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Blind Separation of Coherent Multipath Signals with Impulsive Interference and Gaussian Noise in Time-Frequency Domain
Abstract
Blind separation of multipath fading signals with impulsive interference and Gaussian noise is a very challenging issue due to multipath effects, which are often encountered in practical scenarios. Since the strong coherence among multipath signals leads to the extreme superposition in time-frequency (TF) domain, this paper proposes an iterative three-stage blind source separation (ITS-BSS) algorithm for the separation of coherent multipath signals in the presence of impulsive and Gaussian noise. Specifically, an initial estimation of mixing matrix is firstly implemented by some non-TF based algorithms. Secondly, a subspace-based TF-BSS algorithm is developed to determine the number of sources contributing at each auto-source TF point and then reconstruct corresponding sources. Thirdly, the reconstructed sources at current iteration are used to further improve the estimation accuracy of mixing matrix based on the least-squares (LS) algorithm. The last two stages are repeated by iteratively updating mixing matrix and sources until satisfied performance is achieved or a predefined number of iterations is done. Numerical results on multipath phase-shift keying (PSK) and quadrature amplitude modulation (QAM) signals plus impulsive noise under various signal-to-noise ratio (SNR) conditions are provided to demonstrate the feasibility and effectiveness of the proposed ITS-BSS algorithm.
... The SCA-based mixing matrix estimate approach takes advantage of the signal's linear clustering characteristic, which is sparse enough to solve the mixed vector. As the observed time domain signal often cannot meet the sparse condition, it is often transformed to the TF domain through short time Fourier transform (STFT) and Wigner-Ville Distibution (WVD) [16,17]. A method called degenerate unmixing estimation technique (DEUT) was proposed by Jourjine et al. [18], which requires speech signals to meet W-disjoint orthogonality in TF domain. ...
... Figure 3 shows the decision diagram of the OPTICS algorithm. Set the threshold value α, as shown in Equation (16). The points where the reachability-distance exceeds the threshold value are regarded as outliers which need to be deleted. ...
... Perform this step for all subintervals; 4: Set threshold λ, perform Equation (11) and Equation (12) to SSPs. The processed points set is denoted as Ψ; 5: OPTICS is used to classify and determine the number of sources for Ψ, as shown in Figure 2. Set threshold ρ and use Equation (16) to remove noise points; 6: For the points in each cluster, the local potential value are calculated by Equation (17) to determine the cluster center and obtain the estimated mixing matrixÂ; 7: Equation (24) and Equation (25) are used to calculate the projection parameters. Set parameter µ, and judge the condition in Equation (26). ...
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.
... Sparse component analysis, as a common UBSS method, can separate the source signals by exploiting the sparsity characteristics of sources in the transform domain [21,22]. Generally, the SCA algorithm consists of two steps: mixing matrix estimation and source recovery [23]. ...
... As a comparison, the mixed signals in Figure 3 are also analyzed by the K-means. The estimated mixing matrix is given as follows:Â = 0.7043 0.5703 0.9332 0.7099 −0.8214 −0.3592 (22) Normalized mean square error (NMSE) and the deviation angle are used to evaluate the accuracy of the mixing matrix estimation [40,46], and the calculation formulas are shown in Equations (23) and (24), respectively: ...
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.
... The sound signals recorded by exploiting microphones are usually mixed with unwanted signals such as noise, reverberation [1], and interferences [2]. Of this reverberation is the distraction that happens in the source signal while transmitting from the source to the destination through different paths with variations in length and attenuations. ...
Speech signals observed from distantly placed microphones may have some acoustic interference, such as noise and reverberation. These may lead to the degradation of the quality of blind speech. Hence, it is necessary to process the acquired speech signals to separate the blind source and eliminate the reverberation. Therefore, we proposed a novel speech separation and dereverberation method, which is based on the incorporation of Locally Weighted Projection Regression (LWPR)-based Principal Component Analysis (PCA) and Deep Neural Network (DNN)-based Weighted Prediction Error (WPE). The proposed method preprocesses the mixed reverberant signal prior to the application of Blind Source Separation (BSS) and Blind Dereverberation (BD). The preprocessing of the input sample signals is performed with the exploitation of fast Fourier transform (FFT) and whitening approaches to convert the time domain signal into frequency domain signal and to generate the transformation matrices. Besides, the utilization of LWPR-PCA can perform the BSS and the DNN-WPE can be used to conduct the BD. Moreover, the experimental analysis of our proposed method is compared with the existing RPCA-SNMF, CBF, BA-CNMF, AFMNMF, and ISC-LPKF approaches. The experimental outcomes depict that the proposed method effectively separates the original signal from the mixed reverberant signals.
... Although enhanced speech can be generated with the use of only the phase of the noisy signal and the enhanced amplitude through inverse transformation, the quality of the enhanced speech will be deteriorated with the use of the noise phase. Time-frequency domain information is found in later studies to play an important role in speech signal reconstruction [32] and signal separation [33][34][35][36]. Shinnosuke et al. proposed a method for phase reconstruction by constructing neural networks [37]. ...
