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Register a new userTemporally Nonstationary Component Analysis; Application to Noninvasive Fetal Electrocardiogram Extraction
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Objective: Mixtures of temporally nonstationary signals are very common in biomedical applications. The nonstationarity of the source signals can be used as a discriminative property for signal separation. Herein, a semi-blind source separation algorithm is proposed for the extraction of temporally nonstationary components from linear multichannel mixtures of signals and noises. Methods: A hypothesis test is proposed for the detection and fusion of temporally nonstationary events, by using ad hoc indexes for monitoring the first and second order statistics of the innovation process. As proof of concept, the general framework is customized and tested over noninvasive fetal cardiac recordings acquired from the maternal abdomen, over publicly available datasets, using two types of nonstationarity detectors: 1) a local power variations detector, and 2) a model-deviations detector using the innovation process properties of an extended Kalman filter. Results: The performance of the proposed method is assessed in presence of white and colored noise, in different signal-to-noise ratios. Conclusion and Significance: The proposed scheme is general and it can be used for the extraction of nonstationary events and sample deviations from a presumed model in multivariate data, which is a recurrent problem in many machine learning applications.
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Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral analysis, we propose a data-driven approach to time-frequency analysis that circumvents many of the shortcomings of classic approaches, including the extraction of nonstationary signals with discontinuities in their behavior. The method introduced is equivalent to a {em nonstationary Fourier mode decomposition} (NFMD) for nonstationary and nonlinear temporal signals, allowing for the accurate identification of instantaneous frequencies and their amplitudes. The method is demonstrated on a diversity of time-series data, including on data from cantilever-based electrostatic force microscopy to quantify the time-dependent evolution of charging dynamics at the nanoscale.
This study presents PRISM, a probabilistic simplex component analysis approach to identifying the vertices of a data-circumscribing simplex from data. The problem has a rich variety of applications, the most notable being hyperspectral unmixing in remote sensing and non-negative matrix factorization in machine learning. PRISM uses a simple probabilistic model, namely, uniform simplex data distribution and additive Gaussian noise, and it carries out inference by maximum likelihood. The inference model is sound in the sense that the vertices are provably identifiable under some assumptions, and it suggests that PRISM can be effective in combating noise when the number of data points is large. PRISM has strong, but hidden, relationships with simplex volume minimization, a powerful geometric approach for the same problem. We study these fundamental aspects, and we also consider algorithmic schemes based on importance sampling and variational inference. In particular, the variational inference scheme is shown to resemble a matrix factorization problem with a special regularizer, which draws an interesting connection to the matrix factorization approach. Numerical results are provided to demonstrate the potential of PRISM.
The extraction of nonstationary signals from blind and semi-blind multivariate observations is a recurrent problem. Numerous algorithms have been developed for this problem, which are based on the exact or approximate joint diagonalization of second or higher order cumulant matrices/tensors of multichannel data. While a great body of research has been dedicated to joint diagonalization algorithms, the selection of the diagonalized matrix/tensor set remains highly problem-specific. Herein, various methods for nonstationarity identification are reviewed and a new general framework based on hypothesis testing is proposed, which results in a classification/clustering perspective to semi-blind source separation of nonstationary components. The proposed method is applied to noninvasive fetal ECG extraction, as case study.
Electroencephalogram (EEG) is the recording which is the result due to the activity of bio-electrical signals that is acquired from electrodes placed on the scalp. In Electroencephalogram signal(EEG) recordings, the signals obtained are contaminated predominantly by the Electrooculogram(EOG) signal. Since this artifact has higher magnitude compared to EEG signals, these noise signals have to be removed in order to have a better understanding regarding the functioning of a human brain for applications such as medical diagnosis. This paper proposes an idea of using Independent Component Analysis(ICA) along with cross-correlation to de-noise EEG signal. This is done by selecting the component based on the cross-correlation coefficient with a threshold value and reducing its effect instead of zeroing it out completely, thus reducing the information loss. The results of the recorded data show that this algorithm can eliminate the EOG signal artifact with little loss in EEG data. The denoising is verified by an increase in SNR value and the decrease in cross-correlation coefficient value. The denoised signals are used to train an Artificial Neural Network(ANN) which would examine the features of the input EEG signal and predict the stress levels of the individual.
Objective: Functional coupling between the motor cortex and muscle activity is commonly detected and quantified by cortico-muscular coherence (CMC) or Granger causality (GC) analysis, which are applicable only to linear couplings and are not sufficiently sensitive: some healthy subjects show no significant CMC and GC, and yet have good motor skills. The objective of this work is to develop measures of functional cortico-muscular coupling that have improved sensitivity and are capable of detecting both linear and non-linear interactions. Methods: A multiscale wavelet transfer entropy (TE) methodology is proposed. The methodology relies on a dyadic stationary wavelet transform to decompose electroencephalogram (EEG) and electromyogram (EMG) signals into functional bands of neural oscillations. Then, it applies TE analysis based on a range of embedding delay vectors to detect and quantify intra- and cross-frequency band cortico-muscular coupling at different time scales. Results: Our experiments with neurophysiological signals substantiate the potential of the developed methodologies for detecting and quantifying information flow between EEG and EMG signals for subjects with and without significant CMC or GC, including non-linear cross-frequency interactions, and interactions across different temporal scales. The obtained results are in agreement with the underlying sensorimotor neurophysiology. Conclusion: These findings suggest that the concept of multiscale wavelet TE provides a comprehensive framework for analysing cortex-muscle interactions. Significance: The proposed methodologies will enable developing novel insights into movement control and neurophysiological processes more generally.
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