Blind Separation Research Articles

Statistically Dependent Blind Signal Separation under Relaxed Sparsity

Most traditional blind source separation (BSS) methods are based on the basic assumption that source signals are mutually independent. However, many signals in the real world are often interrelated to each other. In this paper, a novel BSS method is proposed for dependent signals which only relies on the relaxed sparsity of sources. Under this constraint, the column vector of high-dimensional observed signals would be distributed in a specific subspace. According to the representation relation in time-frequency (TF) domain, each column vector of observed signal is uniquely clustered into the subspace, to which it belongs. Furthermore, the estimation of source signals is calculated by the inverse matrix or the pseudo-inverse matrix of the mixing matrix. It is also demonstrated mathematically and experimentally that under relaxed sparsity conditions, proposed subspace clustering methods is promising and hopeful to solve the dependent BSS (DBSS) problems.

Joint Graph Learning and Blind Separation of Smooth Graph Signals Using Minimization of Mutual Information and Laplacian Quadratic Forms

The smoothness of graph signals has found desirable real applications for processing irregular (graph-based) signals. When the latent sources of the mixtures provided to us as observations are smooth graph signals, it is more efficient to use graph signal smoothness terms along with the classic independence criteria in Blind Source Separation (BSS) approaches. In the case of underlying graphs being known, Graph Signal Processing (GSP) provides valuable tools; however, in many real applications, these graphs can not be well-defined <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> and need to be learned from data. In this paper, a GSP-based approach for joint Graph Learning (GL) and BSS of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smooth</i> graph signal sources is proposed, which, to the best of our knowledge, has not been addressed. The minimization of Mutual Information (MI) is exploited in our work because of its desirable advantages, such as having no local minimum and exact (not approximative) modeling of statistical independence. As well as investigating the convergence analysis and identifiability conditions and deriving Cramér-Rao Lower Bound (CRLB), comprehensive experiments of generating (cyclostationary) graph signal mixtures are provided to show the superiority over classic and also GSP-based BSS approaches in the case of the latent sources being <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smooth</i> on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unknown</i> underlying graphs. Based on the provided experimental results, our proposed method performs quite robustly in even high noise levels in both terms of source separation and recovery of underlying graphs.

An Improved GraDe Method for Blind Separation of Graph Signals

An Improved GraDe Method for Blind Separation of Graph Signals

Frequency-Domain Convolutive Bounded Component Analysis Algorithm for the Blind Separation of Dependent Sources

Frequency-Domain Convolutive Bounded Component Analysis Algorithm for the Blind Separation of Dependent Sources

A MLE-based blind signal separation method for time–frequency overlapped signal using neural network

The blind signal separation (BSS) algorithm obtains each original/source signal from the observed signal collected by the receiving antenna or sensor. Objective/loss/cost function and optimization method are two key parts of BSS algorithm. Modifying the objective function and optimization from the perspective of neural network (NN) is a novel concept in BSS domain. L_2 regularization is adopted as a term of maximum likelihood estimation (MLE)-based objective function like in Liu et al. (Sensors 21(3):973, 2021); however, we modified the probability density function (PDF) term of the objective function and used the kernel density estimation method for time–frequency overlapped digital communication signal. Multiple optimizers are studied in this paper, and we figure out the right optimizer for our application scenario. A varies of comparison experiments—whose separation results will be provided in forms of correlation coefficient and performance index—are carried out, which indicate our method can converge quickly and achieve satisfactory separation results with performance index (PI) lower than 0.02 when signal-to-noise ratio (SNR) no less than 10dB. Additionally, it demonstrates performance of our method is better than that of typical separation—FastICA, especially for the lower SNR environment, and it shows that our method is not sensitive to the frequency overlap level (FOL) of the source signal, even FOL as high as 100%; it still can get high-precision separation results with textrm{PI}<0.02.

Single-Channel Blind Signal Separation of the MHD Linear Vibration Sensor Based on Singular Spectrum Analysis and Fast Independent Component Analysis.