Although current attention‐based speech enhancement methods have been proven to be capable of significantly improving the noise reduction performance, a bottleneck has arisen in juggling both detailed features and high‐level features: The more attention paid to such performance indicators as speech intelligibility index and articulation index will lead to the loss of subtle features such as syllable continuity and timbre distortion. To tackle such a problem, we divide the speech enhancement model into multiple stages, with a special attention mechanism introduced in each stage so that the detailed speech information is retained and the features of high levels are captured. In this research, a Multi‐Stage Attention Network (MSANet) is implemented in cascade by using three different attention modules: Self Attention, Channel Attention and Spatial Attention. The attention module in each stage needs only to focus on the features of its corresponding stage, thus giving full play to their respective advantages without affecting or damaging the features of other stages, helping decouple the feature extraction process and obtaining the features capable of complementing one another. The comparisons and ablation experiments show that the performance of MSANet is superior to those of current mainstream time domain or time‐frequency domain state‐of‐the‐art methods. Compared to the baseline, PESQ score of their model (3.11) has increased by 5%, CSIG (4.44) has increased by 2.5%, CBAK (3.63) has increased by 2.8% and COVL (3.81) has increased by 3.8%, which demonstrates the potential of MSANet as speech feature extraction backbones. An implementation of the PyTorch version is available here: http://www.msp‐lab.cn:1436/msp/MSANet.
... The NMSE is the most widely used tool to measure the performance of EEG signal processing [27]. The NMSE is the average squared of normalized error. ...
Artifacts in electroencephalography (EEG) signals have negative effects on the analysis of the EEG signals. Although a number of techniques were developed to remove artifacts, new methods still need to be developed to remove artifacts with high accuracy and minimal data loss from EEG signals. In this context, there has been an increasing trend to combine machine learning and traditional approaches for effective automatic artifact removal. In this work, we have focused on eye-blink artifact removal, which is the most common and critical type of artifact. Unlike other studies, the artifact part of the EEG signal segment was detected by the semantic segmentation deep learning algorithm. Then, Butterworth filter was applied to only the artifact part of the EEG signal segment, and low-frequency noises in the region of interest containing only artifact were filtered. Since there is no filtering in the part of the signal without artifacts, the mean square error (MSE), normalized mean square error (NMSE) and structure similarity metric (SSIM) proved that there was no signal distortion in the non-artifact region of the metric. Thus, it became possible to examine only with the artifact signal segment.
Sparse time‐frequency analysis (STFA) can precisely achieve the spectrum of the local truncated signal. However, when the signal is disturbed by unexpected data loss, STFA cannot distinguish effective signals from missing data interferences. To address this issue and establish a robust STFA model for time‐frequency analysis (TFA) in data loss scenarios, a stationary Framelet transform‐based morphological component analysis is introduced in the STFA. In the proposed model, the processed signal is regarded as a sum of the cartoon, texture and data‐missing parts. The cartoon and texture parts are reconstructed independently by taking advantage of the stationary Framelet transform. Then, the signal is reconstructed for STFA. The forward‐backwards splitting method is employed to split the robust STFA model into the data recovery and robust time‐frequency imaging stages. The two stages are then solved separately by using the alternating direction method of multipliers (ADMM). Finally, several experiments are conducted to show the performance of the proposed robust STFA method under different data loss levels, and it is compared with some existing state‐of‐the‐art time‐frequency methods. The results indicate that the proposed method outperforms the compared methods in obtaining the sparse spectrum of the effective signal when data are missing. The proposed method has a potential value in TFA in scenarios where data is easily lost.
Beamforming is an attractive technique to improve the system performance for multi-input-multi-output (MIMO) communications. Previous works mainly focus on improving the data transmission quality. However, the potential of beamforming for improving the localization quality is not yet fully studied. In this paper, we focus on active beamforming to reduce the user equipment (UE) localization error for millimeter-wave (mmWave) MIMO systems. Such beamforming for localization is of challenge because its optimization cost function (e.g., the localization error bound) also depends on the actual UE location and instantaneous channel states, which are unknown in advance. To address this challenge, a novel successive localization and beamforming (SLAB) scheme is proposed, where the long-term UE location and the instantaneous channel state will be jointly estimated and then the beamforming vector will be successively optimized as per the obtained estimation results. The proposed SLAB scheme will yield a sequence of beamforming weights and UE location estimates, which will converge to the stationary point of the associated optimization problem. Simulation results show that the proposed SLAB scheme achieves a huge performance gain for UE localization compared with state-of-the-art baselines. Index Terms-5G localization, mmWave MIMO, beamforming, Cramer-Rao lower bound.
Sparse component analysis (SCA) is a popular method for addressing underdetermined
blind source separation in array signal processing applications. We are motivated by
problems that arise in the applications where the sources are densely sparse (i.e. the
number of active sources is high and very close to the number of sensors). The separation
performance of current underdetermined source recovery (USR) solutions,
including the relaxation and greedy families, reduces with decreasing the mixing
system dimension and increasing the sparsity level (k). In this paper, we present a
k-SCA-based algorithm that is suitable for USR in low-dimensional mixing systems.
Assuming the sources is at most (m − 1) sparse where m is the number of mixtures;
the proposed method is capable of recovering the sources from the mixtures given the
mixing matrix using a subspace detection framework. Simulation results show that the
proposed algorithm achieves better separation performance in k-SCA conditions compared
to state-of-the-art USR algorithms such as basis pursuit, minimizing norm-L1,
smoothed L0, focal underdetermined system solver and orthogonal matching pursuit.
