Underdetermined Blind Source Separation Algorithm Research Articles

Underdetermined Blind Source Separation of Audio Signals for Group Reared Pigs Based on Sparse Component Analysis.

In order to solve the problem of difficult separation of audio signals collected in pig environments, this study proposes an underdetermined blind source separation (UBSS) method based on sparsification theory. The audio signals obtained by mixing the audio signals of pigs in different states with different coefficients are taken as observation signals, and the mixing matrix is first estimated from the observation signals using the improved AP clustering method based on the "two-step method" of sparse component analysis (SCA), and then the audio signals of pigs are reconstructed by L1-paradigm separation. Five different types of pig audio are selected for experiments to explore the effects of duration and mixing matrix on the blind source separation algorithm by controlling the audio duration and mixing matrix, respectively. With three source signals and two observed signals, the reconstructed signal metrics corresponding to different durations and different mixing matrices perform well. The similarity coefficient is above 0.8, the average recovered signal-to-noise ratio is above 8 dB, and the normalized mean square error is below 0.02. The experimental results show that different audio durations and different mixing matrices have certain effects on the UBSS algorithm, so the recording duration and the spatial location of the recording device need to be considered in practical applications. Compared with the classical UBSS algorithm, the proposed algorithm outperforms the classical blind source separation algorithm in estimating the mixing matrix and separating the mixed audio, which improves the reconstruction quality.

MAGPRIME: An Open‐Source Library for Benchmarking and Developing Interference Removal Algorithms for Spaceborne Magnetometers

AbstractMagnetometers are essential instruments in space physics, but their measurements are often contaminated by various external interference sources. In this work, we present a comprehensive review of existing magnetometer interference removal methods and introduce MAGPRIME (MAGnetic signal PRocessing, Interference Mitigation, and Enhancement), an open‐source Python library featuring a collection of state‐of‐the‐art interference removal algorithms. MAGPRIME streamlines the process of interference removal in magnetic field data by providing researchers with an integrated, easy‐to‐use platform. We detail the design, structure, and functionality of the library, as well as its potential to facilitate future research by enabling rapid testing and customization of interference removal methods. Using the MAGPRIME Library, we present two Monte Carlo benchmark results to compare the efficacy of interference removal algorithms in different magnetometer configurations. In Benchmark A, the Underdetermined Blind Source Separation (UBSS) and traditional gradiometry algorithms surpass the uncleaned boom‐mounted magnetometers, achieving improved correlation and reducing median error in each simulation. Benchmark B tests the efficacy of the suite of MAGPRIME algorithms in a boomless magnetometer configuration. In this configuration, the UBSS algorithm proves to significantly reduce median error, along with improvements in median correlation and signal to noise ratio. This study highlights MAGPRIME's potential in enhancing magnetic field measurement accuracy in various spacecraft designs, from traditional gradiometry setups to compact, cost‐effective alternatives like bus‐mounted CubeSat magnetometers, thus establishing it as a valuable tool for researchers and engineers in space exploration and magnetism studies.

Exploiting Time–Frequency Sparsity for Dual-Sensor Blind Source Separation

This paper explores the important role of blind source separation (BSS) techniques in separating M mixtures including N sources using a dual-sensor array, i.e., M=2, and proposes an efficient two-stage underdetermined BSS (UBSS) algorithm to estimate the mixing matrix and achieve source recovery by exploiting time–frequency (TF) sparsity. First, we design a mixing matrix estimation method by precisely identifying high clustering property single-source TF points (HCP-SSPs) with a spatial vector dictionary based on the principle of matching pursuit (MP). Second, the problem of source recovery in the TF domain is reformulated as an equivalent sparse recovery model with a relaxed sparse condition, i.e., enabling the number of active sources at each auto-source TF point (ASP) to be larger than M. This sparse recovery model relies on the sparsity of an ASP matrix formed by stacking a set of predefined spatial TF vectors; current sparse recovery tools could be utilized to reconstruct N>2 sources. Experimental results are provided to demonstrate the effectiveness of the proposed UBSS algorithm with an easily configured two-sensor array.

A Novel Underdetermined Blind Source Separation Algorithm of Frequency-Hopping Signals via Time-Frequency Analysis

To address the significant performance degradation of conventional underdetermined blind source separation algorithms for frequency-hopping (FH) signals under time-frequency (TF) overlapping conditions, this paper presents a novel three-stage scheme based on the TF distribution of FH signals. In the first stage, key parameters of the FH signal are estimated using a TF binary graph. In the second step, the initial mixing matrix is estimated for non-overlapping and overlapping carrier frequencies employing density peaks clustering and tensor decomposition methods, respectively. In the third step, the final mixing matrix, directions of arrival (DOA), and source signals are estimated using the expectation-maximization algorithm within the nonnegative matrix factorization model. Finally, different segments of the FH signals are spliced together based on the DOAs of different source signals. Comprehensive experimental results demonstrate the superior performance of the proposed algorithm compared to state-of-the-art algorithms. Even at a signal-to-noise ratio of 5 dB, the correlation coefficient of the estimated source signals can still reach 0.91.

