guarantees the adaptive representation of sparsity, and the low-rank representation strategy is first introduced to implement the effective estimation of the mixing matrix and outliers. Extensive experimental results on AR dataset and real EMI signals demonstrate the superiority of r-SBSS, compared to the state-of-the-art methods.

This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones

This paper presents a novel time-frequency (TF) domain nonparametric density estimation independent component analysis (ICA) combined with preprocessing by time-frequency plane Wiener (TFPW) filtering algorithm. It achieves blind separation of over-determined instantaneous linear mixtures of non-stationary sources. The algorithm simultaneously estimates the demixing matrix and the unknown probability density functions of the source signals in TF domain. The proposed method does not require the selection of TF points or TF plane's partition, as the latter is more restrictive to real signals. The TFPW preprocessing improves the algorithm separating effect in noisy data. As simulation shows, it works better than some TF blind separation algorithms

Aiming at the problem of fuzzy C-means (FCM) in the estimation of underdetermined mixing matrix, that the estimation accuracy is not high and the robustness is poor, a density peak clustering (DPC) based on density peak clustering (DPC) is proposed. Improved Kernel-based Fuzzy C-means (KFCM). The kernel function is introduced into the FCM algorithm to construct the KFCM algorithm based on the Gaussian kernel function, which can effectively overcome the influence of noise points and isolated points on the clustering results and improve the estimation accuracy of the mixed matrix; the traditional DPC algorithm is improved and merged with the KFCM algorithm, and thresholds are set for the local density and high-density distance to achieve the initial clustering center of the KFCM algorithm and the automatic determination of the number of cluster centers improves the robustness of the algorithm. Experimental results show that the algorithm has greatly improved the estimation accuracy and robustness of the underdetermined mixed matrix.