Sparse arrays, such as nested arrays and coprime arrays, can achieve a high number of degrees of freedom (DOFs) for direction of arrival (DOA) estimation with a reduced number of antennas. On the other hand, the compressive measurement method provides an effective way to reduce the number of front-end circuit chains. In this paper, we generalized current works on the two categories of methods to a compressed sparse array (CSA) scheme which combines the compressive measurement method and the sparse array together to significantly reduce the system complexity. After introducing the proposed scheme, the Cramar-Rao bound (CRB) of the proposed CSA scheme is derived. We then determine the corresponding existing conditions of the CRB, based on which the number of DOFs is derived and examined for the first time. It is proved that, for a CSA which compressed the output of an L-element sparse array to M < L chains, a higher number of DOFs is obtained as compared to that of the M-element array with the same sparse structure. Furthermore, the DOA estimation accuracy using the M-chain CSA is higher than that using the M-element sparse array due to the extended array aperture. Numerical simulations verify the superiority of the proposed CSA scheme.
In this paper, a blind separation algorithm based on nonparametric probability density estimation (NPDE) for baseband communication signals is proposed. The NPDE method can precisely estimate the probability density of signals, and its good data-driven property guarantees the adaptability of the proposed algorithm. The NPDE method is extended to complex field to fit the complex characteristics of baseband communication signals. The complex update procedure of demixing matrix corresponding to complex channel matrix and signals is also derived in this paper. The experimental results indicate that the proposed algorithm not only can effectively separate the mixture of baseband communication signals, which are modulated with the same or different modulation schemes, but also has better convergence properties and greater signal interference ratio gains than the contrast algorithms. Moreover, even if the local carrier of receiver is unsynchronized to the carrier of received signals due to carrier offsets, the proposed algorithm can also achieve a valid separation.
In this paper, we address underdetermined blind separation of N sources from their M instantaneous mixtures, where N > M, by combining the sparsity and independence of sources. Firstly, we propose an effective scheme to search some sample segments with the local sparsity, which means that in these sample segments, only Q(Q < M ) sources are active. By grouping these sample segments into different sets such that each set has the same Q active sources, the original underdetermined BSS problem can be transformed into a series of locally overdetermined BSS problems. Thus, the blind channel identification task can be achieved by solving these overdetermined problems in each set by exploiting the independence of sources. In the second stage, we will achieve source recovery by exploiting a mild sparsity constraint, which is proven to be a sufficient and necessary condition to guarantee recovery of source signals. Compared with some sparsity-based UBSS approaches, this work relaxes the sparsity restriction about sources to some extent by assuming that different source signals are mutually independent. At the same time, the proposed UBSS approach does not impose any richness constraint on sources. Theoretical analysis and simulation results illustrate the effectiveness of our approach.
It is known that there exist two kinds of methods for direction-of-arrival (DOA) estimation in the literature: the subspace-based method and the sparsity-based method. However, pervious works reveal that the former method cannot address the case in which the number of signals is larger than that of sensors while the latter one always suffers from the influence of basis mismatch. In this paper, to overcome these two shortcomings we propose a new method called covariance matrix reconstruction approach (CMRA) for both uniform linear array (ULA) and sparse linear array (SLA). In particular, by exploiting the Toeplitz structure of the covariance matrix of the array output, we formulate a low-rank matrix reconstruction (LRMR) problem for covariance matrix recovery. The nonconvex LRMR problem is then relaxed by replacing the rank norm with the nuclear norm and solved using the optimization toolbox. Next, we retrieve the DOAs from the recovered covariance matrix by using the subspace-based methods and obtain an estimated number of signals as a byproduct. We also provide two algorithm implementations for the LRMR problem based on duality and alternating direction method of multipliers (ADMM), respectively. It is shown that CMRA can be regarded as an atomic norm minimization (ANM) model or a gridless version of the sparsity-based methods and can recover more signals than sensors with a well-designed array. Numerical experiments are provided to validate the effectiveness of the proposed method in comparison with some of the existing methods.
Independent component analysis (ICA) is one of the most powerful techniques to solve the problem of blind source separation (BSS), and the well-known Fast-ICA is excellent for large-scale BSS. Fast-ICA tries to find the demixing matrix by optimizing the nonlinear objective (cost or contrast) functions. For Fast-ICA, there are three built-in contrast functions to separate non-Gaussian sources, and their derivatives are similar to nonlinearities used in neural networks. However, the contrast functions and their nonlinearities for separating super-Gaussian sources are not optimal owing to their high computational cost, which greatly affect the convergence rate of Fast-ICA. To address this issue, this paper proposes two rational nonlinearities to replace the built-in (original) nonlinearities. The rational nonlinearities are derived by the Chebyshev–Pade approximant from Chebyshev polynomials (series) of the original nonlinearities. To speed up the convergence of Fast-ICA, the degrees in both numerator and denominator of rational functions are designed to be relatively low, and thus the rational polynomials can be quickly evaluated. Simulation results of audio BSS show that the proposed rational nonlinearities can not only improve the convergence rate of Fast-ICA, but also improve the separation performance index; Experiment results of real electrocardiogram data also verify the validity of the proposed approach.
Blind Source Separation (BSS) is a challenging matrix factorization problem that plays a central role in multichannel imaging science. In a large number of applications, such as astrophysics, current unmixing methods are limited since real-world mixtures are generally affected by extra instrumental effects like blurring. Therefore, BSS has to be solved jointly with a deconvolution problem, which requires tackling a new inverse problem: deconvolution BSS (DBSS). In this article, we introduce an innovative DBSS approach, called DecGMCA, based on sparse signal modeling and an efficient alternative projected least square algorithm. Numerical results demonstrate that the DecGMCA algorithm performs very well on simulations. It further highlights the importance of jointly solving BSS and deconvolution instead of considering these two problems independently. Furthermore, the performance of the proposed DecGMCA algorithm is demonstrated on simulated radio-interferometric data.