An MHD vibration sensor, as a new type of sensor used for vibration measurements, meets the technical requirements for the low-noisy measurement of acceleration, velocity, and micro-vibration in spacecraft during their development, launch, and orbit operations. A linear vibration sensor with a runway type based on MHD was independently developed by a laboratory. In a practical test, its output signal was mixed with a large amount of noise, in which the continuous narrowband interference was particularly prominent, resulting in the inability to efficiently carry out the real-time detection of micro-vibration. Considering the high interference of narrowband noise in linear vibration signals, a single-channel blind signal separation method based on SSA and FastICA is proposed in this study, which provides a new strategy for linear vibration signals. Firstly, the singular spectrum of the linear vibration signal with noise was analyzed to suppress the narrowband interference in the collected signal. Then, a FastICA algorithm was used to separate the independent signal source. The experimental results show that the proposed method can effectively separate the useful linear vibration signals from the collected signals with low SNR, which is suitable for the separation of the MHD linear vibration sensor and other vibration measurement sensors. Compared with EEMD, VMD, and wavelet threshold denoising, the SNR of the separated signal is increased by 10 times on average. Through the verification of the actual acquisition of the linear vibration signal, this method has a good denoising effect.

Accelerated Conjugate Gradient for Second-Order Blind Signal Separation

This paper proposes a new adaptive algorithm for the second-order blind signal separation (BSS) problem with convolutive mixtures by utilising a combination of an accelerated gradient and a conjugate gradient method. For each iteration of the adaptive algorithm, the search point and the search direction are obtained based on the current and the previous iterations. The algorithm efficiently calculates the step size for the accelerated conjugate gradient algorithm in each iteration. Simulation results show that the proposed accelerated conjugate gradient algorithm with optimal step size converges faster than the accelerated descent algorithm and the steepest descent algorithm with optimal step size while having lower computational complexity. In particular, the number of iterations required for convergence of the accelerated conjugate gradient algorithm is significantly lower than the accelerated descent algorithm and the steepest descent algorithm. In addition, the proposed system achieves improvement in terms of the signal to interference ratio and signal to noise ratio for the dominant speech outputs.

A novel end‐to‐end deep separation network based on attention mechanism for single channel blind separation in wireless communication

The traditional methods exhibit unstable performance and high complexity for separating co-frequency modulated wireless communication signals under single-channel conditions. In this study, an end-to-end deep separation network based on the attention mechanism is proposed, which employs the encoder-separator-decoder architecture to implement the separation. The encoder can convert the signal into a high-dimensional feature representation for the separator to achieve separation of the signal in a high-dimensional space. The core of the proposed deep separation network is the innovative separator, which is mainly composed of attention-based convolution units with residual connection. The attention-based convolution unit integrates the large kernel convolution and modified global context (GC) block to simultaneously capture the local and global information of the signal. Furthermore, we improve the GC block to implement channel weighting and location weighting for the given feature map, thus further enhancing the adaptability of the model. The experimental results show that the proposed method not only outperforms the traditional methods in separating mixed signals with the same modulation, but also enables the separation of mixed signals with different modulations.

Single-Channel Blind Separation of Unsynchronized Multiuser PSK Signals With Non-Identical Sampling Frequency Offsets

Single-channel blind source separation (SCBSS) of uncoordinated, non-spread, co-frequency interfering multi-user signals is a challenging task. When the multi-user signals have sampling frequency offset (SFO) due to the imperfection of the local oscillator (LO), this problem becomes even more difficult to be solved. In this letter, a select-stitch data-aided channel estimation (CE) initialized per-survivor processing (SS-DCE-PSP) algorithm is proposed for SCBSS of multi-user signals with SFOs caused by imperfect LOs. By dividing a long sequence into a number of segments and selecting the segments with highest detection reliability to stitch together, the time slip and symbol slip due to the non-identical SFOs can be resolved. The data-aided CE in SS-DCE-PSP further enhances the performance of PSP, especially for the initial symbols. Simulation results show that the proposed SS-DCE-PSP algorithm is robust to the normalized SFO up to 10−4, and the BERs obtained by the SS-DCE-PSP algorithm are close (within 0.5dB) to the BERs obtained for multi-user signals without SFOs.