Enabling Boomless CubeSat Magnetic Field Measurements With the Quad‐Mag Magnetometer and an Improved Underdetermined Blind Source Separation Algorithm

AbstractIn situ magnetic field measurements are often difficult to obtain due to the presence of stray magnetic fields generated by spacecraft electrical subsystems. The conventional solution is to implement strict magnetic cleanliness requirements and place magnetometers on a deployable boom. However, this method is not always feasible on low‐cost platforms due to factors such as increased design complexity, increased cost, and volume limitations. To overcome these problems, we propose using the Quad‐Mag CubeSat magnetometer with an improved Underdetermined Blind Source Separation (UBSS) noise removal algorithm. The Quad‐Mag consists of four magnetometer sensors in a single CubeSat form‐factor card that allows distributed measurements of stray magnetic fields. The UBSS algorithm can remove stray magnetic fields without prior knowledge of the magnitude, orientation, or number of noise sources. UBSS is a two‐stage algorithm that identifies signals through cluster analysis and separates them through compressive sensing. We use UBSS with single‐source point detection to improve the identification of noise signals and iteratively‐weighted compressed sensing to separate noise signals from the ambient magnetic field. Using a mock CubeSat, we demonstrate in the lab that UBSS reduces four noise signals producing more than 100 nT of noise at each magnetometer to below the expected instrument resolution (5 nT at 65 Hz). Additionally, we show that the integrated Quad‐Mag and improved UBSS system works well for 1U, 2U, 3U, and 6U CubeSats in simulation. Our results show that the Quad‐Mag and UBSS noise cancellation package enables high‐fidelity magnetic field measurements from a CubeSat without a boom.

Application of Underdetermined Blind Source Separation Algorithm on the Low-Frequency Oscillation in Power Systems

The timely discovery of low-frequency oscillations in power systems and accurate identification of their modal parameters is critical in numerous applications. Therefore, we investigated the feasibility of using multi-channel signals and established a relative theory. An algorithm based on the underdetermined blind source separation (UBSS) algorithm was proposed using this theory. First, the energy ratio function was used to determine the fault occurrence time. Then, the Bayesian information criterion was used to estimate the number of fault sources, and the boundary conditions were set to determine the number of fault sources. Next, the UBSS algorithm was used to analyze raw data, extract individual components that characterize faults, and subsequently measure low-frequency oscillation modal parameters through the Hilbert transform. Finally, the fast independent component analysis (FastICA) algorithm was used to separate noise signal from raw data. This separation considerably reduced noise disturbance and ensured the stability of the proposed method. Model simulation was conducted in MATLAB and experimental measurement revealed that the proposed method effectively reduced noise disturbance and could be applied to conditions with considerable disturbance.

Underdetermined Blind Source Separation for Heart Sound Using Higher-Order Statistics and Sparse Representation

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 l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -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.

Novel underdetermined blind source separation algorithm based on compressed sensing and K‐SVD

AbstractIn this paper, a novel two‐stage underdetermined blind source separation (UBSS) algorithm based on eigenvalue decomposition and compressed sensing (CS) is proposed. UBSS techniques can separate the complex mixed signals into multiple single signal components, which are widely applied in the field of electronic surveillance, spectrum management, radar applications, etc. Our major contributions are summarized as follows: (1) deriving a single source points detection algorithm based on eigenvalue decomposition; (2) proposing a novel hierarchical coupling dictionary training method based on K‐means singular value decomposition; and (3) using the two‐stage method to realize the separation of radar signals under the condition of unknown prior information. In the first stage, we present a single source point detection method involving eigenvalue decomposition to estimate the unknown mixing matrix. In this method, the eigenvector corresponding to the maximum eigenvalue is estimated and clustered as a vector of mixing matrix. The second stage is the recovery of sources from the observed signals utilizing the mixing matrix estimated by the first step. In the second stage, we first build the unified model of UBSS and CS, thus the reconstruction algorithm in the CS field can be applied to UBSS. Then, a hierarchical coupling dictionary training method based on K‐means singular value decomposition is proposed. The dictionary training method obtains the prior training signals by pre‐separation and employs the hierarchical coupling idea to train the dictionary efficiently. Simulations illustrate the validity of the method and show that the proposed method outperforms the traditional methods in source separation, especially in real‐world noncooperative cases without prior knowledge.