This paper introduces a constrained source/filter model for semi- supervised speech separation based on non-negative matrix factorization (NMF). The objective is to inform NMF with prior knowledge about speech, providing a physically meaningful speech separation. To do so, a source/filter model (indicated as Instantaneous Mixture Model or IMM) is integrated in the NMF. Further- more, constraints are added to the IMM-NMF, in order to control the NMF behaviour during separation, and to enforce its physical meaning. In particular, a speech specific constraint - based on the source/filter coherence of speech - and a method for the automatic adaptation of constraints’ weights during separation are presented. Also, the proposed source/filter model is semi-supervised: during training, one filter basis is estimated for each phoneme of a speaker; during separation, the estimated filter bases are then used in the constrained source/filter model. An experimental evaluation for speech separation was conducted on the TIMIT speakers database mixed with various environmental background noises from the QUT- NOISE database. This evaluation showed that the use of adaptive constraints increases the performance of the source/filter model for speaker-dependent speech separation, and compares favorably to fully-supervised speech separation.
In this paper, acoustic echo cancellation with doubletalk detection system for a hand-free telecommunication system is implemented using Matlab. Here adaptive noise canceller with blind source separation (ANC-BSS) system is proposed to remove both background noise and far-end speaker echo signal in presence of double-talk. During the absence of double-talk, far-end speaker echo signal is cancelled by adaptive echo canceller. Both adaptive noise canceller and adaptive echo canceller are implemented using LMS, NLMS, VSLMS and VSNLMS algorithms. The normalized cross-correlation method is used for double-talk detection. VSNLMS has shown its superiority over all other algorithms both for double-talk and in absence of double-talk. During the absence of double-talk it shows its superiority in terms of increment in ERLE and decrement in misalignment. In presence of double-talk, it shows improvement in SNR of near-end speaker signal.
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.
Blind source separation (BSS) is a very popular technique to analyze
multichannel data. In this context, the data are modeled as the linear
combination of sources to be retrieved. For that purpose, standard BSS methods
all rely on some discrimination principle, whether it is statistical
independence or morphological diversity, to distinguish between the sources.
However, dealing with real-world data reveals that such assumptions are rarely
valid in practice: the signals of interest are more likely partially
correlated, which generally hampers the performances of standard BSS methods.
In this article, we introduce a novel sparsity-enforcing BSS method coined
Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve
sparse and partially correlated sources. More precisely, it makes profit of an
adaptive re-weighting scheme to favor/penalize samples based on their level of
correlation. Extensive numerical experiments have been carried out which show
that the proposed method is robust to the partial correlation of sources while
standard BSS techniques fail. The AMCA algorithm is evaluated in the field of
astrophysics for the separation of physical components from microwave data.
A compressive sensing (CS) approach for nonstationary signal separation is proposed. This approach is motivated by challenges in radar signal processing, including separations of micro-Doppler and main body signatures. We consider the case where the signal of interest assumes sparse representation over a given basis. Other signals present in the data overlap with the desired signal in the time and frequency domains, disallowing conventional windowing or filtering operations to be used for desired signal recovery. The proposed approach uses linear time-frequency representations to reveal the data local behavior. Using the L-statistics, only the time-frequency (TF) points that belong to the desired signal are retained, whereas the common points and others pertaining only to the undesired signals are deemed inappropriate and cast as missing samples. These samples amount to reduced frequency observations in the TF domain. The linear relationship between the measurement and sparse domains permits the application of CS techniques to recover the desired signal without significant distortion. We focus on sinusoidal desired signals with sparse frequency-domain representation but show that the analysis can be straightforwardly generalized to nonsinusoidal signals with known structures. Several examples are provided to demonstrate the effectiveness of the proposed approach.
In this article, we describe the role of time-frequency distributions (TFDs) in array processing. We particularly focus on quadratic TFDs (QTFDs). We demonstrate how these distributions can be properly integrated with the spatial dimension to enhance individual source signal recovery and angular estimation. The framework that enables such integration is referred to as spatial TFD (STFD). We present the important milestones of STFDs that have been reached during the last 15 years. Most importantly, we show that array processing creates new perspectives of QTFDs and defines new roles to the autoterms and cross-terms in both problem formulation and solution. Multisensor configurations, in essence, establish a different paradigm and introduces new challenges that did not exist in a single-sensor time-frequency distribution.
This paper presents a new approach based on spatial time-frequency
averaging for separating signals received by a uniform linear antenna
array. In this approach, spatial averaging of the time-frequency
distributions (TFDs) of the sensor data is performed at multiple
time-frequency points. This averaging restores the diagonal structure of
the source TFD matrix necessary for source separation. With spatial
averaging, cross-terms move from their off-diagonal positions in the
source TFD matrix to become part of the matrix diagonal entries. It is
shown that the proposed approach yields improved performance over the
case when no spatial averaging is performed. Further, we demonstrate
that in the context of source separation, the spatially averaged
Wigner-Ville distribution outperforms the combined
spatial-time-frequency averaged distributions, such as the one obtained
by using the Choi-Williams (1989) distribution. Simulation examples
involving the separation of two sources with close AM and FM modulations
are presented
Recently an instantaneous blind source separation (BSS) approach that exploits the bounded magnitude structure of digital communications signals has been introduced. In this paper, we introduce a deflationary adaptive algorithm based on this criterion and provide its convergence analysis. We show that the resulting algorithm is convergent to one of the globally optimal points that correspond to perfect separation. The simulation examples related to the separation of digital communication signals are provided to illustrate the convergence and the performance of the algorithm
This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones
This paper discusses underdetermined (i.e., with more sources than sensors) blind source separation (BSS) using a two-stage sparse representation approach. The first challenging task of this approach is to estimate precisely the unknown mixing matrix. In this paper, an algorithm for estimating the mixing matrix that can be viewed as an extension of the DUET and the TIFROM methods is first developed. Standard clustering algorithms (e.g., K-means method) also can be used for estimating the mixing matrix if the sources are sufficiently sparse. Compared with the DUET, the TIFROM methods, and standard clustering algorithms, with the authors' proposed method, a broader class of problems can be solved, because the required key condition on sparsity of the sources can be considerably relaxed. The second task of the two-stage approach is to estimate the source matrix using a standard linear programming algorithm. Another main contribution of the work described in this paper is the development of a recoverability analysis. After extending the results in , a necessary and sufficient condition for recoverability of a source vector is obtained. Based on this condition and various types of source sparsity, several probability inequalities and probability estimates for the recoverability issue are established. Finally, simulation results that illustrate the effectiveness of the theoretical results are presented.
