Dynamic Decomposition of Spatiotemporal Neural Signals

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals

Spectral Analysis for Signal Detection and Classification : Reducing Variance and Extracting Features

Spectral analysis encompasses several powerful signal processing methods. The papers in this thesis present methods for finding good spectral representations, and methods both for stationary and non-stationary signals are considered. Stationary methods can be used for real-time evaluation, analysing shorter segments of an incoming signal, while non-stationary methods can be used to analyse the instantaneous frequencies of fully recorded signals. All the presented methods aim to produce spectral representations that have high resolution and are easy to interpret. Such representations allow for detection of individual signal components in multi-component signals, as well as separation of close signal components. This makes feature extraction in the spectral representation possible, relevant features include the frequency or instantaneous frequency of components, the number of components in the signal, and the time duration of the components. Two methods that extract some of these features automatically for two types of signals are presented in this thesis. One adapted to signals with two longer duration frequency modulated components that detects the instantaneous frequencies and cross-terms in the Wigner-Ville distribution, the other for signals with an unknown number of short duration oscillations that detects the instantaneous frequencies in a reassigned spectrogram. This thesis also presents two multitaper methods that reduce the influence of noise on the spectral representations. One is designed for stationary signals and the other for non-stationary signals with multiple short duration oscillations. Applications for the methods presented in this thesis include several within medicine, e.g. diagnosis from analysis of heart rate variability, improved ultrasound resolution, and interpretation of brain activity from the electroencephalogram

Time-Frequency Surrogates for Nonstationary Signal Analysis

International audienceThe purpose of the present communication is, after a brief outline of the use of simple surrogates as introduced so far for stationarity tests, to deal with constructions of surrogates in ''time-frequency domains''. Indeed, for transient detection or cross-correlations analysis, one need to construct directly ''surrogate time-frequency distributions'', as opposed to distributions of surrogate time series, and keeping the `geometrical' structure in the plane of the quadratic distribution

Testing Stationarity with Time-Frequency Surrogates

International audienceA method is proposed for testing stationarity in an operational sense, i.e., by both including explicitly an observation scale in the definition and elaborating a stationarized reference so as to reject the null hypothesis of stationarity with a controlled level of statistical significance. While the approach is classically based on comparing local vs. global features in the time-frequency plane, the test operates with a family of stationarized surrogates whose analysis allows for a characterization of the null hypothesis. The general principle of the method is outlined, practical issues related to its actual implementation are discussed and a typical example is provided for illustrating the approach and supporting its effectiveness

Testing Stationarity with Surrogates: A Time-Frequency Approach

International audienceAn operational framework is developed for testing stationarity relatively to an observation scale, in both stochastic and deterministic contexts. The proposed method is based on a comparison between global and local time-frequency features. The originality is to make use of a family of stationary surrogates for defining the null hypothesis of stationarity and to base on them two different statistical tests. The first one makes use of suitably chosen distances between local and global spectra, whereas the second one is implemented as a one-class classifier, the time-frequency features extracted from the surrogates being interpreted as a learning set for stationarity. The principle of the method and of its two variations is presented, and some results are shown on typical models of signals that can be thought of as stationary or nonstationary, depending on the observation scale used

Time-Evolution of the Power Spectrum of the Black Hole X-ray Nova XTE J1550-564

We have studied the time evolution of the power spectrum of XTE J1550-564, using X-ray luminosity time series data obtained by the Rossi X-Ray Timing Explorer satellite. A number of important practical fundamental issues arise in the analysis of these data, including dealing with time-tagged event data, removal of noise from a highly non-stationary signal, and comparison of different time-frequency distributions. We present two new methods to understand the time frequency variations, and compare them to the dynamic power spectrum of Homan et al. All of the approaches provide evidence that the QPO frequency varies in a systematic way during the time evolution of the signal.Comment: 4 pages, 3 figures; 2001 IEEE - EURASIP Workshop on Nonlinear Signal and Image Processing (June 3-6, 2001), and to appear in the proceeding

Characterizing the 410 km Discontinuity Low‐Velocity Layer Beneath the LA RISTRA Array in the North American Southwest

Receiver functions recorded by the 54-station 920 km long Program for Array Seismic Studies of the Continental Lithosphere–Incorporated Research Institutions for Seismology Colorado Plateau/Rio Grande Rift Seismic Transect Experiment (LA RISTRA) line array display a pervasive negative polarity P to S conversion (Pds) arrival preceding the positive polarity 410 km discontinuity arrival. These arrivals are modeled as a low-velocity layer atop the 410 km discontinuity (410-LVL) and are inverted for a velocity profile via a grid search using a five-parameter linear gradient velocity model. Model parameter likelihood and correlations are assessed via calculation of one- and two-dimensional marginal posterior probability distributions. The maximum likelihood model parameter values found are top velocity gradient thickness of 0.0 km with a 4.6% (−0.22 km/s) shear velocity reduction, a 19.8 km constant velocity layer, and bottom gradient thickness of 25.0 km with a 3.5% (+0.17 km/s) shear velocity increase. The estimated mean thickness of the 410-LVL is 32.3 km. The top gradient of the 410-LVL is sharp within vertical resolution limits of P to S conversion (km), and the diffuse 410 km velocity gradient is consistent with hydration of the olivine-wadsleyite phase transformation. The 410-LVL is interpreted as a melt layer created by the Transition Zone Water Filter model. Two secondary observations are found: (1) the 410-LVL is absent from the SE end of the array and (2) an intermittent negative polarity P525s arrival is observed. We speculate that upper mantle shear velocity anomalies above the 410 km discontinuity may manifest Rayleigh-Taylor instabilities nucleated from the 410-LVL melt layer that are being shed upward on time scales of tens of millions of years