Underdetermined Mixing Matrix Estimation Algorithm Based on Single Source Points

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.

Underdetermined mixing matrix estimation by exploiting sparsity of sources

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.

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.

An algorithm for mixing matrix estimation in instantaneous blind source separation

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.

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 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.

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.

An algorithm based on least-mean-square error and sparse features is presented for underdetermined blind source separation (BSS), i.e., situation when the number of observed signals' is less than that of sources. In this paper, using the sparsity of sources, first, we estimate the mixing matrix using a new potential function based on clustering method. Then use the estimated mixing matrix and the selfcorrelation of sources, by searching the accurate values at the source clustering directions, we can obtain the optimal sub-matrix for separation through least-mean-square error criterion, which overcomes the disadvantages of traditional algorithms in searching the optimal sub-matrix. Simulation results show the separated signals have higher SNR, and compared with the other similar method, the proposed approach has better separation performance.

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.

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.

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.