Signal Separation Problem Research Articles

Signal Separation Operator Based on Wavelet Transform for Non-Stationary Signal Decomposition.

This paper develops a new frame for non-stationary signal separation, which is a combination of wavelet transform, clustering strategy and local maximum approximation. We provide a rigorous mathematical theoretical analysis and prove that the proposed algorithm can estimate instantaneous frequencies and sub-signal modes from a blind source signal. The error bounds for instantaneous frequency estimation and sub-signal recovery are provided. Numerical experiments on synthetic and real data demonstrate the effectiveness and efficiency of the proposed algorithm. Our method based on wavelet transform can be extended to other time-frequency transforms, which provides a new perspective of time-frequency analysis tools in solving the non-stationary signal separation problem.

Complex-Valued FastICA Estimator with a Weighted Unitary Constraint: A Robust and Equivariant Estimator

Independent component analysis (ICA), as a statistical and computational approach, has been successfully applied to digital signal processing. Performance analysis for the ICA approach is perceived as a challenging task to work on. This contribution concerns the complex-valued FastICA algorithm in the range of ICA over the complex number domain. The focus is on the robust and equivariant behavior analysis of the complex-valued FastICA estimator. Although the complex-valued FastICA algorithm as well as its derivatives have been widely used methods for approaching the complex blind signal separation problem, rigorous mathematical treatments of the robust measurement and equivariance for the complex-valued FastICA estimator are still missing. This paper strictly analyzes the robustness against outliers and separation performance depending on the global system. We begin with defining the influence function (IF) of complex-valued FastICA functional and followed by deriving its closed-form expression. Then, we prove that the complex-valued FastICA algorithm based on the optimizing cost function is linear-equivariant, depending only on the source signals.

A Novel Enhancement Approach Following MVMD and NMF Separation of Complex Snoring Signals.

Snoring is a prominent characteristic of sleep-disordered breathing, and its detection is critical for determining the severity of the upper airway obstruction and improving daily quality of life. Home snoring analysis is a highly invasive method, but it becomes challenging when a sleeping partner also snores, leading to distorted evaluations in such environments. In this article, we tackle the problem of complex snore signal separation of multiple snorers. This article introduces two audio-based methods that efficiently extract an individual's snoring signal, allowing for the analysis of sleep-breathing disorders in a normal sleeping environment without isolating individuals. In the first method, Principal Component Analysis (PCA) identifies the source components from the finite number of modes generated by the decomposition of the snoring mixture using Multivariate Variational Mode Decomposition (MVMD). The second method applies Blind Source Separation (BSS) based on Non-Negative Matrix Factorization (NMF) to separate the single-channel snoring mixture. Furthermore, the decomposed signals are tuned using the iterative enhancement algorithm to adequately match the source snoring signals. These methods were evaluated by simulating various real-time snoring recordings of 7 subjects (2 men, 2 women, and 3 children). The correlation coefficient between the source and its separated signal was computed to assess the separation results, exhibiting good performance of the methods used. The enhancement approach also demonstrated its efficiency by increasing the correlation over to 80% in both methods. The experimental results show that the proposed algorithms are effective and practical for separating mixed snoring signals.

Separating method for multi-source vibration signals in ultra-weak fiber Bragg grating distributed acoustic sensors

Mixing multi-source vibration signals presents a major challenge in target recognition in distributed fiber optic acoustic sensor systems. This article proposes a deep learning method for separating ultra-weak fiber Bragg grating (UW-FBG) distributed acoustic sensor (DAS) multi-source signals. An experimental setup is constructed to create vibration environments for knocking, fan vibration, and steel pipe friction. The UW-FBG DAS system is used to collect single-source vibration signals, as well as two-source and three-source mixed vibration signals. First, a wavelet denoising algorithm is used to preprocess the data. Second, the datasets are constructed for simulated mixed signals and measured mixed signals. The Conv-TasNet deep learning network is utilized to separate DAS vibration signals. Results demonstrate that the proposed method can separate mixed signals of vibration, fan, and steel pipe friction sources, obtaining the corresponding time–frequency entropy similarity of 97.5%, 92.8% and 90.2%, and compared with commonly used multi-source signal separation methods, it has advantages in separation performance and separation time, and exhibits good robustness in different signal environments. This finding the efficacy of the separation method and provides a valuable solution for DAS multi-source signal separation problems in complex environments.