Binary time-frequency masks are powerful tools for the separation of sources from a single mixture. Perfect demixing via binary time-frequency masks is possible provided the time-frequency representations of the sources do not overlap: a condition we call W-disjoint orthogonality. We introduce here the concept of approximate W-disjoint orthogonality and present experimental results demonstrating the level of approximate W-disjoint orthogonality of speech in mixtures of various orders. The results demonstrate that there exist ideal binary time-frequency masks that can separate several speech signals from one mixture. While determining these masks blindly from just one mixture is an open problem, we show that we can approximate the ideal masks in the case where two anechoic mixtures are provided. Motivated by the maximum likelihood mixing parameter estimators, we define a power weighted two-dimensional (2-D) histogram constructed from the ratio of the time-frequency representations of the mixtures that is shown to have one peak for each source with peak location corresponding to the relative attenuation and delay mixing parameters. The histogram is used to create time-frequency masks that partition one of the mixtures into the original sources. Experimental results on speech mixtures verify the technique. Example demixing results can be found online at http://alum.mit.edu/www/rickard/bss.html.
In this paper, we address the problem of instantaneous frequency (IF) estimation of non-linear, multi-component frequency modulated (FM) signals in the presence of burst missing data samples, where different signal components have distinct amplitude levels. Burst missing data induce significant artifacts in the time-frequency (TF) representations of such signals, thus making identification of true IFs challenging. We propose a technique that involves local peak detection and filtering within a window at each time instant. The threshold for each local TF segment is adapted based on the local maximum values of the signal within the segment. The proposed approach not only mitigates the undesired impacts of the artifacts and cross-terms due to burst missing data samples, but also successfully resolves signal components with distinct amplitude levels and preserves a high resolution of the auto-terms. The effectiveness of the proposed method and its superiority over existing techniques are verified through simulation results.
In this paper, we present an effective time-frequency (TF) analysis of non-stationary frequency modulated (FM) signals in the presence of burst missing data samples. The key concept of the proposed work lies in the reliable sparse recovery of non-parametric FM signals in the joint-variable domains. Specifically, by utilizing the one-dimensional Fourier relationship between the instantaneous auto-correlation function (IAF) and the TF representation (TFR), the proposed approach iteratively recovers missing samples in the IAF domain through sparse reconstruction using, e.g., the orthogonal matching pursuit (OMP) method, while maintaining the TF-domain sparsity. The proposed method, referred to as missing data iterative sparse reconstruction (MI-SR), achieves reliable TFR recovery from the observed data with a high proportion of burst missing samples. This is in contrast to the existing sparse TFR recovery methods which work well only for random missing data samples. In particular, when applied in conjunction with signal-adaptive TF kernels, the proposed method achieves effective suppression of both cross-terms and artifacts due to burst missing samples. The superiority of the proposed technique is verified through analytical results and numerical examples.
This paper proposes a novel method of highly secured time domain cryptosystem to provide security for mobile voice calls. Using a modified version of Blind Source Separation (BSS) algorithms, the proposed cryptosystem provides a complete solution for highly secured communications between the two ends of any voice call without the need for modifying the existing mobile network infrastructure. Moreover, this system can be easily connected to any type of mobile equipment. To overcome the bandwidth expansion usually associated with BSS algorithms, the proposed system uses a modified key generation process to limit the bandwidth occupied by the encrypted speech signal. Evaluation of the modified encryption and decryption algorithms proved the validity of these changes for speech signals in terms of signal to noise ratio and residual intelligibility.
This paper develops a unifying framework for signal reconstruction from interferometric measurements that is broadly applicable to various applications of interferometry. In this framework, the problem of signal reconstruction in interferometry amounts to one of basis analysis. Its applicability is shown to extend beyond conventional temporal interferometry, which leverages the relative delay between the two arms of an interferometer, to arbitrary degrees of freedom of the input signal. This allows for reconstruction of signals supported in other domains (e.g., spatial) with no modification to the underlying structure except for replacing the standard temporal delay with a generalized delay, that is, a practically realizable unitary transformation for which the basis elements are eigenfunctions. Under the proposed model, the interferometric measurements are shown to be linear in the basis coefficients, thereby enabling efficient and fast recovery of the desired information. While the corresponding linear transformation has only a limited number of degrees of freedom set by the structure of the interferometer giving rise to a highly constrained sensing structure, we show that the problem of signal recovery from such measurements can still be carried out compressively. This signifies significant reduction in sample complexity without introducing any additional randomization as is typically done in prior work leveraging compressive sensing techniques. We provide performance guarantees under constrained sensing by proving that the transformation satisfies sufficient conditions for successful reconstruction of sparse signals using concentration arguments. We showcase the effectiveness of the proposed approach using simulation results, as well as actual experimental results in the context of optical modal analysis of spatial beams.
