Search

The underdetermined blind source separation (UBSS) has been considered to be a novel signal processing technique, which can separate the fault source signals from their mixtures. The mixing matrix estimation is a major step in the UBSS, this paper focuses on boosting the accuracy level of the estimated mixing matrix in the underdetermined case. Since the traditional clustering algorithms may not capture the signal characteristics well and secure a satisfactory estimation of the mixing matrix, an effective two-stage clustering algorithm is proposed to estimate the mixing matrix through a combination of hierarchical clustering and K-means. More specifically, first, the sum of frequency points energy in the time-frequency (TF) domain is calculated to estimate the number of source signals before clustering, and the initial clustering centers are obtained with a hierarchical clustering algorithm. Second, after eliminating outliers deviating from the initial clustering centers with the cosine distance, the new clustering centers are obtained by recalculating the mean value of each sub-cluster. Finally, the new clustering centers are set as the initial clustering centers of the K-means algorithm to estimate the mixing matrix. Extensive simulations and experiments show that the proposed method can effectively separate the source signals and ensure an estimate of the mixing matrix that is substantially more accurate than the K-means algorithm alone.

This study proposes a new approach to determine harmonic contributions in distribution networks. The approach effectively combines underdetermined blind source separation (UBSS) and form similarity distance (FSD), and it aims to minimise the negative impacts of harmonic source coupling and background harmonic fluctuations. Considering the underdetermined measurement, UBSS is introduced to estimate the harmonic emission current in the light of the sparsity of source signals. Through analysing the form variation features of harmonic time series, FSD is applied to identify the relatively stable background harmonics for utility equivalent harmonic impedance calculation. Furthermore, a complete procedure of harmonic contribution assessment is presented. To verify the high performance of the proposed approach, the simulation study and field test are both conducted, and a detailed comparative analysis of different approaches is carried out. The results show that the proposed approach is able to more accurately determine harmonic contributions than the existing methods, and has better robustness against significant harmonic source coupling and drastic background harmonic fluctuations.

Due to the lack of sufficient prior information, how to estimate the mixing matrix in multiple underdetermined blind source separation (UBSS) models is a difficult problem. This study proposes an algorithm, which is used for the estimation of mixing matrix in instantaneous UBSS. Firstly, we propose an efficient single-source-points detection criterion with the transformation for the mixed signal vector, which is used as the basis for the clustering process. There are some shortcomings in the classical clustering algorithms, including the dependence on input parameters, restrictions on the data dimension, the requirement of the prior knowledge of the source signals and high complexity. To overcome these drawbacks, the modified density peaks clustering algorithm is used for the estimation of the initial clustering centers to adapt to different circumstances. Based on the idea of mean clustering, the single source points near each initial cluster center are processed, respectively, and the final estimation results of the mixing matrix are obtained. A variety of simulation experiments demonstrate the universality and validity of the proposed algorithm. The proposed method also has excellent performance even under the circumstance of low signal-to-noise ratio.

In practical engineering applications, the vibration signals collected by sensors often contain outliers, resulting in the separation accuracy of source signals from the observed signals being seriously affected. The mixing matrix estimation is crucial to the underdetermined blind source separation (UBSS), determining the accuracy level of the source signals recovery. Therefore, a two-stage clustering method is proposed by combining hierarchical clustering and K-means to improve the reliability of the estimated mixing matrix in this paper. The proposed method is used to solve the two major problems in the K-means algorithm: the random selection of initial cluster centers and the sensitivity of the algorithm to outliers. Firstly, the observed signals are clustered by hierarchical clustering to get the cluster centers. Secondly, the cosine distance is used to eliminate the outliers deviating from cluster centers. Then, the initial cluster centers are obtained by calculating the mean value of each remaining cluster. Finally, the mixing matrix is estimated with the improved K-means, and the sources are recovered using the least square method. Simulation and the reciprocating compressor fault experiments demonstrate the effectiveness of the proposed method.

