Underdetermined Blind Source Separation Research Articles

Blind Source Separation for Under-Determined Mixtures Based on Time-Frequency Analysis

Blind source separation (BSS) is an effective method for the fault diagnosis and classification of mixture signals with multiple vibration sources. The traditional BSS algorithm is applicable to the number of observed signals is no less to the source signals. But BSS performance is limit for the under-determined condition that the number of observed signals is less than source signals. In this research, we provide an under-determined BSS method based on the advantage of time-frequency analysis and empirical mode decomposition (EMD). It is suitable for weak feature extraction and pattern recognition. Firstly, vibration signal is decomposed by using EMD. The number of source signals are estimated and the optimal observed signals are selected according to the EMD. Then, the vibration signal and the optimal observed signals are used to construct the multi-channel observed signals. In the end, BSS based on time-frequency analysis are used to the constructed signals. Gearbox signals are used to verify the effectiveness of this method.

Weak Fault Diagnosis of Metro Gearbox Based on Adaptive Variable Parameter SR and Underdetermined BSS

Weak Fault Diagnosis of Metro Gearbox Based on Adaptive Variable Parameter SR and Underdetermined BSS

A Mixing Matrix Estimation Algorithm for Underdetermined Blind Source Separation

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.

Explicit–implicit mapping approach to nonlinear blind separation of sparse nonnegative dependent sources from a single mixture: pure component extraction from nonlinear mixture mass spectra

The nonlinear, nonnegative single‐mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into nonnegative dependent component (source) signals. The problem is difficult and is a special case of the underdetermined blind source separation problem. However, it is practically relevant for the contemporary metabolic profiling of biological samples when only one sample is available for acquiring mass spectra; afterwards, the pure components are extracted. Herein, we present a method for the blind separation of nonnegative dependent sources from a single, nonlinear mixture. First, an explicit feature map is used to map a single mixture into a pseudo multi‐mixture. Second, an empirical kernel map is used for implicit mapping of a pseudo multi‐mixture into a high‐dimensional reproducible kernel Hilbert space. Under sparse probabilistic conditions that were previously imposed on sources, the single‐mixture nonlinear problem is converted into an equivalent linear, multiple‐mixture problem that consists of the original sources and their higher‐order monomials. These monomials are suppressed by robust principal component analysis and hard, soft, and trimmed thresholding. Sparseness‐constrained nonnegative matrix factorizations in reproducible kernel Hilbert space yield sets of separated components. Afterwards, separated components are annotated with the pure components from the library using the maximal correlation criterion. The proposed method is depicted with a numerical example that is related to the extraction of eight dependent components from one nonlinear mixture. The method is further demonstrated on three nonlinear chemical reactions of peptide synthesis in which 25, 19, and 28 dependent analytes are extracted from one nonlinear mixture mass spectra. The goal application of the proposed method is, in combination with other separation techniques, mass spectrometry‐based non‐targeted metabolic profiling, such as biomarker identification studies. Copyright © 2015 John Wiley & Sons, Ltd.

Underdetermined BSS Based on K-means and AP Clustering

Underdetermined blind source separation (UBSS) is a hard problem to solve since its mixing system is not invertible. The well-known "two-step approach" has been widely used to solve the UBSS proble...

Blind source separation with adaptive learning rates for image encryption

In this study, we present a technique for image encryption problem based on the underdetermined blind source separation (BSS) principle with adaptive learning rates. The encryption process is transferred as the underdetermined BSS problem and is treated by means of the key images to achieve decryption. By properly generating the key images and constructing the underdetermined mixing matrix, the proposed BSS technique can achieve the security. The proposed BSS with adaptive learning rates approach is implemented by the interval type-2 fuzzy cerebellar model articulation controller (T2FCMAC) and particle swarm optimization. The T2FCMAC system is a more generalized system with better learning ability to provide the adaptive learning rate of the BSS. Besides, the particle swarm optimization is utilized to enhance the performance of convergence. Computer simulation results are shown to illustrate the effectiveness of the proposed approach.

Novel mixing matrix estimation approach in underdetermined blind source separation

This paper proposes the use of density-based spatial clustering of application with noise (DBSCAN) and the Hough transform to estimate the mixing matrix in underdetermined blind source separation. First, phase-angle-based single source time-frequency point detection is employed to improve signal sparsity. To overcome the limitation of the K-means clustering algorithm, which requires prior knowledge of the number of sources, the DBSCAN classification algorithm is adopted to automatically estimate the number of sources and then further estimate the mixing matrix. The Hough transform is employed to modify the cluster center in order to enhance the estimation accuracy of the mixing matrix. Simulation results show that the proposed approach can effectively estimate the number of sources and the mixing matrix with high accuracy. The proposed approach performs better than the K-means method and the DBSCAN algorithm alone.

Fast underdetermined BSS architecture design methodology for real time applications.