Signals with the time-varying frequency content are generally well represented in the joint time-frequency domain; however, the most commonly used methods for time-frequency distributions (TFDs) calculation generate unwanted artifacts, making the TFDs interpretation more difficult. This downside can be circumvented by compressive sensing (CS) of the signal ambiguity function (AF), followed by the TFD reconstruction based on the sparsity constraint. The most critical step in this approach is a proper CS-AF area selection, with the CS-AF size and shape being generally chosen experimentally, hence decreasing the overall reliability of the method. In this paper, we propose a method for an automatic data driven CS-AF area selection, which removes the need for the user input. The AF samples picked by the here-proposed algorithm ensure the optimal amount of data for the sparse TFD reconstruction, resulting in higher TFD concentration and faster sparse reconstruction algorithm convergence, as shown on examples of both synthetical and real-life signals.
In this paper, we propose a robust direction-ofarrival (DOA) estimation algorithm in the context of sparse reconstruction, where some array sensors are mis-calibrated. In this case, conventional DOA estimation algorithms suffer from degraded performance or even failed operations. In the proposed approach, the mis-calibrated sensor observations are treated as outliers, and a weighting factor is adaptively optimized and applied to each sensor in order to effectively mitigate the effect of the outliers. An algorithm based on the maximum correntropy criterion is then developed to yield robust DOA estimation. Simulation results are presented to verify the effectiveness and superiority of the proposed approach compared with conventional DOA estimation algorithms.
Blind Source Separation (BSS) plays a key role to analyze multichannel data since it aims at recovering unknown underlying elementary sources from observed linear mixtures in an unsupervised way. In a large number of applications, multichannel measurements contain corrupted entries, which are highly detrimental for most BSS techniques. In this article, we introduce a new robust BSS technique coined robust Adaptive Morphological Component Analysis (rAMCA). Based on sparse signal modeling, it makes profit of an alternate reweighting minimization technique that yields a robust estimation of the sources and the mixing matrix simultaneously with the removal of the spurious outliers. Numerical experiments are provided that illustrate the robustness of this new algorithm with respect to aberrant outliers on a wide range of blind separation instances. In contrast to current robust BSS methods, the rAMCA algorithm is shown to perform very well when the number of observations is close or equal to the 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.
We present a blind source separation algorithm named GCC-NMF that combines unsupervised dictionary learning via non-negative matrix factorization (NMF) with spatial localization via the generalized cross correlation (GCC) method. Dictionary learning is performed on the mixture signal, with separation subsequently achieved by grouping dictionary atoms, at each point in time, according to their spatial origins. The resulting source separation algorithm is simple yet flexible, requiring no prior knowledge or information. Separation quality is evaluated for three tasks using stereo recordings from the publicly available SiSEC signal separation evaluation campaign: 3 and 4 concurrent speakers in reverberant environments, speech mixed with real-world background noise, and noisy recordings of a moving speaker. Performance is quantified using perceptually motivated and SNR-based measures with the PEASS and BSS Eval toolkits, respectively. We evaluate the effects of model parameters on separation quality, and compare our approach with other unsupervised and semi-supervised speech separation and enhancement approaches. We show that GCC-NMF is a flexible source separation algorithm, outperforming task-specific approaches in each of the three settings, including both blind as well as several informed approaches that require prior knowledge or information.
This paper depicts an improved speech enhancement method based on wavelets techniques, with the goal of ameliorating the speech quality for mobile phones. In the developed algorithm, optimized filters are designed and used as mothers wavelets for the classical algorithm of speech enhancement based on discrete wavelet transform. The cutoff frequency of the optimized wavelets filters is iteratively adjusted in order to satisfy the perfect reconstruction conditions. The evaluation of performances in the term of the noise reduction and the perceptual quality proves the efficiency of the optimized algorithm in the field of the noise reduction. The developed algorithm is evaluated for different noisy conditions with stationary and non stationary noise.
The concept of simultaneous source has recently become of interest in seismic exploration, due to its efficient or economic acquisition or both. The blended data overlapped between shot records are acquired in simultaneous source acquisition. Separating the blended data and recovering the single-shot seismic signals (the recovery) are of great importance in the scenario of current workflows, which can be called seismic simultaneous source separation. In the context of general random time-dithering firing, we propose an alternative method to separate the blended data by combining patchwise dictionary learning with sparse inversion, in which the dictionary is directly learned from the measured blended data. Apart from the sparse coding used for the coefficients, an additional regularization term on the dictionary is particularly designed to remove the severe interference noise. The efficient and flexible alternating direction method of multipliers (ADMM) is used to update the dictionary in the used alternating optimization scheme. The results obtained from the synthetic and real examples reasonably suggest that the separated seismic signals by using dictionary learning are more accurate and robust compared with that using the fixed transform basis, such as the local discrete cosine transform. The learned dictionary tailors for the recovery and is similar to the local seismic waveform, which improves the sparsity of the recovery substantially and is highly advantageous for producing the promised results.
