An algorithm for mixing matrix estimation in instantaneous blind source separation

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 presents a simple yet effective way of improving the estimate of the mixing matrix, in instantaneous blind source separation, by using only reliable data.The paper describes how the idea of detecting single source data is implemented by selecting only the data which remain for two consecutive frames in the same spatial signature. Such data, which are most likely to belong to a single source, are then used to accurately identify the spatial directions of the sources and, hence, the mixing matrix.The paper also presents a refined histogram procedure which improves on the potential function method to estimate the mixing matrix, in the two dimensional case (two sensors).The approach was experimentally evaluated and submitted to the first Stereo Audio Source Separation Evaluation Campaign (SASSEC), with good results in matrix estimation both for development and test data.Keywordsblind source separationsingle source datamatrix estimationpotential function method

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 separation of non-stationary sources using continuous density hidden Markov models

An important application of sparse representation is underdetermined blind source separation (BSS), where the number of sources is greater than the number of observations. Within the stochastic framework, this paper discusses recoverability of underdetermined BSS based on a two-stage sparse representation approach. The two-stage approach is effective when the source matrix is sufficiently sparse. The first stage of the two-stage approach is to estimate the mixing matrix, and the second is to estimate the source matrix by minimizing the 1-norms of the source vectors subject to some constraints. After estimating the mixing matrix and fixing the number of nonzero entries of a source vector, we estimate the recoverability probability (i.e., the probability that the source vector can be recovered). A general case is then considered where the number of nonzero entries of the source vector is fixed and the mixing matrix is drawn from a specific probability distribution. The corresponding probability estimate on recoverability is also obtained. Based on this result, we further estimate the recoverability probability when the sources are also drawn from a distribution (e.g., Laplacian distribution). These probability estimates not only reflect the relationship between the recoverability and sparseness of sources, but also indicate the overall performance and confidence of the two-stage sparse representation approach for solving BSS problems. Several simulation results have demonstrated the validity of the probability estimation approach.

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 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.

The problem of underdetermined blind audio source separation is usually addressed under the framework of sparse signal representation. In this paper, we develop a novel algorithm for this problem based on compressed sensing which is an emerging technique for efficient data reconstruction. The proposed algorithm consists of two stages. The unknown mixing matrix is firstly estimated from the audio mixtures in the transform domain, as in many existing methods, by a K-means clustering algorithm. Different from conventional approaches, in the second stage, the sources are recovered by using a compressed sensing approach. This is motivated by the similarity between the mathematical models adopted in compressed sensing and source separation. Numerical experiments including the comparison with a recent sparse representation approach are provided to showthe good performance of the proposed method.

Since roller bearing is one of the most vulnerable components, bearing faults usually occur in an unprepared situation with multiple faults, and the quantity of sensors is limited in the real-time working environment, resulting in an underdetermined blind source separation (UBSS) problem to extract the fault features. Because the collected signals are usually not independent and not sparse enough, traditional methods of separating signals cannot perform well. In this paper, an optimized intrinsic characteristic-scale decomposition (OICD) method is proposed to solve the underdetermined problem. Meanwhile, the constraint error factor is introduced to overcome the drawback that the ideal ending condition of ICD is not proper for the vibration signal of bearing. In addition, given that non-negative matrix factorization (NMF) is not limited by the source signal independence and sparsity, an improved UBSS model is constructed, and the PCs are used as the input matrix of local NMF to obtain the separation signal. Ultimately, envelope analysis is utilized to detect the source signal feature. Both simulated and experimental vibration signals are used to verify the effectiveness of the proposed approach. Besides, the traditional method is juxtaposed with the suggested method. The results indicate that the proposed method is effective in dealing with the compound faults separation of the rotating machinery.

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.

One (of) important application of sparse component analysis (SCA) is in underdetermined blind source separation (BSS). Within a probability framework, this paper focuses on recoverability problem of underdetermined BSS based on a two-stage SCA approach. We consider a general case in which both sources and mixing matrix are randomly drawn. First, we present a recoverability probability estimate under the condition that the nonzero entry number of a source column vector is fixed. Next, we define the sparsity degree of a signal, and establish the relationship between the sparsity degree of sources and recoverability probability. Finally, we explain how to use the relationship to guarantee the performance of BSS. Several simulation results have demonstrated the validity of the probability estimation approach.

Traditionally, radar signals have been analysed in either the time or the frequency domain. Joint time–frequency representations characterise signals over a time–frequency plane. They thus combine time-domain and frequency-domain analyses to yield a potentially more revealing picture of the temporal localisation of a signal&apos;s spectral components. Therefore, for air target returns with time-varying frequency content, joint time–frequency representations offer a powerful analysis tool. A concise review of time–frequency transforms is provided as background and is needed to appreciate how time–frequency processing methods can improve conventional time or frequency processing methods. The authors use time–frequency analysis techniques for the detection of a manoeuvring aircraft using high frequency (HF) radar in heavily cluttered regions. They compare the ability of different time–frequency transforms to resolve several experimental aircraft returns. The relative speeds of the different transforms are also quantitatively studied. The results clearly demonstrate that time–frequency analysis techniques can significantly improve the detection performance of the HF radar and add considerable physical insight over what can be achieved by conventional Fourier transform methods currently used by HF radars.

The successful implementation of speech processing systems in the real world depends on its ability to handle adverse acoustic conditions with undesirable factors such as room reverberation and background noise. In this study, an extension to the established multiple sensors degenerate unmixing estimation technique (MENUET) algorithm for blind source separation is proposed based on the fuzzy c-means clustering to yield improvements in separation ability for underdetermined situations using a nonlinear microphone array. However, rather than test the blind source separation ability solely on reverberant conditions, this paper extends this to include a variety of simulated and real-world noisy environments. Results reported encouraging separation ability and improved perceptual quality of the separated sources for such adverse conditions. Not only does this establish this proposed methodology as a credible improvement to the system, but also implies further applicability in areas such as noise suppression in adverse acoustic environments.

With the increasing investment in the construction of power facilities and the use of higher voltage level, the noise generated by high voltage substation has become an unavoidable issue. The noise of the high-voltage substation is a mixture which is mixed by different noise sources. The mixed noise must be separated to several independent noise signals firstly for researching. An algorithm combined with the Wavelet Transform and the Sparse Component Analysis was presented in this paper which can separate the single channel mixed noise signal of high-voltage substation. The single channel blind source separation can be changed to the underdetermined blind source separation by setting two augmented signals which are the low-frequency part and the high-frequency part separated from the original noise signal by the Wavelet Transform. Then the signals of different noise sources can be separated by the Sparse Component Analysis. It is proved by the simulation and experiment in 330kV high-voltage substation that the algorithm can solve not only the underdetermined blind source separation, but also the single-channel blind source separation effectively.

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.