Constraints on the Optical Depth to Reionization from Balloon-borne Cosmic Microwave Background Measurements

We assess the uncertainty with which a balloon-borne experiment, nominally called Tau Surveyor (τS), can measure the optical depth to reionization σ(τ) with given realistic constraints of instrument noise and foreground emissions. Using a τS fiducial design with six frequency bands between 150 and 380 GHz, with white and uniform map noise of 7 μK arcmin, achievable with a single midlatitude flight, and including Planck's 30 and 44 GHz data, we assess the error σ(τ) obtained with three foreground models and as a function of sky fraction f sky between 40% and 54%. We carry out the analysis using both parametric and blind foreground separation techniques. We compare the σ(τ) values to those obtained with low-frequency and high-frequency versions of the experiment called τS-lf and τS-hf, which have only four and up to eight frequency bands with narrower and wider frequency coverage, respectively. We find that with τS, the lowest constraint is σ(τ) = 0.0034, obtained for one of the foreground models with f sky = 54%. σ(τ) is larger, in some cases by more than a factor of 2, for smaller sky fractions, with τS-lf, or as a function of foreground model. The τS-hf configuration does not lead to significantly tighter constraints. The exclusion of the 30 and 44 GHz data, which give information about synchrotron emission, leads to significant τ misestimates. Decreasing noise by an ambitious factor of 10, while keeping f sky = 40%, gives σ(τ) = 0.0031. The combination of σ(τ) = 0.0034, baryon acoustic oscillation data from DESI, and future cosmic microwave background B-mode lensing data from the CMB-S3/CMB-S4 experiments could give σ(∑m ν ) = 17 meV.

Reconstruction algorithm of haze image based on blind separation model of polarized orthogonal airlight.

Polarization-based dehazing methods can enhance the quality of haze images. However, existing methods tend to a manual selection of sky area and bias coefficient to estimate the degree of polarization (DoP) of the airlight, which leads to inaccurate estimation of the airlight. Aiming at the problem, a reconstruction algorithm based on the blind separation model of polarized orthogonal airlight is proposed. Importantly, the depth-dependent DoP of the airlight is automatically estimated without manual selection of sky area and bias coefficient. To reduce the interference of white objects on the estimation of airlight at infinity, an adaptive estimation method using the deviation between the DoP of the airlight and incident light is proposed. In order to accurate estimate the airlight from the airlight at infinity, a blind separation model of the airlight with multi-regularization constraints is established based on the decomposition of the airlight at infinity into a pair of polarized components with orthogonal angles. The experimental results show that the method effectively improves the visibility of scenes under different haze concentrations, especially in dense or heavy haze weather.

Robust blind separation of smooth graph signals using minimization of graph regularized mutual information

The smoothness of the graph signals on predefined/constructed graphs appears in many natural applications of processing unstructured (i.e., graph-based) data. In the case of latent sources being smooth graph signals, blind source separation (BSS) quality can be significantly improved by exploiting graph signal smoothness along with the classic measures of statistical independence. In this paper, we propose a BSS method benefiting from the minimization of mutual information as a well-known independence criterion and also graph signal smoothness term of the estimated latent sources, and show that its performance is superior and fairly robust to the state-of-the-art classic and Graph Signal Processing (GSP)-based methods, even in the case of the smooth graph signal sources being heavily corrupted. In addition to the comprehensive complexity and convergence analysis, the asymptotic performance of the proposed method is comprehensively compared with that of the Cramér-Rao Bound (CRB) to illustrate the asymptotic efficiency of the proposed method. Besides, the comprehensive real-world analysis of separating mixed images and speech signals illustrates the applicability and efficiency of the proposed method in real-world scenarios.

FPGA based Hardware Co-Simulation Implementation for RealTime Image Blind Separation using ICA Algorithms

The use of mixed image sources requires digital preprocessing to separate them, for making easier their storage and improve their quality. The ICALAB for Image Processing method is one of the solutions proposed for the blind efficient separation of signals without prior knowledge of the source images. Nevertheless, to choose the appropriate algorithm with the most efficient separation index, several tests are carried out on a certain number of algorithms, with off-line processing of image samples bases, by means of software tools which are generally installed on a computer, such as ICALAB, TIPICA, GIFT, NMFLAB, model identification UBSS, ... Thus, in order to perform the image separation processing in real time, this study aims to develop a rapid prototyping embedded system for implementing the blind source separation concept. It mainly provides a promising approach for implementing twelve efficient blind image separation algorithms on the ZYBO Z7 FPGA board, using Xilinx System Generator (XSG) for Real Time Hardware Co-simulation. As an application example, this study deals with the blind separation of two e-frames mixture, and then provides the adequate algorithm, basing on the calculation of the Performance Index (PI), and the separated images results. Keywords—Blind Image Separation; Hardware CoSimulation; Independent Component Algorithm (ICA); Xilinx System Generator (XSG); Zynq-7000; VHDL.