Underdetermined blind source separation (UBSS) is a hot and challenging problem in signal processing. In the traditional UBSS algorithm, the number of source signals is often assumed to be known, which is very inconvenient in practice. In addition, it is more difficult to obtain the accurate estimation of mixing matrix in the underdetermined case. However, this information has a great influence on the source separation results, which can easily lead to poor separation performance. In this paper, a novel UBSS algorithm is presented to carry out a combined source signal number estimation and source signal separation task. First, in the proposed algorithm, we design a gap-based detection method to detect the number of source signals by eigenvalue decomposition. Then, the estimation of the mixing matrix is processed using a higher-order cumulant-based method so that the uniqueness of the estimated mixing matrix is guaranteed. Furthermore, an improved l1 -norm minimization algorithm is proposed to estimate the source signals. Meanwhile, the pre-conditioned conjugate gradient technology is employed to accelerate the convergence rate such that the computational load is reduced. Finally, a series of simulation experiments with synthetic heart sound data and image reconstruction results demonstrate that the proposed algorithm achieves better separating property than the state-of-the-art algorithms.

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.

Considering the time-delayed mixing model of the underdetermined blind source separation problem, we propose a novel mixing matrix estimation algorithm in this paper. First, we introduce the short-time Fourier transform (STFT) to transform the mixed signals from the time domain to the time–frequency domain. Second, a neoteric transformation matrix is addressed to construct the linear clustering property of STFT coefficients. Then, a preeminent detection algorithm is raised to identify the single source points. After eliminating the low-energy points and outliers in the time–frequency domain, a potential function of clustering approach is put forward to cluster the single source points and obtain the clustering centers. Finally, the mixing matrix can be estimated through the derivation and calculation. The experimental results validate that the proposed algorithm not only accurately estimates the mixing matrix for the time-delayed mixing model of the underdetermined blind source separation problem but also has certain universality for different array structures. Therefore, both the effectiveness and superiority of the proposed algorithm have been verified.

In order to achieve accurate recovery signals under the underdetermined circumstance in a comparatively short time, an algorithm based on plane pursuit (PP) is proposed. The proposed algorithm selects the atoms according to the correlation between received signals and hyper planes, which are composed by column vectors of the mixing matrix, and uses these atoms to recover source signals. Simulation results demonstrate that the PP algorithm has low complexity and higher accuracy as compared with basic pursuit (BP), orthogonal matching pursuit (OMP), and adaptive sparsity matching pursuit (ASMP) algorithms.

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.

We propose a novel source recovery algorithm for underdetermined blind source separation, which can result in better accuracy and lower computational cost. On the basis of the model of underdetermined blind source separation, the artificial neural network with single-layer perceptron is introduced into the proposed algorithm. Source signals are regarded as the weight vector of single-layer perceptron, and approximate l 0 -norm is taken into account for output error decision rule of the perceptron, which leads to the sparse recovery. Then the procedure of source recovery is adjusting the weight vector of the perceptron. What's more, the optimal learning factor is calculated and a descent sequence of smoothed parameter is used during iteration, which improves the performance and significantly decreases computational complexity of the proposed algorithm. The simulation results reveal that the algorithm proposed can recover the source signal with high precision, while it requires lower computational cost.

In this study, a new algorithm subspace complementary matching pursuit (SCMP) is developed for source recovery of underdetermined blind source separation. The proposed SCMP is more simplified than the conventional complementary matching pursuit (CMP) algorithm. SCMP algorithm selects more than one atom in each iteration to reduce computational complexity, and replaces the l 2 norm minimisation involved in CMP with the approximate l 0 norm minimisation to ensure higher recovery accuracy. Numerical results show that, compared with the existing algorithms for source recovery, such as CMP, orthogonal CMP (OCMP), optimised OCMP and sparsity adaptive CMP, the proposed SCMP algorithm significantly reduces the computational time with improved recovery accuracy.

Underdetermined blind source separation based on compressed sensing (CS) has already been proven to be an effective mechanism from an experimental viewpoint. In this study, we develop a theoretical result and show that, under a certain sparsity constraint for the restricted isometry property, the accuracy of CS when retrieving sources is guaranteed. This theoretical result can be regarded as a generalization of the blocked polynomial deterministic matrix theory and has been confirmed using numerical examples.

