Underdetermined Blind Source Separation Using Sparse Coding

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.

Underdetermined Blind Source Separation Method for Speech Signals Based on SOM-DPC and Compressed Sensing

Underdetermined blind source separation has received increasing attention in recent years as an effective method for speech-signal processing. Hence, a self-organizing mapping-density peak clustering and compressed sensing approach, which is a two-step approach, is proposed herein to improve the accuracy of underdetermined blind source separation. The approach features the following two aspects: (1) A mixing matrix estimation method based on self-organizing mapping and density peak clustering, which can intuitively determine the number of source signals, remove outliers, and determine the column vector of the mixing matrix based on local density; (2) a compressed sensing-based source signal reconstruction method, which can exploit the sparsity of signals in the frequency domain and use a hierarchical coupling method to reconstruct the source signal accurately and efficiently under the premise that the prior knowledge of the signal is unknown. The proposed method does not require the number of source signals and exhibits excellent performance under different noise conditions. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed method.

Sparse Component Analysis (SCA) Based on Adaptive Time-Frequency Thresholding for Underdetermined Blind Source Separation (UBSS)

Blind source separation (BSS) recovers source signals from observations without knowing the mixing process or source signals. Underdetermined blind source separation (UBSS) occurs when there are fewer mixes than source signals. Sparse component analysis (SCA) is a general UBSS solution that benefits from sparse source signals which consists of (1) mixing matrix estimation and (2) source recovery estimation. The first stage of SCA is crucial, as it will have an impact on the recovery of the source. Single-source points (SSPs) were detected and clustered during the process of mixing matrix estimation. Adaptive time-frequency thresholding (ATFT) was introduced to increase the accuracy of the mixing matrix estimations. ATFT only used significant TF coefficients to detect the SSPs. After identifying the SSPs, hierarchical clustering approximates the mixing matrix. The second stage of SCA estimated the source recovery using least squares methods. The mixing matrix and source recovery estimations were evaluated using the error rate and mean squared error (MSE) metrics. The experimental results on four bioacoustics signals using ATFT demonstrated that the proposed technique outperformed the baseline method, Zhen's method, and three state-of-the-art methods over a wide range of signal-to-noise ratio (SNR) ranges while consuming less time.

An Underdetermined Convolutional Blind Separation Algorithm for Time–Frequency Overlapped Wireless Communication Signals with Unknown Source Number

It has been challenging to separate the time–frequency (TF) overlapped wireless communication signals with unknown source numbers in underdetermined cases. In order to address this issue, a novel blind separation strategy based on a TF soft mask is proposed in this paper. Based on the clustering property of the signals in the sparse domain, the angular probability density distribution is obtained by the kernel density estimation (KDE) algorithm, and then the number of source signals is identified by detecting the peak points of the distribution. Afterward, the contribution degree function is designed according to the cosine distance to calculate the contribution degrees of the source signals in the mixed signals. The separation of the TF overlapped signals is achieved by constructing a soft mask matrix based on the contribution degrees. The simulations are performed with digital signals of the same modulation and different modulation, respectively. The results show that the proposed algorithm has better anti-aliasing and anti-noise performance than the comparison algorithms.

Component spectra extraction and quantitative analysis for preservative mixtures by combining terahertz spectroscopy and machine learning

Preservatives are universally used in synergistic combination to enhance antimicrobial effect. Identify compositions and quantify components of preservatives are crucial steps in quality monitoring to guarantee merchandise safety. In the work, three most common preservatives, sorbic acid, potassium sorbate and sodium benzoate, are deliberately mixed in pairs with different mass ratios, which aresupposedto be the "unknown" multicomponent systems and measured by terahertz (THz) time-domain spectroscopy. Subsequently, three major challenges have been accomplished by machine learning methods in this work. The singular value decomposition (SVD) effectively obtains the number of components in mixed preservatives. Then, the component spectra are successfully extracted by non-negative matrix factorization (NMF) and self-modeling mixture analysis (SMMA), which match well with the measured THz spectra of pure reagents. Moreover, the support vector machine for regression (SVR) designed an underlying model to the target components and simultaneously identify contents of each individual component in validation mixtures with decision coefficient R² = 0.989. By taking advantages of the fingerprint-based THz technique and machine learning methods, our approach has been demonstrated the great potential to be served as a useful strategy for detecting preservative mixtures in practical applications.

Fault Feature Extraction for Reciprocating Compressors Based on Underdetermined Blind Source Separation

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.

A Novel Underdetermined Blind Source Separation Method Based on OPTICS and Subspace Projection

In recent years, the problem of underdetermined blind source separation (UBSS) has become a research hotspot due to its practical potential. This paper presents a novel method to solve the problem of UBSS, which mainly includes the following three steps: Single source points (SSPs) are first screened out using the principal component analysis (PCA) approach, which is based on the statistical features of signal time-frequency (TF) points. Second, a mixing matrix estimation method is proposed that combines Ordering Points To Identify the Clustering Structure (OPTICS) with an improved potential function to directly detect the number of source signals, remove noise points, and accurately calculate the mixing matrix vector; it is independent of the input parameters and offers great accuracy and robustness. Finally, an improved subspace projection method is used for source signal recovery, and the upper limit for the number of active sources at each mixed signal is increased from m−1 to m. The unmixing process of the proposed algorithm is symmetrical to the actual signal mixing process, allowing it to accurately estimate the mixing matrix and perform well in noisy environments. When compared to previous methods, the source signal recovery accuracy is improved. The method’s effectiveness is demonstrated by both theoretical and experimental results.