In this paper, we introduce;the effective uses of Gerschgorin radii of the unitary transformed covariance matrix for source number estimation. There are two approaches; likelihood and heuristic, used for developing the detection criteria. The likelihood approach combines the Gerschgorin radii to the well-known source number detectors and improves their detection performances for Gaussian and white noise processes. It is verified that the Gerschgorin likelihood estimators (GLE), are the Gerschgorin MDL criterion does not tend to underestimate at small or moderate data samples. The heuristic approach applying the Gerschgorin disk estimator (GDE) developed from the projection concept, overcomes the problem in cases of small data samples, an unknown noise model, and data dependency. Furthermore, the detection performances of both approaches through the suggested rotations and averaging can be further improved. Finally, the proposed and existing criteria are evaluated in various conditions by using simulated and measured experimental data.
To achieve better mitigation of both cochannel interference (CCI) and intersymbol interference, a new structure using generalized estimation of multipath signals in conjunction with maximal-ratio combining diversity for wireless communications over multipath channels is introduced. In this structure, the signal replicas received from multiple paths are first independently produced by a bank of blind spatial filters and then constructively combined by a diversity combining receiver for final signal estimate. The new scheme can be applied on single antenna array or between multiple antenna subarrays. It will be shown, from both theoretical analysis and numerical experiments, that the new scheme provides both space diversity gains and path diversity gains while suppressing the CCIs.
Blind Source Separation is a widely used technique to analyze multichannel
data. In many real-world applications, its results can be significantly
hampered by the presence of unknown outliers. In this paper, a novel algorithm
coined rGMCA (robust Generalized Morphological Component Analysis) is
introduced to retrieve sparse sources in the presence of outliers. It
explicitly estimates the sources, the mixing matrix, and the outliers. It also
takes advantage of the estimation of the outliers to further implement a
weighting scheme, which provides a highly robust separation procedure.
Numerical experiments demonstrate the efficiency of rGMCA to estimate the
mixing matrix in comparison with standard BSS techniques.
In this paper, an improved version of the noncircular complex FastICA (nc-FastICA) algorithm is proposed for the separation of digital communication signals. Compared with the original nc-FastICA algorithm, the proposed algorithm is asymptotically efficient for digital communication signals, i.e., its estimation error can be made much smaller by adaptively choosing the approximate optimal nonlinear function. Thus, the proposed algorithm can have a significantly improved performance for the separation of digital communication signals. Simulations confirm the efficiency of the proposed algorithm.
Blind source separation (BSS) techniques have traditionally been applied in wireless communication systems to separate signals of interest from multiple sources or users in the absence of training data. Such techniques have received comparatively little attention to date in the context of radar systems, and this is mainly because the signal needed for matched filtering (coherent processing) is known a priori. In practice, active and passive radar systems are required to operate in a congested spectrum where an effective interference mitigation capability is critical to successful operation. This study considers the application of the generalised estimation of multipath signals (GEMS) algorithm for BSS to estimate interference waveforms present in the same frequency channel as the signal of interest (SOI). Interference components at the receiving node(s) of the system are reconstructed using these estimates, with site-dependent complex-scales, time-delays and Doppler-shifts to account for multipath effects, and then subtracted from the data in the time domain. A practical demonstration of the proposed method is illustrated using real data from an experimental high frequency radar system that receives a mixture of frequency-modulated and amplitude-modulated continuous waveforms.
A novel method of single-channel source separation based on independent component analysis (ICA) is presented in this study. The method utilizes the generalized period character of radar signals to structure a multi-dimensional matrix and then uses said matrix to accomplish ICA. Simulation results demonstrate the proposed method’s effectiveness.
A new direction-of-arrival estimator for coherent signals in spatially correlated noise is devised in this paper. By constructing a set of fourth-order cumulant based Toeplitz matrices, the coherent signals can be decorrelated. Moreover, by utilizing the joint diagonalization structure of these Toeplitz matrices, a new cost function that does not require any a priori information of the source number is developed. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.
We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function with Lipschitzian gradient, a nonsmooth proximable function, and linear composite functions. This is a full splitting approach, in the sense that the gradient and the linear operators involved are applied explicitly without any inversion, while the nonsmooth functions are processed individually via their proximity operators. This work brings together and notably extends several classical splitting schemes, like the forward–backward and Douglas–Rachford methods, as well as the recent primal–dual method of Chambolle and Pock designed for problems with linear composite terms.
An image edge detection method of river regime is presented for river model images. This method of self-adaptive thresholding Canny edge detection can extracts the edges of river regime automatically. It not only inherits the advantages of traditional Canny Algorithm, but also uses the improved maximum variance ratio method to calculate the values of Canny gradient threshold self-adaptively. And on this basis, morphological connected domain segmentation be used to suppress the interference edge of the image. This method achieves the automatic identification and extraction of river regime of the model. Tests showed that proposed algorithm has good robustness and high extraction precision, so that the next step of width measurement will be easier and preciser.
Blind separation of sparse sources (BSSS) is discussed. The BSSS method based on the conventional K-means clustering is very fast and is also easy to implement. However, the accuracy of this method is generally not satisfactory. The contribution of the vector x(t) with different modules is theoretically proved to be unequal, and a weighted K-means clustering method is proposed on this grounds. The proposed algorithm is not only as fast as the conventional K-means clustering method, but can also achieve considerably accurate results, which is demonstrated by numerical experiments.
The problem of underdetermined blind audio source separation is usually addressed under the framework of sparse signal representation. In this paper, we develop a novel algorithm for this problem based on compressed sensing which is an emerging technique for efficient data reconstruction. The proposed algorithm consists of two stages. The unknown mixing matrix is firstly estimated from the audio mixtures in the transform domain, as in many existing methods, by a K-means clustering algorithm. Different from conventional approaches, in the second stage, the sources are recovered by using a compressed sensing approach. This is motivated by the similarity between the mathematical models adopted in compressed sensing and source separation. Numerical experiments including the comparison with a recent sparse representation approach are provided to show the good performance of the proposed method.