Underdetermined source separation becomes more challenging when the observed mixtures are distorted. A novel framework for source separation from mixtures affected by clipping distortion is presented. Our method exploits knowledge about the geometry of clipped mixtures when the sources are disjoint in time. This knowledge constrains a convex optimisation problem, which we formulate and solve to recover the sources. This paper develops work previously published substantially by implementing novel preprocessing steps inspired by geometric observations of clipped mixtures of time-disjoint sources. Evaluation experiments showed a significant increase in objective recovery performance for the proposed method compared with sequential approaches for speech and synthetic sources.

In order to solve the problems of the mixing matrix estimation and estimate the number of the of the sources in the underdetermined blind source separation, we proposed a improved density-based clustering algorithm which can first estimate the number of the source signals. In this paper, to avoid clustering algorithm that have problems in initial value selection and local extreme values. We exploit the particle swarm optimization algorithm(PSO) to overcome these problems. The simulation results show that our algorithm can effectively estimate the number of the sources and have a higher accuracy compared with other clustering algorithms.

To identify the major vibration and radiation noise, a source contribution quantitative estimation method is proposed based on underdetermined blind source separation. First, the single source points (SSPs) are identified by directly searching the identical normalized time-frequency vectors of mixed signals, which can improve the efficiency and accuracy in identifying SSPs. Then, the mixing matrix is obtained by hierarchical clustering, and source signals can also be recovered by the least square method. Second, the optimal combination coefficients between source signals and mixed signals can be calculated based on minimum redundant error energy. Therefore, mixed signals can be optimally linearly combined by source signals via the coefficients. Third, the energy elimination method is used to quantitatively estimate source contributions. Finally, the effectiveness of the proposed method is verified via numerical case studies and experiments with a cylindrical structure, and the results show that source signals can be effectively recovered, and source contributions can be quantitatively estimated by the proposed method.

Underdetermined blind source separation (UBSS) is a hot topic in signal processing, which aims at recovering the source signals from a number of observed mixtures without knowing the mixing system. Recently, expectation-maximization algorithm shows a great potential in the UBSS. However, the final separation results depend strongly on the parameter initialization, leading to poor separation performance. In this paper, we propose an effective algorithm that combines tensor decomposition and nonnegative matrix factorization (NMF). In the proposed algorithm, we first employ tensor decomposition to estimate the mixing matrix, and NMF source model is used to estimate the source spectrogram factors. Then a series of iterations are derived to update the model parameters. At the same time, the spatial images of source signals are estimated with Wiener filters constructed from the learned parameters. Therefore, time-domain sources can be obtained through inverse short-time Fourier transform. Finally, plenty of experimental results demonstrate the effectiveness and advantages of our proposed algorithm over the compared algorithms.

Mixing matrix estimation is very important for underdetermined blind source separation. To solve the problems of existing methods for mixing matrix estimation such as low estimation accuracy, a detection method for single source points (SSPs) is proposed based on local stationarity and distribution symmetry in this paper, and then mixing matrix estimation is obtained through clustering algorithm. The proposed method does not require region division of hypersphere and is easy to operate, so as to effectively eliminate pseudo SSPs and improve the clustering features of observed signals. The simulation results show that the proposed method has higher accuracy than the traditional methods.

The aim of this paper is to propose a multiple ocular artifacts (OAs) removal method using the high order tensor algorithm. Four categories high order tensor methods are adopted to separate the real electroencephalogram (EEG) and ocular signals by underdetermined blind source separation (UBSS) model. The correlation coefficient and the non-negativity are adopted to choose the suitable UBSS algorithm. The ocular components are identified by the kurtosis value after separating between EEG and ocular signals. Then, the free-ocular sources components are reconstructed to EEG without OAs. The simulations show that the proposed method can effectively remove the OAs. At the same time, it also can retain the useful information after removing OAs.