The Real Eigenpairs of Symmetric Tensors and Its Application to Independent Component Analysis.

It has been proved that the determination of independent components (ICs) in the independent component analysis (ICA) can be attributed to calculating the eigenpairs of high-order statistical tensors of the data. However, previous works can only obtain approximate solutions, which may affect the accuracy of the ICs. In addition, the number of ICs would need to be set manually. Recently, an algorithm based on semidefinite programming (SDP) has been proposed, which utilizes the first-order gradient information of the Lagrangian function and can obtain all the accurate real eigenpairs. In this article, for the first time, we introduce this into the ICA field, which tends to further improve the accuracy of the ICs. Note that the number of eigenpairs of symmetric tensors is usually larger than the number of ICs, indicating that the results directly obtained by SDP are redundant. Thus, in practice, it is necessary to introduce second-order derivative information to identify local extremum solutions. Therefore, originating from the SDP method, we present a new modified version, called modified SDP (MSDP), which incorporates the concept of the projected Hessian matrix into SDP and, thus, can intellectually exclude redundant ICs and select true ICs. Some cases that have been tested in the experiments demonstrate its effectiveness. Experiments on the image/sound blind separation and real multi/hyperspectral image also show its superiority in improving the accuracy of ICs and automatically determining the number of ICs. In addition, the results on hyperspectral simulation and real data also demonstrate that MSDP is also capable of dealing with cases, where the number of features is less than the number of ICs.

Indirect Approach to Identify Girder Bridge Element Stiffness Based on Blind Source Separation

The indirect method of using a passing vehicle to identify modal properties of a girder bridge has become attractive recently. Compared to the direct method, which requires a lot of sensors installed directly on the bridge itself, the indirect method only requires a single sensor installed on the vehicle to indirectly measure the response of the bridge. However, it is difficult to eliminate the adverse effect of road surface roughness. An indirect approach based on blind source separation is proposed for the first time in this study to identify the bridge element stiffness where two movable vehicles are used. Two identical vehicles stay at rest at the designated measurement points and their vertical accelerations are collected. After one measurement, the two vehicles move to other designated measurement points and the accelerations are collected again. The same procedure is repeated until the two vehicles have moved over all the designated measurement points. Then the blind source separation technique is employed to extract the fundamental mode shape of the bridge and the improved direct stiffness method is adopted to estimate the bridge element stiffness based on the collected data, which are used to monitor the health of the bridge structure and to maintain structure safety and natural symmetry. The proposed method only requires the output response of the vehicle due to the involvement of the blind separation technique. In addition, the proposed method can overcome the adverse effect of road surface roughness because the vehicles only move between two measurements and they stay at rest during one measurement. Numerical simulation was conducted to validate the proposed method, and the effect of various factors such as bridge damping ratio and measurement noise was investigated. Field measurement on Min-Xie bridge in Chongqing city was also carried out to further investigate the feasibility of the proposed method and showed that it can perform well in extracting the fundamental mode shape and evaluating bridge element stiffness.

Blind Fault Extraction of Rolling-Bearing Compound Fault Based on Improved Morphological Filtering and Sparse Component Analysis.

In order to effectively separate and extract bearing composite faults, in view of the non-linearity, strong interference and unknown number of fault source signals of the measured fault signals, a composite fault-diagnosis blind extraction method based on improved morphological filtering of function (SMF), density peak clustering (DPC) and orthogonal matching pursuit (OMP) is proposed. In this method, the function is used as the structural element of the morphological filter for the first time to improve the traditional morphological filter. After the observation signal is processed by the improved morphological filter, the impact characteristics of the signal are improved, and the signal meets the sparsity. Then, on the premise that the number of clustering is unknown, the density peak algorithm is used to cluster sparse signals to obtain the clustering center, which is equivalent to the hybrid matrix. Finally, the hybrid matrix is transformed into a sensing matrix, and the signal is transformed into the frequency domain to complete the compressive sensing and reconstruction of the signal in the frequency domain. Both simulation and measured signal results show that this algorithm can effectively complete the blind separation of rolling bearing faults when the number of fault sources is unknown, and the time cost can be reduced by about 75%.

