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In recent years, the problem of underdetermined blind source separation (UBSS) has become a research hotspot due to its practical potential. This paper presents a novel method to solve the problem of UBSS, which mainly includes the following three steps: Single source points (SSPs) are first screened out using the principal component analysis (PCA) approach, which is based on the statistical features of signal time-frequency (TF) points. Second, a mixing matrix estimation method is proposed that combines Ordering Points To Identify the Clustering Structure (OPTICS) with an improved potential function to directly detect the number of source signals, remove noise points, and accurately calculate the mixing matrix vector; it is independent of the input parameters and offers great accuracy and robustness. Finally, an improved subspace projection method is used for source signal recovery, and the upper limit for the number of active sources at each mixed signal is increased from m−1 to m. The unmixing process of the proposed algorithm is symmetrical to the actual signal mixing process, allowing it to accurately estimate the mixing matrix and perform well in noisy environments. When compared to previous methods, the source signal recovery accuracy is improved. The method’s effectiveness is demonstrated by both theoretical and experimental results.

This paper proposed an improved sparse component analysis (SCA) approach to improve the performance of underdetermined blind source separation for the acoustic/speech sources. First, the pre-processing to build a sparse model for acoustic/speech sources is described. Then, the proposed SCA approach designs an improved K-means clustering algorithm based on ant colony algorithm to estimate the mixture matrix, and utilize a method based on orthogonal matching pursuit algorithm to re-cover the signals. Experiment results demonstrate that the improved clustering algorithm can enhance the global searching ability which benefits for the proposed SCA approach to achieve a higher estimation accuracy of mixture matrix, and the improved method in the second step can make the proposed SCA approach work well for recovering the multi-channel blind source signals.

Recently, many researches have been done to solve the challenging problem of Blind Source Separation (BSS) problems in the underdetermined cases, and the “Two-step” method is widely used, which estimates the mixing matrix first and then extracts the sources. To estimate the mixing matrix, conventional algorithms such as Single-Source-Points (SSPs) detection only exploits the sparsity of original signals. This paper proposes a new underdetermined mixing matrix estimation method for time-delayed mixtures based on the receiver prior exploitation. The prior information is extracted from the specific structure of the complex-valued mixing matrix, which is used to derive a special criterion to determine the SSPs. Moreover, after selecting the SSPs, Agglomerative Hierarchical Clustering (AHC) is used to automaticly cluster, suppress, and estimate all the elements of mixing matrix. Finally, a convex-model based subspace method is applied for signal separation. Simulation results show that the proposed algorithm can estimate the mixing matrix and extract the original source signals with higher accuracy especially in low SNR environments, and does not need the number of sources before hand, which is more reliable in the real non-cooperative environment.

We propose a new method for underdetermined blind source separation based on the time---frequency domain. First, we extract the time---frequency points that are occupied by a single source, and then, we use clustering methods to estimate the mixture matrix A. Second, we use the parallel factor (PARAFAC), which is based on nonnegative tensor factorization, to synthesize the estimated source. Simulations using mixtures of audio and speech signals show that this approach yields good performance.

Most existing algorithms for the underdetermined blind source separation (UBSS) problem are two-stage algorithm, i.e., mixing parameters estimation and sources estimation. In the mixing parameters estimation, the previously proposed traditional clustering algorithms are sensitive to the initializations of the mixing parameters. To reduce the sensitiveness to the initialization, we propose a new algorithm for the UBSS problem based on anechoic speech mixtures by employing the visual information, i.e., the interaural time difference (ITD) and the interaural level difference (ILD), as the initializations of the mixing parameters. In our algorithm, the video signals are utilized to estimate the distances between microphones and sources, and then the estimations of the ITD and ILD can be obtained. With the sparsity assumption in the time-frequency domain, the Gaussian potential function algorithm is utilized to estimate the mixing parameters by using the ITDs and ILDs as the initializations of the mixing parameters. And the time-frequency masking is used to recover the sources by evaluating the various ITDs and ILDs. Experimental results demonstrate the competitive performance of the proposed algorithm compared with the baseline algorithms.

The underdetermined blind source separation method based on sparse component analysis in the time–frequency domain is introduced to estimate the modal parameters in this study. This study attempts to reveal the relationship with the modal parameter identification methods based on the time–frequency representation. A five-degree-of-freedom mass-spring-damper system and a real experiment conducted on a TC4 titanium-alloy column are used to confirm the proposed method. Furthermore the proposed method is applied to extract the time-varying modal parameters of the column in the temperature-varying environment. The extracted results evidently show the thermal effect on the modal parameters.