In this paper, we consider the problem of separation of unknown number of sources from their underdetermined convolutive mixtures via time-frequency (TF) masking. We propose two algorithms, one for the estimation of the masks which are to be applied to the mixture in the TF domain for the separation of signals in the frequency domain, and the other for solving the permutation problem. The algorithm for mask estimation is based on the concept of angles in complex vector space. Unlike the previously reported methods, the algorithm does not require any estimation of the mixing matrix or the source positions for mask estimation. The algorithm clusters the mixture samples in the TF domain based on the Hermitian angle between the sample vector and a reference vector using the well known k -means or fuzzy c -means clustering algorithms. The membership functions so obtained from the clustering algorithms are directly used as the masks. The algorithm for solving the permutation problem clusters the estimated masks by using k -means clustering of small groups of nearby masks with overlap. The effectiveness of the algorithm in separating the sources, including collinear sources, from their underdetermined convolutive mixtures obtained in a real room environment, is demonstrated.
In this paper, we propose a new blind source separation (BSS) method called TIme–Frequency Ratio Of Mixtures (TIFROM) which uses time–frequency (TF) information to cancel source signal contributions from a set of linear instantaneous mixtures of these sources. Unlike previously reported TF BSS methods, the proposed approach only requires slight differences in the TF distributions of the considered signals: it mainly requests the sources to be cancelled to be “visible”, i.e. to occur alone in a tiny area of the TF plane, while they may overlap in all the remainder of this plane. By using TF ratios of mixed signals, it automatically determines these single-source TF areas and identifies the corresponding parts of the mixing matrix. This approach sets no conditions on the stationarity, independence or non-Gaussianity of the sources, unlike classical independent component analysis methods. It achieves complete or partial BSS, depending on the numbers N and P of sources and observations and on the number of visible sources. It is therefore of interest for underdetermined mixtures (i.e. N>P), which cannot be processed with classical methods. Detailed results concerning mixtures of speech and music signals are presented and show that this approach yields very good performance.
We give a general overview of the use and possible misuse of blind source separation (BSS) and independent component analysis (ICA) in the context of neuroinformatics data processing. A clear emphasis is given to the analysis of electrophysiological recordings, as well as to functional magnetic resonance images (fMRI). Two illustrative examples include the identification and removal of artefacts in both kinds of data, and the analysis of a simple fMRI. A second part of the paper addresses a set of currently open challenges in signal processing. These include the identification and analysis of independent subspaces, the study of networks of functional brain activity, and the analysis of single-trial event-related data.
We consider the class of iterative shrinkage-thresholding algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods, which can be viewed as an ex- tension of the classical gradient algorithm, is attractive due to its simplicity and thus is adequate for solving large-scale problems even with dense matrix data. However, such methods are also known to converge quite slowly. In this paper we present a new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically. Initial promising nu- merical results for wavelet-based image deblurring demonstrate the capabilities of FISTA which is shown to be faster than ISTA by several orders of magnitude.
Multivariate analysis methods such as independent component analysis (ICA) have been applied to the analysis of functional magnetic resonance imaging (fMRI) data to study brain function. Because of the high dimensionality and high noise level of the fMRI data, order selection, i.e., estimation of the number of informative components, is critical to reduce over/underfitting in such methods. Dependence among fMRI data samples in the spatial and temporal domain limits the usefulness of the practical formulations of information-theoretic criteria (ITC) for order selection, since they are based on likelihood of independent and identically distributed (i.i.d.) data samples. To address this issue, we propose a subsampling scheme to obtain a set of effectively i.i.d. samples from the dependent data samples and apply the ITC formulas to the effectively i.i.d. sample set for order selection. We apply the proposed method on the simulated data and show that it significantly improves the accuracy of order selection from dependent data. We also perform order selection on fMRI data from a visuomotor task and show that the proposed method alleviates the over-estimation on the number of brain sources due to the intrinsic smoothness and the smooth preprocessing of fMRI data. We use the software package ICASSO (Himberg et al. [ 2004]: Neuroimage 22:1214-1222) to analyze the independent component (IC) estimates at different orders and show that, when ICA is performed at overestimated orders, the stability of the IC estimates decreases and the estimation of task related brain activations show degradation.
In this paper, the effective using of Gerschgorin radii for source number detection is introduced. In practical projects, we do not know any prior information. For example, there may have several sources, and some sources are probably very near, and some also may have different SNRs (signal-to-noise ratio). Here we use a new improved Gerschgorin radii method (NDGE) for source number detection. Firstly, in order to deflate the radii, the covariance matrix is transformed with a unitary matrix. Then, the criterion of Gerschgorin radii is modified with weighing and averaging. Finally, the result of computer simulations shows that this new method can solve the problem well.
A novel high-resolution time-frequency representation method is proposed for source detection and classification in over-the-horizon radar (OTHR) systems. A data-dependent kernel is applied in the ambiguity domain to capture the target signal components, which are then resolved using root-MUSIC based coherent spectrum estimation. This two-step procedure is particularly effective for analysing a multicomponent signal with time-varying complex time-Doppler signatures. By using the different time-Doppler signatures, important target manoeuvring information, which is difficult to extract using other linear and bilinear time-frequency representation methods, can be easily revealed using the proposed method