Efficient blind nonparametric dependent signal extraction algorithm for determined and underdetermined mixtures

Blind source separation (BSS) consists in processing a set of observed mixed signals to separate them into a set of original components. Most of the current blind separation methods assumes that the source signals are “as statistically independent as possible” given the observed data. In many real-world situations, however, this hypothesis does not hold. In order to cope with such signals, a first geometric method was proposed that separates statistically dependent signals, provided that they are nonnegative and locally orthogonal.This paper presents a new geometric method for the separation of nonnegative source signals which relies on a working assumption that is weaker than local orthogonality. The separation problem is expressed as the identification of relevant facets of the data cone. After a rigorous proof of the proposed method, the details of the separation algorithm are given. Experiments on signals from various origins clearly show the efficiency of the new procedure.

Blind separation for dependent sources and multi-Gaussian sources is a challenging problem. This letter proposes a new adaptive blind source separation algorithm, which is referred to as vector auto-regressive diagonalization (VAR-JD), to deal with this problem. This algorithm estimates demixing matrix by matrix joint JD of a set of matrices containing the estimated VAR coefficients. Compared with traditional adaptive BSS method, which assumes that source signals are mutual independent and no more than one Gaussian source signal exists, the proposed VAR-JD algorithm is not only able to separate independent source signals but also dependent source signals, and there is no demand for the number of Gaussian source signals. Simulation results on the separation of synthetic and communication signals demonstrate the effectiveness of the proposed approach. This latter is important to anti-jamming communications. Moreover, VAR-JD is suitable for determined mixtures and can extend easily to overdetermined mixtures.

In this paper, we address the problem of blind extraction and separation of a continuous chaotic signal from a linear mixture consisting of some chaotic signal and/or random signals. The problem of blind extraction is firstly formulated as a problem of the synchronization-based parameter estimation. Then an efficient least square based parameter estimation method is introduced to determine the desired extracting vector. The proposed blind signal extraction scheme is applicable to blind separation of chaotic signals by formulating the separation problem as the extraction of each chaotic source. Numerical simulation shows that the proposed approach can blindly extract and separate the desired chaotic signals and it is also robust to measurement noise.

Independent component analysis (ICA) has shown much success in blind source separation and channel equalization. Its applications to remotely sensed images are investigated in recent years. Linear spectral mixture analysis (LSMA) has been widely used for subpixel detection and mixed pixel classification in remote sensing image processing and already studied in Chapters 3, 8–10, . It models the spectral signature of an image pixel vector as a linear mixture of spectral signatures of targets present in the image data and the target abundance fractions are assumed to be unknown, but nonrandom constants. This chapter combines these two approaches to one, called ICA-based linear spectral random mixture analysis (LSRMA), which describes an image pixel vector as a random process resulting from a random composition of multiple spectral signatures of distinct targets in the image data. It differs from LSMA in that the abundance fractions of the target signatures in LSRMA are considered to be unknown random independent signal sources. Two major advantages can be benefited from LSRMA. First, LSRMA does not require any prior knowledge of the targets used in the linear mixture model. Second and most importantly, LSRMA models each of target signatures as an independent random signal source so that the spectral variability of target signatures can be captured more effectively in a stochastic manner. The only required knowledge for LSRMA is the number of signal sources, p assumed to be present in the image data. This number is estimated by Neyman-Pearson detection theory-based eigen-thresholding methods to be investigated in Chapter 17.

In this work, the Cumulative Distribution Function (CDF) and the Probability Density Function (PDF) are examined for a data set of finite elements. The CDF and the PDF are valid only for the theoretical asymptotes when the number of elements in the set approaches infinity. The equivalent functions defined for a finite set are currently unknown. In various fields, especially in signal processing, data size is usually statistically limited and more accurate analysis is often required for the validation of new algorithms. In this work, discontinuous CDF (DCDF) is defined and proposed for measuring the ‘statistical distance’ and the ‘statistical error’. These new definitions enable comparisons of different data sets with each other and with the theoretical asymptotic function CDF. The proposed statistical functions are illustrated on Gaussian distributed data.

The extraction of fetal electrocardiogram (FECG) from the composite maternal ECG signal is discussed. This problem can be deduced to blind source extraction. Barros and Cichocki presented an objective function by using blind signal extraction along with prior information about the autocorrelation property of the FECG from the noisy free measurements. However, it is realistic to extract the FECG from noisy measurements. We extend the work for the noisy case and propose a new algorithm for the FECG extraction with additive noise. Simulation results confirm the validity of the proposed method.

There is a large family of contrast (or cost) functions in blind source separation that can yield learning algorithms for extracting single source signals from linear mixtures. One of these families is based on higher order statistics (HOSs), which assumes the statistical independence of source signals and their non-Gaussianity (all except one) in order to successfully extract them one by one. In cases in which source signals exhibit unit variance and the mixing matrix is orthonormal, many HOS contrast functions are equivalent (e.g., kurtosis, fourth cumulant, and fourth moment). However, these contrast functions are estimated in practice from a finite data set, which introduces stochastic errors, so their equivalence has remained uncertain. Our letter introduces error bounds for several sample-based HOS contrast functions, which demonstrate their dependence upon different source signal statistics and, thus, more importantly, provide a foundation for comparing them in terms of accuracy.