In this paper, we propose a high speed architecture design methodology for the Under-determined Blind Source Separation (UBSS) algorithm using our recently proposed high speed Discrete Hilbert Transform (DHT) targeting real time applications. In UBSS algorithm, unlike the typical BSS, the number of sensors are less than the number of the sources, which is of more interest in the real time applications. The DHT architecture has been implemented based on sub matrix multiplication method to compute M point DHT, which uses N point architecture recursively and where M is an integer multiples of N. The DHT architecture and state of the art architecture are coded in VHDL for 16 bit word length and ASIC implementation is carried out using UMC 90 - nm technology @V DD = 1V and @ 1MHZ clock frequency. The proposed architecture implementation and experimental comparison results show that the DHT design is two times faster than state of the art architecture.

Underdetermined Convolutive BSS: Bayes Risk Minimization Based on a Mixture of Super-Gaussian Posterior Approximation

This paper considers the underdetermined blind source separation (BSS) of convolutively mixed super-Gaussian signals that include speech, audio, and various other sparse signals. Here, the separation is performed in three steps. In the first and second steps, the mixing matrix and the sources at each time-frequency location are estimated by minimizing the Bayes risk (or the posterior risk) with squared loss. In the final third step, the permutation alignment is conducted by considering the correlation between adjacent spectral bins as in many conventional algorithms. To overcome any computationally intractable integrations involving a complex-valued super-Gaussian source prior, the posterior distribution of the sources is approximated as a mixture of super-Gaussians. The posterior means of the mixing matrix and the sources are obtained with Metropolis-Hastings within Gibbs sampling and the weighted sum of individual super-Gaussians, respectively. Overall, this approximation leads to a separation that is computationally lighter than and as accurate as the algorithm without the approximation. The simulation results of the synthetically generated data in a virtual room with reverberation show that the estimates of the mixing matrix in the first step and the sources in the second step are more accurate than the estimates from the state-of-the-art algorithms in terms of the mixing error ratio (MER) and the signal-to-distortion ratio (SDR). The experiment was also conducted with recorded data in a real room environment using a public benchmark dataset. Results show that the proposed algorithm gives a better performance compared to the state-of-the-art algorithms in terms of the SDR.

Mixing Matrix Estimation based on Directional Density Detection and Hough Transform

Mixing matrix estimation (MME) algorithm was proposed for the mixing matrix estimation problem of underdetermined blind source separation. The algorithm is based on a combination of processing of isolated time–frequency points from local directional density detection and Hough transform (HT). Firstly, signal sparsity was strengthened through the processing of single-source time–frequency points in the transform domain. Next, HT was applied to the directional straight lines in the scatter plot and realized the spatial transformation. The number of source signals and mixing matrix were estimated by determining the local maxima of cumulative array. To deal with the peak values clustering issue that commonly arises with HT, the local directional density detection method was used to identify and eliminate isolated time–frequency points. HT was then used to improve the accuracy of MME. The experimental results indicate that the proposed method is able to achieve MME under the condition when the number of source signals is unknown. Further, the accuracy of estimation is better than other commonlyused methods such as K-means.

A Time–Frequency Domain Blind Source Separation Method for Underdetermined Instantaneous Mixtures

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.

A Complex Mixing Matrix Estimation Algorithm Based on Single Source Points

This paper considers the complex mixing matrix estimation in the under-determined blind source separation. An effective estimation algorithm through detecting single source points contributed by only one source is proposed. First, the single source points are detected by utilizing the real and the imaginary components of the time---frequency coefficients of mixed signals. The algorithm is suitable for the case in which the mixing matrix is complex, while traditional algorithms usually estimate the real mixing matrix. Then, through modeling and calculating, the mixing matrix of mixed signals can be estimated. Finally, the clustering process is improved in order to get more accurate results. The algorithm can estimate the complex mixing matrix when the number of sensors is less than that of sources. The experimental results validate the efficiency of the estimation algorithm.

Nonnegative Mixture for Underdetermined Blind Source Separation Based on a Tensor Algorithm

In this study, a tensor algorithm is proposed to blindly separate an instantaneous linear underdetermined mixture with non-stationary sources and nonnegative mixing matrix. It proceeds in two steps: 1) estimating the mixing matrix and 2) recovering the source signals. First, a canonical tensor model is constructed using a fourth-order cumulant tensor of the observed signals to estimate the mixing matrix. Then, an improved hierarchical alternating least squares algorithm is used to decompose the canonical tensor model, which ensures that all elements of the mixing matrix are positive. Finally, the sources are recovered using a minimum mean-squared error beamformer approach without any hypothetical limitation. We apply two classes of data (speech signals and biomedical signals) to substantiate the effectiveness of the proposed algorithm for underdetermined blind source separation.