An Antijamming Method Based on Multichannel Singular Spectrum Analysis and Affinity Propagation for UWB Ranging Sensors

Ultra-wideband impulse radio system has received extensive attention due to their high resolution and poor interception possibility. But the specific electromagnetic threat posed by its complex work environment cannot be ignored. In all kinds of active jamming signals, smart noise jamming plays an important role in modern radar electronic warfare, and most traditional anti-jamming methods have less suppression effect. In this paper, the mechanism of smart noise jamming on the UWB ranging sensor is discussed first. On this basis, an anti-smart noise jamming method based on multichannel singular spectrum analysis and kurtosis characteristic is proposed. Experiments show that smart noise jamming is more threatening to the UWB system than other noise modulation jamming. And the improved algorithm proposed in this paper can suppress the jamming better. After the anti-jamming processing, the average detection probability can reach more than 95%. Meanwhile, the method is improved by adding the affinity propagation (AP) clustering algorithm to solve the underdetermined signal separation problem in the case of compound jamming. The advantage is that it does not have to estimate the number of signals first. Even if the SJR is -10 dB, the waveform similarity between the separation signal and the source signal can reach 0.7 or more.

A Survey of Optimization Methods for Independent Vector Analysis in Audio Source Separation

With the advent of the era of big data information, artificial intelligence (AI) methods have become extremely promising and attractive. It has become extremely important to extract useful signals by decomposing various mixed signals through blind source separation (BSS). BSS has been proven to have prominent applications in multichannel audio processing. For multichannel speech signals, independent component analysis (ICA) requires a certain statistical independence of source signals and other conditions to allow blind separation. independent vector analysis (IVA) is an extension of ICA for the simultaneous separation of multiple parallel mixed signals. IVA solves the problem of arrangement ambiguity caused by independent component analysis by exploiting the dependencies between source signal components and plays a crucial role in dealing with the problem of convolutional blind signal separation. So far, many researchers have made great contributions to the improvement of this algorithm by adopting different methods to optimize the update rules of the algorithm, accelerate the convergence speed of the algorithm, enhance the separation performance of the algorithm, and adapt to different application scenarios. This meaningful and attractive research work prompted us to conduct a comprehensive survey of this field. This paper briefly reviews the basic principles of the BSS problem, ICA, and IVA and focuses on the existing IVA-based optimization update rule techniques. Additionally, the experimental results show that the AuxIVA-IPA method has the best performance in the deterministic environment, followed by AuxIVA-IP2, and the OverIVA-IP2 has the best performance in the overdetermined environment. The performance of the IVA-NG method is not very optimistic in all environments.

Improving sparse representation with deep learning: A workflow for separating strong background interference

Revealing hidden reservoirs that are severely shielded by strong background interference (SBI) is critical to subsequent refined interpretation. To enhance the characterization of these reservoirs, current interpretation workflows merge multiple attribute information, necessitating intensive human expertise. As an alternative, we regard SBI suppression as a signal separation problem and develop a workflow to suppress SBI by cascading a sparse representation method and deep learning. SBI has coherent morphological characteristics in seismic sections; reservoir seismic responses, such as channels and karst caves, have a narrow spatial distribution, exhibiting abrupt morphological characteristics. As their morphologies differ, we select two 2D sparse representation dictionaries to identify their individual components. Through the morphological component analysis (MCA) technique, we can obtain adequate SBI separation results. However, the MCA separation is inevitably limited because 2D dictionaries cannot adequately represent 3D structures, but 3D dictionaries are not viable due to computing constraints. As an extension, we use 3D deep learning to improve the separation results based on the 2D MCA results. Specifically, the network is fed with training samples from a region with better SBI suppression results obtained by the MCA method. After learning a direct mapping from noisy data to SBI, the network can improve the separation results and remove more SBI than the previous conventional method. Field data experiments demonstrate that our separation workflow successfully enhances reservoir structures after removing SBI.

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.

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.

Accurate SAR Image Recovery From RFI Contaminated Raw Data by Using Image Domain Mixed Regularizations

Radio frequency interference (RFI) suppression is a hot topic in synthetic aperture radar (SAR) imaging. Mathematically, the RFI suppression problem can be considered as an underdetermined signal separation problem to extract the signal of interest (SOI) from the RFI contaminated raw data. The regularization-based method can exploit both the prior knowledge of RFI and SOI and, therefore, has the advantage of solving the underdetermined problem and preserving the information of SOI. Current regularization methods make use of the RFI prior well by exploiting low-rank representation (LRR) or sparse representation (SR), but the prior knowledge of SOI has not been sufficiently studied and used. In some literature, the sparsity of the raw data or range profile was exploited to formulate the regularization term, which we found to be inadequate in describing the SOI property. In this article, we explore the features of SAR images and propose an RFI suppression model with a combination of multiple image domain regularizations to preserve different types of targets. An efficient solution to the optimization problem is proposed based on the alternating direction multiplier method (ADMM). The proposed method can accurately recover both the sparse strong targets, and the nonsparse regions in the illuminated area and its performance is validated by measured data.

