Blind Separation of Noisy Multivariate Data Using Second - Order Statistics
نویسنده
چکیده
A second-order method for blind source separation of noisy instantaneous linear mixtures is presented and analyzed for the case where the signal order k and noise covariance GGH are unknown. Only a data set X of dimension n> k and of sample size m is observed, where X = AP + GW. The quality of separation depends on source-observation ratio }, the degree of spectral diversity, and the second-order nonstationarity of the underlying sources. The algorithm estimates the Second-Order separation transform A, the signal Order, and Noise, and is therefore referred to as SOON. SOON iteratively estimates: 1) k using a scree metric, and 2) the values of AP, G, and W using the Expectation-Maximization (EM) algorithm, where W is white noise and G is diagonal. The final step estimates A and the set of k underlying sources P using a variant of the joint diagonalization method, where P has k independent unit-variance elements. Tests using simulated Auto Regressive (AR) gaussian data show that SOON improves the quality of source separation in comparison to the standard second-order separation algorithms, i.e., Second-Order Blind Identification (SOBI) [3] and SecondOrder Non-Stationary (SONS) blind identification [4]. The sensitivity in performance of SONS and SOON to several algorithmic parameters is also displayed in these experiments. To reduce sensitivities in the pre-whitening step of these algorithms, a heuristic is proposed by this thesis for whitening the data set; it is shown to improve separation performance. Additionally the application of blind source separation techniques to remote sensing data is discussed. Analysis of remote sensing data collected by the AVIRIS multichannel visible/infrared imaging instrument shows that SOON reveals physically significant dynamics within the data not found by the traditional methods of Principal Component Analysis (PCA) and Noise Adjusted Principal Component Analysis (NAPCA). Thesis Supervisor: David H. Staelin Title: Professor of Electrical Engineering
منابع مشابه
Research of Blind Signals Separation with Genetic Algorithm and Particle Swarm Optimization Based on Mutual Information
Blind source separation technique separates mixed signals blindly without any information on the mixing system. In this paper, we have used two evolutionary algorithms, namely, genetic algorithm and particle swarm optimization for blind source separation. In these techniques a novel fitness function that is based on the mutual information and high order statistics is proposed. In order to evalu...
متن کاملResearch of Blind Signals Separation with Genetic Algorithm and Particle Swarm Optimization Based on Mutual Information
Blind source separation technique separates mixed signals blindly without any information on the mixing system. In this paper, we have used two evolutionary algorithms, namely, genetic algorithm and particle swarm optimization for blind source separation. In these techniques a novel fitness function that is based on the mutual information and high order statistics is proposed. In order to evalu...
متن کاملBlind Separation of Jointly Stationary Correlated Sources
The separation of unobserved sources from mixed observed data is a fundamental signal processing problem. Most of the proposed techniques for solving this problem rely on independence or at least uncorrelation assumption for source signals. This paper introduces a technique for cases that source signals are correlated with each other. The method uses Wold decomposition principle for extracting ...
متن کاملDiagnosing Manufacturing Variation Using Second-Order and Fourth-Order Statistics
This article discusses a method that can aid in diagnosing root causes of product and process variability in complex manufacturing processes, when large amounts of multivariate in-process measurement data are available. A linear structured model, similar to the standard factor analysis model, is used to generically represent the variation patterns that result from the root causes. Blind source ...
متن کاملIndependent Component Analysis as a tool for the dimensionality reduction and the representation of hyperspectral images
Independent Component Analysis (ICA) is a multivariate data analysis process largely sudied these last years in the signal processing community for blind source separation. This paper proposes to show the interest of ICA as a tool for unsupervised analysis of hyperspectral images. The commonly used Principal Component Analysis (PCA) is the mean square optimal projection for gaussian data leadin...
متن کامل