Blind signal separation for coprime planar arrays: An improved coupled trilinear decomposition method

AbstractIn this study, the problem of blind signal separation for coprime planar arrays is investigated. For coprime planar arrays comprising two uniform rectangular subarrays, we link the signal separation to the tensor‐based model called coupled canonical polyadic decomposition (CPD) and propose an improved coupled trilinear decomposition approach. The output data of coprime planar arrays are modeled as a coupled tensor set that can be further interpreted as a coupled CPD model, allowing a signal separation to be achieved using coupled trilinear alternating least squares (TALS). Furthermore, in the procedure of the coupled TALS, a Vandermonde structure enforcing approach is explicitly applied, which is shown to ensure fast convergence. The results of Monto Carlo simulations show that our proposed algorithm has the same separation accuracy as the basic coupled TALS but with a faster convergence speed.

A Novel Improved Threshold Adaptive Forgetting Variable Step Size Blind Separation Model for Weak Signal Detection

The online blind source separation (BSS) is seriously disturbed by strong noise when extracting weak signals and has the defects that it cannot both give consideration to convergence speed and steady-state error. In order to solve the abovementioned problems, a novel improved threshold adaptive forgetting variable step size blind separation model (ITAFBS) for weak signal detection is proposed. Firstly, an improved lifting wavelet transform (ILWT) is proposed to reduce the noise of weak signals. In ILWT, a threshold function containing an adjustment factor is proposed to reduce the constant deviation so as to ensure a high signal-to-noise ratio and low distortion after denoising. Then, the separation index (SI) is constructed according to the convergence conditions of the BSS model. An adaptive variable step size blind separation model based on the SI is studied. At the initial stage of separation, the step size is increased to obtain a fast convergence rate, and at the end of separation and the step size is shortened to obtain a small steady-state error. Finally, the forgetting factor is introduced into the model to reduce the error accumulation in the early stage of the algorithm, and the Fourier norm is introduced to improve the convergence speed and separation accuracy of the model. The simulation and experimental results show that ITAFBS has a good performance in multi-frequency weak signal detection. Compared with other methods, the ITAFBS has a faster convergence speed and minimum steady-state error.

Cluster Migration Distance for Performance Degradation Assessment of Water Pump Bearings.

Because the signal of water pump bearing is seriously disturbed by noise and the fault evolution is complex, it is difficult to describe the performance degradation trend of water pump bearing in a timely and accurate manner using the traditional performance degradation index (PDI). In this paper, a new Cluster Migration Distance (CMD) algorithm is proposed. The extraction of the indicator includes the following four steps: First, the relevant blind separation is used to extract the useful signal of the monitored bearing from the mixed signal; secondly, the impact component is further enhanced by wavelet packet analysis. Then, the redundancy of the original feature vectors is eliminated using our previously proposed KJADE (Kernel Joint Approximate Diagonalization of Eigen-matrices) method. Finally, the newly proposed CMD index is computed as PDI. By calculating the offset trajectory of the feature cluster centroid in the continuous running process of the bearing, CMD can aptly deal with the complex and variable features in the fault evolution process of the water pump bearing. The whole-life monitoring data of a 220 KW water pump system are processed. The results show that the proposed CMD index has better early-warning ability and monotonicity than the traditional kurtosis index.

Robust approach for blind separation of noisy mixtures of independent and dependent sources

The framework of this article is to introduce a new efficient Blind Source Separation (BSS) method that handles mixtures of noise-contaminated independent / dependent sources. In order to achieve that, one can minimize a criterion that fuses a separating part, based on Kullback–Leibler divergence to set apart the observed mixtures of either dependent or independent sources, with a regularization part that employs the bilateral total variation (BTV) for the purpose of denoising the observations. The proposed algorithm utilizes a primal-dual algorithm to remove the noise, while a gradient descent method is implemented to retrieve the source signals. Our algorithm has shown its effectiveness and efficiency toward the noisy dependent / independent sources and also surpassed the standard BSS algorithms through different experimental results.