As chaotic masking signal refers to a seemingly random and irregular signal occurring in a deterministic system, it is highly confidential to load the signal needed to be transmitted into chaotic masking signal as a carrier signal for transmission.In this paper, an improved information encryption based on lorenz chaotic masking system and speech signal extraction based on joint diagonalization blind extraction algorithm are designed.The performance comparison between the proposed algorithm and FastICA blind extraction algorithm based on negative entropy maximization is analyzed quantitatively and qualitatively in the simulation experiment. The effectiveness of information encryption under chaos masking and the reliability of the algorithm based on joint diagonalization blind extraction are verified.

A time–frequency blind signal separation method applicable to underdetermined mixtures of dependent sources

The time-dependent reliability model of component is developed with the order statistic and the probability differential equation. The relationship between reliability and time and the relationship between failure rate and time are studied. First, the failure mechanism of component is analyzed when random load acts for multiple times, and from the statistic meaning of random load action, the cumulative distribution function and the probability density function of equivalent load are derived with the order statistic. Further, the reliability model of component under random repeated load is built with the stress-strength interference theory. The loading process is described with the Poisson stochastic process, and the time-dependent reliability model of component without strength degeneration and the model with strength degeneration are derived respectively. The result shows that reliablity decreases with time and the failure rate also decreases with time when strength degeneration is not considered and can be neglected. When strength degeneration is obvious and is considered, reliability decreases with time more obviously and the failure rate has the whole feature of bathtub curve.

In the period of real time mechanical analysis and life style detection to the excavation tunnel equipment's cutter head, it is a necessity for the signals sensed by detection unit to be pretreatment processed. It closely concerns with the accuracy and validity of whole mechanical analysis results. By analyzing the features of all possible interference, this paper gives a study on signals initial processing applying method of digital filter and blind signal extraction. Simulation results show that the proposed scheme is effective enough to the mechanical analysis task.

Uniform order statistics generated by two simulation methods are compared by means of Pitman’s measure of closeness. This measure, as a probability, is shown to be asymptotically 1/2. Some results are also established for fixed points of the cumulative distribution function (CDF) for a uniform order statistic. These fixed points are important for calculations involving the joint distribution of these order statistics.

This paper is to deal with the blind extraction problem of chaotic signals by using a linear mixing model. In this model, a novel method to describe the distance function in a high dimensional space is proposed which relates the kernel function to objective function. When adopting the artificial bee colony algorithm (ABCA) as an alternative method to solve a multi-modal optimization problem, its analysis under a Markov chain model is also presented. The simulation results show that the objective function of this article has low complexity, and the artificial bee colony algorithm converges to a local minimum quickly. To be specific, the target function is constructed by combining the advantages of the proliferation exponent and the distance kernel function. The proliferation exponent can reflect the chaotic properties of a signal to a large extent, and the distance kernel can help to describe the statistical properties in a higher dimension. Due to the fact that only one frame of time-delay embedded signal is adopted, the computational complexity of our target function is low. The artificial bee colony algorithm is shown to be advantageous over other swarm algorithms. Although adopting ABCA for our evaluation function seems easy, we analyze why this algorithm can work, in contrast to the fact that most literature only runs some simulations to confirm its usefulness. Our analysis is only for a special case when the number of employed bees is set to be 2 and the process of onlooker bees and scouts are temporarily omitted. With smaller complexity than the methods based on proliferation exponents and kurtosises, simulations show that our method can have excellent performance when evaluated by correlation coefficients.

We give under weak assumptions a complete combinatorial characterization of identifiability for linear mixtures of finite alphabet sources, with unknown mixing weights and unknown source signals, but known alphabet. This is based on a detailed treatment of the case of a single linear mixture. Notably, our identifiability analysis applies also to the case of unknown number of sources. We provide sufficient and necessary conditions for identifiability and give a simple sufficient criterion together with an explicit construction to determine the weights and the source signals for deterministic data by taking advantage of the hierarchical structure within the possible mixture values. We show that the probability of identifiability is related to the distribution of a hitting time and converges exponentially fast to one when the underlying sources come from a discrete Markov process. Finally, we explore our theoretical results in a simulation study. Our work extends and clarifies the scope of scenarios for which blind source separation becomes meaningful.

There are a large variety of applications that require considering sources that usually behave light or strong dependence and this is not the case that common blind signal separation (BSS) algorithms can do. The purpose of this paper is to develop non-parametric BSS algorithm for linear dependent source signals, which is proposed under the framework of contrast method. The contrast function is derived from the Schweizer-Wolff measure of pairwise dependence between the variables. Simulation results show that the proposed algorithm is able to separate the dependent signals and yield ideal performance.