Diagnosis of Roller Bearings Compound Fault Using Underdetermined Blind Source Separation Algorithm Based on Null-Space Pursuit

In order to solve the problem of underdetermined blind source separation (BSS) in the diagnosis of compound fault of roller bearings, an underdetermined BSS algorithm based on null-space pursuit (NSP) was proposed. In this algorithm, the signal model of faulty roller bearing is firstly used to construct an appropriate differential operator in null space. With the constructed differential operator, the mixed signals collected by the vibration sensor are decomposed into a series of stacks of narrow band signal containing the characteristics of faulty bearing. Finally, the underdetermined problem is transformed to an overdetermined problem by combining the narrow band signals and the original mixed signals into a new group of observed signals. In this way, the separation of the mixed signals can be realized. Experiments and engineering data analyses show that the problem of underdetermined BSS can be solved effectively by this approach, and then the compound fault of the roller bearing can be separated.

UBSS and blind parameters estimation algorithms for synchronous orthogonal FH signals

By using the sparsity of frequency hopping(FH) signals,an underdetermined blind source separation(UBSS) algorithm is presented. Firstly, the short time Fourier transform(STFT) is performed on the mixed signals. Then, the mixing matrix, hopping frequencies, hopping instants and the hooping rate can be estimated by the K-means clustering algorithm. With the estimated mixing matrix, the directions of arrival(DOA) of source signals can be obtained. Then, the FH signals are sorted and the FH pattern is obtained. Finally, the shortest path algorithm is adopted to recover the time domain signals. Simulation results show that the correlation coefficient between the estimated FH signal and the source signal is above 0.9 when the signal-to-noise ratio(SNR) is higher than 0 d B and hopping parameters of multiple FH signals in the synchronous orthogonal FH network can be accurately estimated and sorted under the underdetermined conditions.

A new method for blind separation of nonstationary sources

The development of nonstationary signal blind separation, especially an underdetermined mixture of nonstationary sources, has become increasingly important for mechanical multi-fault diagnosis. In this paper, a novel algorithm based on the adaptive parametric time-frequency analysis theory to blindly separate the mixtures of nonstationary sources is presented. The computer simulations illustrate the applicability of our approach, and the performance of the algorithm is successfully tested on the underdetermined blind source separation of five vibration signals of a high speed train from one instantaneous mixture of these signals.

A Linear Source Recovery Method for Underdetermined Mixtures of Uncorrelated AR-Model Signals Without Sparseness

Conventional sparseness-based approaches for instantaneous underdetermined blind source separation (UBSS) do not take into account the temporal structure of the source signals. In this work, we exploit the source temporal structure and propose a linear source recovery solution for the UBSS problem which does not require the source signals to be sparse. Assuming the source signals are uncorrelated and can be modeled by an autoregressive (AR) model, the proposed algorithm is able to estimate the source AR coefficients from the mixtures given the mixing matrix. We prove that the UBSS problem can be converted into a determined problem by combining the source AR model together with the original mixing equation to form a state-space model. The Kalman filter is then applied to obtain a linear source estimate in the minimum mean-squared error sense. Simulation results using both synthetic AR signals and speech utterances show that the proposed algorithm achieves better separation performance compared with conventional sparseness-based UBSS algorithms.

Low complexity underdetermined blind source separation system architecture for emerging remote healthcare applications.

In this paper, we have proposed a low complexity architecture for the Under-determined Blind Source Separation (UBSS) algorithm targeting remote healthcare applications. UBSS algorithm, departing from the typical BSS convention-equal number of the sources and sensors present, which is of tremendous interest in the field of Biomedical signal processing especially for remote health care applications. Since such applications are constrained by the on-chip area and power consumption limitation due to the battery backup, a low complexity architecture needs to be formulated. In this paper, firstly we have introduced UBSS architecture, followed by the identification of the most computationally intensive module N-point Discrete Hilbert Transform (DHT) and finally proposed a low complexity DHT architecture design to make the entire UBSS architecture suitable for such resource constrained applications. The proposed DHT architecture implementation and experimental comparison results show that the proposed design saves 50.28%, 48.40% and 46.27% on-chip area and 53.25%, 48.01% and 45.95% power consumption when compared to the state of the art method for N = 32, 64 and 128 respectively. Furthermore the proposed DHT architecture works for N = 2m point, but the state of art architecture works for N = 4m point, where m is an integer.

Underdetermined Blind Sources Separation Based on Nonnegative Tri-Matrix Factorization

In this paper, a nonnegative tri-Matrix factorization (NTMF) algorithm is proposed for underdetermined blind sources separation with the assumption of that the source signals are nonnegative and sparse. By incorporating the regularization and sparse penalty into the cost function, a novel multiplicative update rules is proposed to solve the problem of UBSS based on NTMF. The simulation results are presented to show the validity and competitive performances of the proposed algorithm.

Audio-visual underdetermined blind source separation algorithm based on Gaussian potential function

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.