The aim of this paper is to propose a fully automatic system using the underdetermined blind source separation (UBSS) method and kurtosis to remove ocular artifacts (OAs) from scalp electroencephalogram (EEG). The fully automatic system about OAs rejection is devised with the fourth-order tensor method (FOOBI). Firstly, the FOOBI method decomposes multiple EEG channels into a relative large number of source components. The kurtosis value is used to identify the ocular components in these source components. Then, the free-ocular sources components are reconstructed to EEG without OAs. The simulations show that the FOOBI method can completely separate the ocular signals from the observed signals. The data that have got rid of the OAs are used to classify with the epileptic EEG. The classification accuracy acquired by FOOBI method is better than the independent component analysis (ICA). The results inferred that the FOOBI method can not only completely remove the OAs from the observed signals but also preserve an amount of useful information of EEG. Compared with the ICA method, this fully automatic system is more suitable to remove OAs.

With the increasing construction of high-voltage substation, the distance between resident area and substation is getting closer. Noise of substations has been an unavoidable problem which can be controlled better by analyzing it. Otherwise, the operational conditions of equipment in substation can be predicted by comparing the measured noise signals with the signals during normal operation. Corona noise emitted by high voltage transmission line, environmental quasi-stationary noise and noumenon noise generated by electric appliances are three main types of the noise signals in the substation which can't be measured independently by traditional methods. An Underdetermined Blind Source Separation (UBSS) algorithm based on the Sparse Component Analysis (SCA) was proposed to separate the mixed 220kV substation noise in this paper which can be applied to overcome the shortage of Independent Component Analysis (ICA). The feasibility of the algorithm was verified in the simulation and the experiment before using it to separate the substation noise. An approach to feature extraction based on the wavelet modulus maxima was employed to analyze the separated noise. All the results show that SCA can separat mixed substation noise efficiently.

For the purpose of estimating the mixing matrix under the nonstrictly sparse condition, this paper presents the algorithms to approximate the mixing matrix in two different situations in which the source vectors are 1-sparse and (m - 1)-sparse. When the source signals are 1-sparse, we use the generalized spherical coordinate transformation to convert the matrix of observation signals into the new one, which makes the process of estimating column A become the process of finding the center point of these new data. For the situation that source signals are (m - 1)-sparse, we propose a new algorithm for the underdetermined mixtures blind source separation based on hyperplane clustering. The algorithm firstly finds out the linearly independent vectors from the observations, and secondly determines all the normal vectors of hyperplanes by analyzing the number of observations that are in the same hyperplane. Finally, we identify the column vectors of the mixing matrix A by calculating the vectors which are orthogonal to the clustered normal vectors. These two new algorithms for estimating the mixing matrix are more suitable for the general cases as they have lower requirement for the sparsity of the observations.

International audience; This paper considers the blind separation of non-stationary 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 thanks 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.

An objective of blind source separation (BSS) is to recover potential source signals from their mixtures without a prior knowledge of the mixing process. In this paper, a new underdetermined blind source separation (UDBSS) approach, based on the local mean decomposition (LMD) method and the AMUSE algorithm, is proposed. To make the UDBSS problem simpler, some extra observation signals are first constructed using the LMD method. Thus the underdetermined blind source separation problem is transformed into an (over-)determined one. Subsequently, the well known AMUSE algorithm is applied to these new observations to estimate the source signals. The proposed method does not resort to the sparsity constraint which is included in most of the former researches. The theoretical analysis and simulation results illustrate the effectiveness of the proposed UDBSS method.

If a piece of picture could contain a sequence of video frames, it is amazing. This paper develops a new video compression approach based on underdetermined blind source separation. Underdetermined blind source separation, which can be used to efficiently enhance the video compression ratio, is combined with various off-the-shelf codecs in this paper. Combining with MPEG-2, video compression ratio could be improved slightly more than 33 %. As for combing with H.264, twice compression ratio could be achieved with acceptable PSNR, according to different kinds of video sequences.

In this paper, we propose a fast method to resolve the sparse recovery problem in underdetermined blind source separation. Our method is a modified version of recently proposed method (SL0), which is faster than original SL0 method while acquiring the same estimation quality. Comparison between our method and orthogonal matching pursuit (OMP) is given from viewpoints of efficiency and estimation quality. Experiments using synthetic data show that our method is faster than OMP especially when noise in the source vector exists and can acquire better estimation quality than OMP when signal is sufficiently sparse. We also apply the method to underdetermined blind source separation using real world data. It is experimentally shown that our method is much faster than OMP, while providing almost the same accuracy.

Sparse reconstruction based on the relevance vector machine (RVM) in underdetermined blind source separation (UBSS) was discussed in the paper. The Laplace Priors were modeled using a hierarchical form in the paper. The posterior over the estimated parameters was formulated based on Bayesian principle. Based on the hierarchical priors, an iterative algorithm for sparse reconstruction was derived using MAP criterion. Then a fast iterative algorithm was derived through the analysis of the characteristic of the likelihood. Finally, the fast iterative algorithm was tested by the simulations.