Separation of dual-tracer PET signals using a deep stacking network

In this study, a method based on a deep stacking network is proposed to solve the signal separation problem of dynamic dual-tracer PET. The advantage of this method is that it avoids requirements for prior information of tracers, and a staggered injection. The proposed model is pre-trained with restricted Boltzmann machines and fine-tuned in a manner, which the output of the last training epoch was used as additional input in the current epoch to update the model parameters. We train the network to learn the complex relationship between dual-tracer time-activity curves and separated single tracer data using a mean square error objective function. Monte Carlo simulations are employed to test the accuracy and robustness of the proposed method on the total counts and reconstruction algorithm. Quantification results show that the proposed method outperforms the existing approach. Experiments with real data further validate previous results on synthetic data.

Removing residual airborne sensor motion for measuring seismic signals from a drone

Acquiring seismic data using drones requires excellent knowledge of the drone’s motion since positional measurements made from an airborne sensor represent a combination of sensor and ground motion. Recent advancements in laser Doppler vibrometry and repeat lidar surveys show that the frequency and resolution of non-contact motion measurements is increasing to the point necessary for measuring seismic signals. We explore the conditions under which separation of sensor motion from ground motion can be accomplished in practice. We assume (i) that the translation and rotation of a stabilized airborne sensor follows an analytic form in time that is either known or can be estimated from the sensor’s measurements, (ii) that the seismic signal we observe has compact support contained within the measurement window, and (iii) that the ground motion can be described by a rigid translation. We analyze the effectiveness of our signal separation problem as a function of peak signal, sensor noise level, sensor rotation angle, and sensor point sampling density by defining a boundary where SNR = 0 dB for various combinations of these parameters. We find that under the set of assumptions, lower rotation angles, lower sensor noise, and denser point samplings on the ground provide better signal separation using our method.

Density estimation using entropy maximization for semi-continuous data

Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. Such data appear in several real-life situations like blind signal separation problems, modeling of loss data in finance and insurance, sales of consumer goods, daily precipitation data, to name a few. In this paper, we present a novel algorithm to estimate the density function for semi-continuous data using the principle of maximum entropy. Unlike existing methods in the literature, our algorithm provides a consistent estimate of the true maximum entropy distribution and considers both the discrete and continuous parts of the semi-continuous distribution simultaneously. Using simulations, we show that the estimate of the entropy produced by our algorithm has significantly less bias compared to existing methods. An application to the daily rainfall data is provided.

Analysis of an adaptive short-time Fourier transform-based multicomponent signal separation method derived from linear chirp local approximation

Recently, a direct method of the time–frequency approach, called the signal separation operator (SSO), which is based on sinusoidal signal approximation, was introduced to solving the inverse problem of multicomponent signal separation. In a very recent paper “Direct signal separation via extraction of local frequencies with adaptive time-varying parameters”, the authors obtained a more accurate component recovery formula derived from the linear chirp (also called linear frequency modulation signal) approximation at any local time. However the theoretical analysis of the recovery formula derived from linear chirp local approximation has not been studied there. In this paper, we carry out the analysis of SSO based on the adaptive short-time Fourier transform (STFT). We study both the sinusoidal signal-based model and the linear chirp-based model, and obtain the error bounds for the instantaneous frequency estimation and component recovery. The error bounds are derived by studying the approximation to the STFT of each component and by the assumption of the decrease of the Fourier transform of the window function for STFT. These results provide a mathematical guarantee to the proposed adaptive STFT-based non-stationary multicomponent signal separation method. In addition, experiments are provided to illustrate the general theory.

Accurate AM-FM signal demodulation and separation using nonparametric regularization method

In this paper we propose a novel adaptive nonparametric regularization (NPR) method for solving optimization problems with linear constraint. The regular parameter in NPR algorithm is adaptively updated. We prove that the NPR is convergent and provide an early stop method (ESM) with a termination criterion to handle the perturbation problem which is unsolved in other methods such as the augmented Lagrange method (ALM). We then introduce a new differential operator which can absolutely annihilate the amplitude-modulated and frequency-modulated (AM-FM) signals (AM-FM operator, AFO). The proposed operator is a precise operator and thus can obtain a more accurate solution in operator based signal demodulation and separation problems. We apply the NPR algorithm in signal demodulation and separation based on the AFO and propose signal demodulation (NPR-AFOSD) and separation (NPR-AFOSS) algorithms. The experimental results on both synthetic AM-FM signals and the real-life data demonstrate that the proposed demodulation and separation methods are more effective and robust than the state-of-the-art methods.