Eliminating the Permutation Ambiguity of Convolutive Blind Source Separation by Using Coupled Frequency Bins

Blind source separation (BSS) is a typical unsupervised learning method that extracts latent components from their observations. In the meanwhile, convolutive BSS (CBSS) is particularly challenging as the observations are the mixtures of latent components as well as their delayed versions. CBSS is usually solved in frequency domain since convolutive mixtures in time domain is just instantaneous mixtures in frequency domain, which allows to recover source frequency components independently of each frequency bin by running ordinary BSS, and then concatenate them to form the Fourier transformation of source signals. Because BSS has inherent permutation ambiguity, this category of CBSS methods suffers from a common drawback: it is very difficult to choose the frequency components belonging to a specific source as they are estimated from different frequency bins using BSS. This paper presents a tensor framework that can completely eliminate the permutation ambiguity. By combining each frequency bin with an anchor frequency bin that is chosen arbitrarily in advance, we establish a new virtual BSS model where the corresponding correlation matrices comply with a block tensor decomposition (BTD) model. The essential uniqueness of BTD and the sparse structure of coupled mixing parameters allow the estimation of the mixing matrices free of permutation ambiguity. Extensive simulation results confirmed that the proposed algorithm could achieve higher separation accuracy compared with the state-of-the-art methods.

Low-Element Image Restoration Based on an Out-of-Order Elimination Algorithm

To reduce the consumption of receiving devices, a number of devices at the receiving end undergo low-element treatment (the number of devices at the receiving end is less than that at the transmitting ends). The underdetermined blind-source separation system is a classic low-element model at the receiving end. Blind signal extraction in an underdetermined system remains an ill-posed problem, as it is difficult to extract all the source signals. To realize fewer devices at the receiving end without information loss, this paper proposes an image restoration method for underdetermined blind-source separation based on an out-of-order elimination algorithm. Firstly, a chaotic system is used to perform hidden transmission of source signals, where the source signals can hardly be observed and confidentiality is guaranteed. Secondly, empirical mode decomposition is used to decompose and complement the missing observed signals, and the fast independent component analysis (FastICA) algorithm is used to obtain part of the source signals. Finally, all the source signals are successfully separated using the out-of-order elimination algorithm and the FastICA algorithm. The results show that the performance of the underdetermined blind separation algorithm is related to the configuration of the transceiver antenna. When the signal is 3 × 4 antenna configuration, the algorithm in this paper is superior to the comparison algorithm in signal recovery, and its separation performance is better for a lower degree of missing array elements. The end result is that the algorithms discussed in this paper can effectively and completely extract all the source signals.

A Novel Underdetermined Blind Source Separation Method and Its Application to Source Contribution Quantitative Estimation

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.

A Regularized Weighted Smoothed L₀ Norm Minimization Method for Underdetermined Blind Source Separation

Compressed sensing (CS) theory has attracted widespread attention in recent years and has been widely used in signal and image processing, such as underdetermined blind source separation (UBSS), magnetic resonance imaging (MRI), etc. As the main link of CS, the goal of sparse signal reconstruction is how to recover accurately and effectively the original signal from an underdetermined linear system of equations (ULSE). For this problem, we propose a new algorithm called the weighted regularized smoothed L 0 -norm minimization algorithm (WReSL0). Under the framework of this algorithm, we have done three things: (1) proposed a new smoothed function called the compound inverse proportional function (CIPF); (2) proposed a new weighted function; and (3) a new regularization form is derived and constructed. In this algorithm, the weighted function and the new smoothed function are combined as the sparsity-promoting object, and a new regularization form is derived and constructed to enhance de-noising performance. Performance simulation experiments on both the real signal and real images show that the proposed WReSL0 algorithm outperforms other popular approaches, such as SL0, BPDN, NSL0, and L p -RLSand achieves better performances when it is used for UBSS.

Homotopy Methods Based on $l_{0}$ -Norm for Compressed Sensing

This paper proposes two homotopy methods for solving the compressed sensing (CS) problem, which combine the homotopy technique with the iterative hard thresholding (IHT) method. The homotopy methods overcome the difficulty of the IHT method on the choice of the regularization parameter value, by tracing solutions of the regularized problem along a homotopy path. We prove that any accumulation point of the sequences generated by the proposed homotopy methods is a feasible solution of the problem. We also show an upper bound on the sparsity level for each solution of the proposed methods. Moreover, to improve the solution quality, we modify the two methods into the corresponding heuristic algorithms. Computational experiments demonstrate effectiveness of the two heuristic algorithms, in accurately and efficiently generating sparse solutions of the CS problem, whether the observation is noisy or not.

Big Data Blind Separation

Data or signal separation is one of the critical areas of data analysis. In this work, the problem of non-negative data separation is considered. The problem can be briefly described as follows: given X∈Rm×N, find A∈Rm×n and S∈R+n×N such that X=AS. Specifically, the problem with sparse locally dominant sources is addressed in this work. Although the problem is well studied in the literature, a test to validate the locally dominant assumption is not yet available. In addition to that, the typical approaches available in the literature sequentially extract the elements of the mixing matrix. In this work, a mathematical modeling-based approach is presented that can simultaneously validate the assumption, and separate the given mixture data. In addition to that, a correntropy-based measure is proposed to reduce the model size. The approach presented in this paper is suitable for big data separation. Numerical experiments are conducted to illustrate the performance and validity of the proposed approach.