A Local Dominance Based Single Source Points Detector for Mixing Matrix Estimation

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.

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 mixing matrix estimation by exploiting sparsity of sources

Recently, many researches have been done to solve the speech separation problems in the underdetermined cases, and the Two-step method is widely used, which estimates the mixing matrix first and then separates the sources. Subspace projection is an effective method for signal separation, whereas it has some limitations because it fixes the active number at the Time-Frequency (TF) point as a constant. A commonly used solution is to add an extra step to estimate the active source number at every TF point, which will increase the computation cost greatly. This paper provides a new convex-model-based subspace projection method with enhanced functionality, which can be used for Underdetermined Blind Source Separation (UBSS). The model takes into account both projection and size of the signal's subspace, without estimating the real source numbers at the TF points. Simulation results show that the proposed method overcomes the shortage of conventional subspace method and achieves higher separation performance. Furthermore, the proposed algorithm can be employed as a preprocessing technology in the fields of acoustic signals enhancement, recognition, and biomedical images, etc.

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 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

The physical mechanism and signal characteristics of acoustic scattering are the vital basis for target recognition. But underwater target acoustic scattering components are aliasing in time-frequency (TF) domain, for which the target elastic acoustic scattering characteristics are difficult to detect. Additionally, the existing blind source separation methods are effective only on condition that the number of array elements is equal to or greater than the number of the source signals. To address these problems, a novel TF domain blind source extraction method of separating target acoustic scattering components is proposed in this paper. The method only uses the TF energy characteristic differences among the target acoustic scattering components, and special limitations on target echo structures are unnecessary. Image morphology filter is used to remove the cross-term interference from time-frequency distribution (TFD) of the received array signals. Then, the single source which shows maximum energy concentration at the corresponding auto-term TF points is extracted through three operations: i) selecting the single source auto-term TF points from the auto-term ones; ii) constructing the spatial TFD matrix according to the selected single source auto-term TF points; iii) obtaining the single source by decomposing the eigenvalue of their spatial TFD matrix. Finally, the extracted single signal is excluded by the tightening process from the received array signals, and each single signal is separated successively by repeating the above steps. In addition, a signal processing model which can describe the physical characteristics of the target echoes is established based on the separated signal components. Simulations illustrate that the image morphological filter can remove the cross-term interference and improve the TF resolution of the Wigner-Ville distribution. Anechoic pool experimental results show that the TF domain blind source extraction algorithm can well separate each target acoustic scattering component, it can also achieve a higher output signal-to-noise ratio. Furthermore, the separated elastic acoustic scattering components are in good agreement with the results computed by the surface wave generating theory, so the method can provide the robust and reliable feature for underwater target recognition.

Pipelined signal adaptive hardware implementation of an optimal time-frequency (TF) filter has been designed. It is based on the real-time results of TF analysis and on the TF analysis-based instantaneous frequency (IF) estimation. The implemented pipelining technique allows the filter to overlap in execution unconditional steps performimg in neighboring TF instants and, therefore, to significantly enhance time performance. The improvement corresponding to the one clock cycle by a TF point is achieved, which means that the improvement by a TF point can reach even 50% in some TF points. The design is tested on multicomponent signals.).

This paper presents a new time-frequency (TF) underdetermined blind source separation approach based on Wigner-Ville distribution (WVD) and Khatri-Rao product to separate N non-stationary sources from M(M <; N) mixtures. First, an improved method is proposed for estimating the mixing matrix, where the negative value of the auto WVD of the sources is fully considered. Then after extracting all the auto-term TF points, the auto WVD value of the sources at every auto-term TF point can be found out exactly with the proposed approach no matter how many active sources there are as long as N ≤ 2M-1. Further discussion about the extraction of auto-term TF points is made and finally the numerical simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing ones.

Underdetermined blind source separation (UBSS) deals with the problem of estimating n source signals from m measurements (n > m), with an unknown mixing process. Most researches pay attention to the sparsity of speech to recover source signals, such as the DUET (degenerate unmixing estimation technique) algorithm, which can separate any number of sources using only two mixtures with the help of estimation of mixing parameters but cant be used in the time-varying system. We develop a block-online algorithm for a dynamic environment that is based on mixing parameter estimation from reliable time-frequency points determined by the total power and FCM (Fuzzy C-Means) clustering of parameter estimates for every time-frame. To track the variable mixing parameters, the estimated ones from the previous frame can be used to initialize FCM in the current frame with changed mixing measure instead of random initialization in case of the conventional FCM. Thus, an online adaptive algorithm of UBSS with the time-varying matrix is realized.

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.

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.

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.

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.