Separation of stationary and non-stationary sources with a generalized eigenvalue problem
نویسندگان
چکیده
Non-stationary effects are ubiquitous in real world data. In many settings, the observed signals are a mixture of underlying stationary and non-stationary sources that cannot be measured directly. For example, in EEG analysis, electrodes on the scalp record the activity from several sources located inside the brain, which one could only measure invasively. Discerning stationary and non-stationary contributions is an important step towards uncovering the mechanisms of the data generating system. To that end, in Stationary Subspace Analysis (SSA), the observed signal is modeled as a linear superposition of stationary and non-stationary sources, where the aim is to separate the two groups in the mixture. In this paper, we propose the first SSA algorithm that has a closed form solution. The novel method, Analytic SSA (ASSA), is more than 100 times faster than the state-of-the-art, numerically stable, and guaranteed to be optimal when the covariance between stationary and non-stationary sources is time-constant. In numerical simulations on wide range of settings, we show that our method yields superior results, even for signals with time-varying group-wise covariance. In an application to geophysical data analysis, ASSA extracts meaningful components that shed new light on the Pi 2 pulsations of the geomagnetic field.
منابع مشابه
Blind 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 کاملBlind Source Separation via Generalized Eigenvalue Decomposition
In this short note we highlight the fact that linear blind source separation can be formulated as a generalized eigenvalue decomposition under the assumptions of non-Gaussian, non-stationary, or non-white independent sources. The solution for the unmixing matrix is given by the generalized eigenvectors that simultaneously diagonalize the covariance matrix of the observations and an additional s...
متن کاملRecursive complex BSS via generalized eigendecomposition and application in image rejection for BPSK
Under the assumptions of non-Gaussian, non-stationary, or non-white independent sources, linear blind source separation can be formulated as generalized eigenvalue decomposition. Here we provide an elegant method of doing this on-line, instead of waiting for a sufficiently large batch of data. This is done through a recursive generalized eigendecomposition algorithm that tracks the optimal solu...
متن کاملGeneralized Eigenvector Blind Speech Separation under Coherent Noise in a Gsc Configuration
This paper deals with a new technique for multi-channel separation of speech signals from convolutive mixtures under coherent noise. We demonstrate how the scaled transfer functions from the sources to the microphones can be estimated even in the presence of stationary coherent noise. The key to this are generalized eigenvalue decompositions of the power spectral density (PSD) matrices of the n...
متن کاملIMPLEMENTATION OF EXTENDED KALMAN FILTER TO REDUCE NON CYCLO-STATIONARY NOISE IN AERIAL GAMMA RAY SURVEY
Gamma-ray detection has an important role in the enhancement the nuclear safety and provides a proper environment for applications of nuclear radiation. To reduce the risk of exposure, aerial gamma survey is commonly used as an advantage of the distance between the detection system and the radiation sources. One of the most important issues in aerial gamma survey is the detection noise. Various...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Neural networks : the official journal of the International Neural Network Society
دوره 33 شماره
صفحات -
تاریخ انتشار 2012