A WHT Signal Detection-Based FLO-TF-UBSS Algorithm Under Impulsive Noise Environment

Linear frequency modulated (LFM) signal is used to describe radar echo signal, and Wigner–Hough transform (WHT) is a useful detection tool for LMF signals. The noise in radar echo signal has strong pulse under complex environment, which belongs to $$\alpha $$ stable distribution process. The WHT method degenerates under $$\alpha $$ stable distribution environment. Hence, fractional lower-order pseudo-Wigner–Ville distribution (FLO-PWVD) time–frequency method is introduced, and fractional lower-order pseudo-Wigner–Hough transform (FLO-PWHT) method based on the FLO-PWVD method and Hough transform is proposed for the detection of LFM signals. When the LFM signals are overlapped in time domain and generalized signal-to-noise ratio (GSNR) is relatively low, the FLO-PWHT method degenerate, even which cannot work. Therefore, fractional lower-order spacial time–frequency matrix is applied to substitute spacial time–frequency distribution matrix, and a new fractional lower-order spacial time–frequency underdetermined blind source separation (FLO-TF-UBSS) algorithm employing the time–frequency underdetermined blind source separation algorithm (TF-UBSS) is proposed in this paper. Also, we combine the FLO-PWHT method with the FLO-TF-UBSS algorithm and propose a fractional lower-order spatial time–frequency underdetermined blind source separation pseudo-Wigner–Hough transform (FLO-TF-UBSS-PWHT) method. The simulation results show that the FLO-PWHT method is obviously better than the existing PWHT algorithm under $$\alpha $$ stable distribution noise or Gaussian noise environment, which is robust. The FLO-TF-UBSS algorithm can effectively downgrade mean square error of the reconstructed LFM signals, and its performance is better than the existing TF-UBSS and minimum dispersion BSS algorithms. The FLO-TF-UBSS-PWHT algorithm can work well in the cases of time domain overlapping and relatively low GSNR; its performance is better than the FLO-PWHT algorithm, which has certain toughness. Finally, we apply the FLO-PWVD, FLO-TF-UBSS, and FLO-PWHT methods to analyze and extract fault features of the bearing outer race fault signal in DE; the experimental results illustrate their performance superiority.

Underdetermined blind separation of overlapped speech mixtures in time-frequency domain with estimated number of sources

Noise suppression and the estimation of the number of sources are two practical issues in applications of underdetermined blind source separation (UBSS). This paper proposes a noise-robust instantaneous UBSS algorithm for highly overlapped speech sources in the short-time Fourier transform (STFT) domain. The proposed algorithm firstly estimates the unknown complex-valued mixing matrix and the number of sources, which are then used to compute the STFT coefficients of corresponding sources at each auto-source time-frequency (TF) point. After that, the original sources are recovered by the inverse STFT. To mitigate the noise effect on the detection of auto-source TF points, we propose a method to effectively detect the auto-term location of the sources by using the principal component analysis (PCA) of the STFTs of noisy mixtures. The PCA-based detection method can achieve similar UBSS outcome as some filtering-based methods. More importantly, an efficient method to estimate the mixing matrix is proposed based on subspace projection and clustering approaches. The number of sources is obtained by counting the number of the resultant clusters. Evaluations have been carried out by using the speech corpus NOIZEUS and the experimental results have shown improved robustness and efficiency of the proposed algorithm.

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.

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.

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.

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.

Algorithm for underdetermined blind source separation based on DSNMF

The decomposed left matrix of Non-negative Matrix Factorization(NMF) is required to be full column rank,which limits of its application to Underdetermined Blind Source Separation(UBSS).To address this issue,an algorithm for UBSS based on determinant and sparsity constraint of NMF,named DSNMF,was proposed in this paper.On the basis of standard NMF,determinant criterion was used for constraining the left matrix of NMF,while sparsity was used for constraining the right one.In this way,the reconstruction error,the uniqueness of mixing matrix and the spasity of original sources can be equipoised,which leads to the underdetermined blind separation of mixing matrix and original sources.The simulation results show that DSNMF both works well for good and poor sparsity of sources separation.

Underdetermined blind separation of non-sparse sources using spatial time-frequency distributions

Recently, a number of underdetermined blind source separation (UBSS) approaches have been proposed to separate n source signals from m (m<n) mixtures. The majority of these methods depend on the assumption that the source signals are sparse in either time domain or other transformation domains. While the sparsity assumption is reasonable for some applications, such as the separation of speech signals, it is restrictive for many other applications. In this paper, we propose a new time-frequency UBSS algorithm without resort to any sparsity conditions. We show that under some mild constraints, our algorithm can separate up to 2m−1 sources from m (m⩾3) instantaneous linear mixtures. Theoretical analysis and simulation results show the effectiveness of the proposed algorithm.