This paper considers mixing matrix estimation for underdetermined blind source separation. First, we propose an effective detection algorithm to identify single source points where only one source occurs. The detection algorithm finds single source points by utilizing the time---frequency coefficients of mixed signals and the complex conjugates of the coefficients. Then, a method based on probability density is proposed in order to find more reliable single source points and cluster them. Finally, the mixing matrix is obtained through re-selecting and clustering single source points. The experimental results indicate that the algorithm can accurately estimate the mixing matrix when there are fewer sensors than sources.

This paper considers the complex-valued mixing matrix estimation and direction-of-arrival (DOA) estimation of synchronous orthogonal frequency hopping (FH) signals in the underdetermined blind source separation (UBSS). A novel mixing matrix estimation algorithm is proposed by detecting single source points (SSPs) where only one source contributes its power. Firstly, the proposed algorithm distinguishes the SSPs by the comparison of the normalized coefficients of time frequency (TF) points, which is more effective than existing detection algorithms. Then, mixing matrix of FH signals can be estimated by the hierarchical clustering method. To sort synchronous orthogonal FH signals, a modified subspace projection method is presented to obtain the DOAs of FH. One superiority of this paper is that the estimation accuracy of the mixing matrix can be significantly improved by the proposed SSPs detection criteria. Another superiority of this paper is that synchronous orthogonal FH signals can be sorted in underdetermined condition. The experimental results demonstrate the efficiency of the two proposed algorithms.

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.

In order to separate and extract compound fault features of a vibration signal from a single channel, a novel signal separation method is proposed based on improved sparse non-negative matrix factorization (SNMF). In view of the traditional SNMF failure to perform well in the underdetermined blind source separation, a constraint reference vector is introduced in the SNMF algorithm, which can be generated by the pulse method. The square wave sequences are constructed as the constraint reference vector. The output separated signal is constrained by the vector, and the vector will update according to the feedback of the separated signal. The redundancy of the mixture signal will be reduced during the constantly updating of the vector. The time&ndash, frequency distribution is firstly applied to capture the local fault features of the vibration signal. Then the high dimension feature matrix of time&ndash, frequency distribution is factorized to select local fault features with the improved SNMF method. Meanwhile, the compound fault features can be separated and extracted automatically by using the sparse property of the improved SNMF method. Finally, envelope analysis is used to identify the feature of the output separated signal and realize compound faults diagnosis. The simulation and test results show that the proposed method can effectively solve the separation of compound faults for rotating machinery, which can reduce the dimension and improve the efficiency of algorithm. It is also confirmed that the feature extraction and separation capability of proposed method is superior to the traditional SNMF algorithm.

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.

In this article, we consider the problem of sources separation from their underdetermined instantaneous mixtures via time-domain. First, we introduced an algorithm based on differential kurtosis to separate non-stationary sources one by one under underdetermined case. Then, the rest sources are recovered using an algorithm based on second-order statistics. The simulation results show that the proposed method can separate sources of super- and sub-Gaussian distributions, and it has superior performance compared to other conventional methods.

In this paper, we consider the problem of underdetermined blind source separation (UBSS), i.e., there are more sources than mixtures. By exploiting the time-frequency (TF) sparsity of the source signals, some TF-UBSS algorithms have recently been proposed in the literature. These algorithms require that the number of active sources at any TF point should not exceed one or be strictly less than the number of mixtures. In this paper, we show that if the number of sources is greater than the number of mixtures by one, the sparsity assumption can be further relaxed. Especially, it is allowed to have as many sources as mixtures at any TF point in this case. Then we propose a new TF-UBSS method to recover the sources. The relaxation on the maximum number of active sources at TF points ensures that the TF-based methods can be used in a wider range of applications.

Recently, a number of underdetermined blind source separation (UBSS) approaches have been proposed to separate n source signals from m (m=3) instantaneous linear mixtures. Theoretical analysis and simulation results show the effectiveness of the proposed algorithm.