A New Method for Separating EMI Signal Based on CEEMDAN and ICA

Aiming at the problem of electromagnetic interference signal separation, we propose a single-channel blind source separation method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and independent component analysis (ICA). Firstly, decompose the mixed interference signal by CEEMDAN to obtain a series of intrinsic mode functions (IMF). Secondly, combine them into a new multi-dimensional signal and solve its correlation matrix, and use singular value decomposition to obtain the eigenvalues of the matrix, and then use it to estimate the source number. Thirdly, select those IMFs whose correlation coefficients with the observed signal are bigger and regard them together with the original signal after denoising as new observed signals. Finally, recover the source signals by fast independent component analysis (Fast-ICA). We also extend our method to multi-channel BBS, and experiment results show that our method can eliminate unnecessary noise in the signal and perform well.

Blind signal separation based on widely linear complex autoregressive process of order one

In this paper, the blind signal separation problem of complex baseband signal is addressed. A widely linear complex autoregressive process of order one is employed to represent the temporal structure of complex sources. We formulate a new contrast function by a convex combination of generalized autocorrelations and the statistics of the innovation. And the proposed contrast function is optimized by gradient method. Simulation results show that the proposed algorithm is better than the comparison algorithm in convergence speed and convergence accuracy.

EnerGAN++: A Generative Adversarial Gated Recurrent Network for Robust Energy Disaggregation

Energy disaggregation, namely the separation of the aggregated household energy consumption signal into its additive sub-components, bears resemblance to the signal (source) separation problem and poses several challenges, not only as an ill-posed problem, but also, due to unsteady appliance signatures, abnormal behaviour that is usually detected in appliances operation and the existence of noise in the aggregated signal. In this paper, we propose EnerGAN++, a model based on Generative Adversarial Networks (GAN) for robust energy disaggregation. We attempt to unify the autoencoder (AE) and GAN architectures into a single framework, in which the autoencoder achieves a non-linear power signal source separation. EnerGAN++ is trained adversarially using a novel discriminator, to enhance robustness to noise. The discriminator performs sequence classification, using a recurrent convolutional neural network to handle the temporal dynamics of an appliance energy consumption time series. In particular, the proposed architecture of the discriminator leverages the ability of Convolutional Neural Networks (CNN) in rapid processing and optimal feature extraction, among with the need to infer the data temporal character and time dependence. Experimental results indicate the proposed method's superiority compared to the current state of the art.

Using Data Imputation for Signal Separation in High-contrast Imaging

Abstract To characterize circumstellar systems in high-contrast imaging, the fundamental step is to construct a best point-spread function (PSF) template for the noncircumstellar signals (i.e., starlight and speckles) and separate it from the observation. With existing PSF construction methods, the circumstellar signals (e.g., planets, circumstellar disks) are unavoidably altered by overfitting and/or self-subtraction, making forward modeling a necessity to recover these signals. We present a forward modeling–free solution to these problems with data imputation using sequential nonnegative matrix factorization (DI-sNMF), which first converts this signal separation problem to a “missing data” problem in statistics by flagging the regions that host circumstellar signals as missing data, then attributes PSF signals to these regions. We mathematically prove it to have negligible alteration to circumstellar signals when the imputation region is relatively small, which thus enables precise measurement of these circumstellar objects. We apply it to simulated point-source and circumstellar disk observations to demonstrate its proper recovery of them. We apply it to Gemini Planet Imager K1-band observations of the debris disk surrounding HR 4796A, finding a tentative trend that the dust is more forward scattering as the wavelength increases. We expect DI-sNMF to be applicable to other general scenarios where the separation of signals is needed.

Adaptive blind equalization for a MIMO chaotic communication system

There exist few blind solutions for chaotic MIMO channel equalization. In this work, a chaotic MIMO channel equalization framework is proposed. The objective function to be minimized in the proposed solution is obtained by adopting the objective function developed for chaotic SISO channel equalization. Furthermore, an optimum filter that minimizes the proposed cost function is designed to recover chaotic input signals assuming that the channel is known. The stationary point of the adaptive solution is equal to the optimal filter if the adaptive filter coefficients change sufficiently slowly. The adaptive solution is contrasted with the optimum filter in terms of mean-square error and bit error rate performances. In addition, the proposed solution reconstructs chaotic input signals at the same time. Consequently, it can be applied to multiple signal separation problems as well.