Traditional blind source separation is based on over- determined, but the underdetermined is more consistent with actual situation, based on sparse representation, Bofill proposed "two step" method to solve the problem under some assumptions. The accuracy of the mixture affects the recovery of sources, avoiding the subjectivity of choosing parameter, using the fuzzy C-means clustering to get the mixing matrix estimation; at the same time, to lessen the requirement of sparsity, combining ICA with SCA, based on the criterion of negentropy, sources can be separated. The test shows that the algorithm proposed here get a good result.

This paper proposes a method to separate audio signals when number of sources is more than the number of the sensors used and the number of source signals is not known in advance. The proposed method is for underdetermined blind source separation where time frequency masking is used to remove some of the signals from the mixtures till the number of mixtures is equal to the number of sources and then kurtosis maximization method is used to separate the remaining signals. In this paper we separate four signals from two mixtures under instantaneous conditions. The results obtained are better than conventional methods.

An algorithm is presented for underdetermined blind source separation, i.e., the number of observed signals is less than that of original sources. Traditional solutions based on minimizing the L1-norm have some disadvantages in searching the optimal sub-matrix for separation. In the proposed algorithm, first we use a potential function to estimate the mixing matrix by clustering method. Then we present an improved L1-norm algorithm by weighting the observed signals vectors at the different source clustering directions. This method makes good use of the super-Gaussian property of sources and overcomes the disadvantages of L1-norm-based solutions. Furthermore, the case of an arbitrary mixing matrix is discussed in this paper. Simulation results have shown that the proposed approach can give better separation results than traditional methods in terms of signal-to-noise ratio.

This paper presents a new approach to blind separation of sources using sparse representation in an underdetermined mixture. Firstly, we transform the observations into the new ones within the generalized spherical coordinates, through which the estimation of the mixing matrix is formulated as the estimation of the cluster centers. Secondly, we identify the cluster centers by a new classification algorithm, whereby the mixing matrix is estimated. The simulation results have shown the efficacy of the proposed algorithm.

The underdetermined blind source separation problem using a filtering approach is addressed. An extension of the FastICA algorithm is devised which exploits the disparity in the kurtoses of the underlying sources to estimate the mixing matrix and thereafter achieves source recovery by employing the lscr 1-norm algorithm. Besides, we demonstrate how promising FastICA can be to extract the sources. Furthermore, we illustrate how this scenario is particularly appropriate for the separation of temporomandibular joint (TMJ) sounds

This paper addresses the underdetermined blind source separation problem, using a filtering approach. We have developed an extension of the FastICA algorithm which exploits the disparity in the kurtoses of the underlying sources to estimate the mixing matrix and thereafter the recovery of the sources is achieved by employing the l1-norm algorithm. Also, we demonstrate how promising FastICA can be to extract the sources, without utilizing the l1-norm algorithm. Furthermore, we illustrate how this scenario is particularly suitable to the separation of the temporomandibular joint (TMJ) sounds, crucial in the diagnosis of temporomandibular disorders (TMDs).

The underdetermined case in blind source separation, that is, separation of n sources from m (m

We consider the underdetermined blind source separation problem with linear instantaneous and convolutive mixtures when the input signals are sparse, or have been rendered sparse. In the underdetermined case the problem requires solving three sub-problems: detecting the number of sources, estimating the mixing matrix, and finding an adequate inversion strategy to obtain the sources. This paper solves the first two problems. We assume that the number of sources is unknown, and estimate it by means of an information theoretic criterion (MDL). Then the mixing matrix is expressed in spheric coordinates and we estimate sequentially the angles and amplitudes of each column, and their order. The performance of the method is illustrated through simulations.

The problem of underdetermined blind source separation is addressed. An advanced classification method based upon competitive learning is proposed for automatically determining the number of active sources over the observation. Its introduction in underdetermined blind source separation successfully overcomes the drawback of an existing method, in which the goal of separating more sources than the number of available mixtures is achieved by exploiting the sparsity of the nonstationary sources in the time-frequency domain. Simulation studies are presented to support the proposed approach.

In this work, we propose and analyze a method to solve the problem of underdetermined blind source separation (and identification) that employs the ideas of sparse component analysis (SCA) and independent component analysis (ICA). The main rationale of the approach is to allow the possibility of reaching a method that is more robust with respect to the degree of sparseness of the involved signals and more effective in the use of information brought by multiple sensors. The ICA-based solution is tested with the aid of three representative scenarios and its performance is compared with that of one of the soundest SCA techniques available, the DEMIXN algorithm.