In modern electronic warfare, multiple input multiple output (MIMO) radar has become an important tool for electronic reconnaissance and intelligence transmission because of its anti-stealth, high resolution, low intercept and anti-destruction characteristics. As a common MIMO radar signal, discrete frequency coding waveform (DFCW) has a serious overlap of both time and frequency, so it cannot be directly used in the current radar signal separation problems. The existing fuzzy clustering algorithms have problems in initial value selection, low convergence rate and local extreme values which will lead to the low accuracy of the mixing matrix estimation. Consequently, a novel mixing matrix estimation algorithm based on data field and improved fuzzy C-means (FCM) clustering is proposed. First of all, the sparsity and linear clustering characteristics of the time–frequency domain MIMO radar signals are enhanced by using the single-source principal value of complex angular detection. Secondly, the data field uses the potential energy information to analyze the particle distribution, thus design a new clustering number selection scheme. Then the particle swarm optimization algorithm is introduced to improve the iterative clustering process of FCM, and finally get the estimated value of the mixing matrix. The simulation results show that the proposed algorithm improves both the estimation accuracy and the robustness of the mixing matrix.

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.

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.

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.

The source recovery step in underdetermined blind source separation is probed in this paper. DUET is famous method in underdetermined blind source separation. However, it requires the sources are approximately disjoint. To obtain good results in sources recovery, an improved DUET algorithm is proposed for two mixtures. The algorithm utilizes DUET after the rotation of the mixing matrix and mixtures. Several speech signals experiments demonstrate its performance and practical.

This chapter contains sections titled: Introduction Underdetermined Blind Source Separation of Speeches in Reverberant Environments Sparseness of Speech Sources Binary Mask Approach to Underdetermined BSS MAP-Based Two-Stage Approach to Underdetermined BSS Experimental Comparison with Binary Mask Approach and MAP-Based Two-Stage Approach Concluding Remarks References

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.

The underdetermined blind source separation problem is the one of separating a large number of sources using a smaller number of mixtures. The DUET algorithm presents a solution to the underdetermined blind source separation problem, demixing an arbitrary number of speech signals from only 2 anechoic mixtures of them. Here the DUET method is presented as a general framework for extending classic array processing methods to the underdetermined blind source separation problem.

The DUET blind source separation algorithm can demix an arbitrary number of speech signals using anechoic mixtures of the signals. DUET however is limited in that it relies upon source signals which are mixed in an anechoic environment and which are sufficiently sparse such that it is assumed that only one source is active at a given time frequency point. The DUET-ESPRIT (DESPRIT) blind source separation algorithm extends DUET to situations where sparsely echoic mixtures of an arbitrary number of sources overlap in time frequency. This paper outlines the development of the DESPRIT method and demonstrates its properties through various experiments conducted on synthetic and real world mixtures.

Underdetermined blind source separation and sparse component analysis aim at to recover the unknown source signals under the assumption that the observations are less than the source signals and the source signals can be sparse expressed. Many methods to deal with this problem related to clustering. For underdetermined blind source separation model, this paper gives a new plane clustering algorithm to estimate the mixture matrix based on sparse sources information. Good performance of our method is shown by simulations.

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.

We examine the problem of blind separation of nonstationary sources in the underdetermined case, where there are more sources than sensors. Since time-frequency (TF) signal processing provides effective tools for dealing with nonstationary signals, we propose a new separation method that is based on time-frequency distributions (TFDs). The underlying assumption is that the original sources are disjoint in the time-frequency (TF) domain. The successful method recovers the sources by performing the following four main procedures. First, the spatial time-frequency distribution (STFD) matrices are computed from the observed mixtures. Next, the auto-source TF points are separated from cross-source TF points thanks to the special structure of these mixture STFD matrices. Then, the vectors that correspond to the selected auto-source points are clustered into different classes according to the spatial directions which differ among different sources; each class, now containing the auto-source points of only one source, gives an estimation of the TFD of this source. Finally, the source waveforms are recovered from their TFD estimates using TF synthesis. Simulated experiments indicate the success of the proposed algorithm in different scenarios. We also contribute with two other modified versions of the algorithm to better deal with auto-source point selection.