On spurious and real fluctuations of dynamic functional connectivity during rest

Functional brain networks reconfigure spontaneously during rest. Such network dynamics can be studied by dynamic functional connectivity (dynFC); i.e., sliding-window correlations between regional brain activity. Key parameters-such as window length and cut-off frequencies for filtering-are not yet systematically studied. In this letter we provide the fundamental theory from signal processing to address these parameter choices when estimating and interpreting dynFC. We guide the reader through several illustrative cases, both simple analytical models and experimental fMRI BOLD data. First, we show how spurious fluctuations in dynFC can arise due to the estimation method when the window length is shorter than the largest wavelength present in both signals, even for deterministic signals with a fixed relationship. Second, we study how real fluctuations of dynFC can be explained using a frequency-based view, which is particularly instructive for signals with multiple frequency components such as fMRI BOLD, demonstrating that fluctuations in sliding-window correlation emerge by interaction between frequency components similar to the phenomenon of beat frequencies. We conclude with practical guidelines for the choice and impact of the window length. (C) 2014 Elsevier Inc. All rights reserved.

Adaptive frequency tracking and application to biomedical signals

Yann Prudat

The main information of a signal resides in its frequency, its amplitude (or its power) and in their temporal evolution. Thus, a great number of methods for instantaneous frequency estimation have been proposed in the literature. Most of these algorithms use an adaptive filter-based (notch or bandpass filter) structure. In many applications, the information of interest is present in more than one signal. However, to our knowledge no algorithm able to track the frequency on several signals has been presented in the literature. Usually, frequency components are estimated and extracted on each signal independently. Artifacts or noise relative to a specific signal can thus disturb the frequency estimation process. Moreover, low amplitude components present in every signal (but non dominant) will not be estimated. The objective in the first part of this thesis is to develop different methods able to extend existing frequency tracking algorithm in order to improve the quality of the estimate, in terms of estimation variance and robustness with respect to noise. The proposed methods can be applied to algorithms using adaptive filters for the frequency estimation. For the multi-signal frequency tracking extension, these methods use the redundancy of information present in the signals under study. A first approach uses a unique filter for every signal. A set of weights is computed, depending on a measure of the estimate quality, and makes it possible to balance the influence of each signal on the tracking filter update. The second approach consists in using a different adaptive filter for each signal. A set of constraints links the central frequencies of each filter so that they are as similar as possible. Both methods yield frequency estimates more robust with respect to noise and more stable, without any decrease in estimation accuracy. For the harmonic frequency tracking, we propose a method using the information present in the harmonic component to improve the estimate of the fundamental frequency. The proposed methods also permit to extract the signal components corresponding to the estimated frequencies. These components are very useful for subsequent study. In the second part of this thesis, the algorithms developed in the first part are applied to biomedical signals. Two different applications are studied in this work : electrocardiograms and electroencephalograms. Firstly, a frequency tracking algorithm as well as its multi-signal extension are used to predict the success of electrical cardioversion attempts in patients suffering from atrial fibrillation. The instantaneous frequency is estimated using the algorithms and the corresponding signal component is extracted from electrocardiograms recorded prior to the attempt. With a few parameters computed on the estimated frequency and the corresponding signal component, we were able to predict the result of the cardioversion attempt on our database comprising 18 patients with a success rate of 94% for both algorithms. We think that this result can be very useful for helping the clinician to choose the appropriate therapy for atrial fibrillation management. The developed algorithms are also used to track the oscillatory components present in electroencephalograms. The performance of the basic algorithm is illustrated using single-trial electroencephalogram signals from a visual evoked potential experiment. The algorithm is used to track the gamma component (30-50 Hz). It is able to successfully track the spectral component in spite of the fact that large amplitude variations are present in the signal. A complex version of the multi-signal extension is also used to have an algorithm able to track multiple frequency components on multiple signals. The performance of this algorithm is also illustrated with single-trial electroencephalogram signals. It was shown to be able to correctly track up to four frequency components simultaneously. The quality of the estimation is improved using multiple lead signals.

EPFL2009

Sampling methods for parametric non-bandlimited signals

Irena Maravic

Sampling theory has experienced a strong research revival over the past decade, which led to a generalization of Shannon's original theory and development of more advanced formulations with immediate relevance to signal processing and communications. For example, it was recently shown that it is possible to develop exact sampling schemes for a large class of non-bandlimited signals, namely, certain signals with finite rate of innovation. A common feature of such signals is that they have a parametric representation with a finite number of degrees of freedom and can be perfectly reconstructed from a finite number of samples. The goal of this thesis is to advance the sampling theory for signals of finite rate of innovation and consider its possible extensions and applications. In the first part of the thesis, we revisit the sampling problem for certain classes of such signals, including non-uniform splines and piecewise polynomials, and develop improved schemes that allow for stable and precise reconstruction in the presence of noise. Specifically, we develop a subspace approach to signal reconstruction, which converts a nonlinear estimation problem into the simpler problem of estimating the parameters of a linear model. This provides an elegant and robust framework for solving a large class of sampling problems, while offering more flexibility than the traditional scheme for bandlimited signals. In the second part of the thesis, we focus on applications of our results to certain classes of nonlinear estimation problems encountered in wideband communication systems, most notably ultra-wideband (UWB) systems, where the bandwidth used for transmission is much larger than the bandwidth or rate of information being sent. We develop several frequency domain methods for channel estimation and synchronization in UWB systems, which yield high-resolution estimates of all relevant channel parameters by sampling a received signal below the traditional Nyquist rate. We also propose algorithms that are suitable for identification of more realistic UWB channel models, where a received signal is made up of pulses with different pulse shapes. Finally, we extend our results to multidimensional signals, and develop exact sampling schemes for certain classes of parametric non-bandlimited 2-D signals, such as sets of 2-D Diracs, polygons or signals with polynomial boundaries.

EPFL2004

How to take advantage of aliasing in bandlimited signals

Luciano Sbaiz, Patrick Vandewalle, Martin Vetterli

In signal processing systems, aliasing is normally treated as a disturbing signal. That motivates the need for effective analog, optical and digital anti-aliasing filters. However, aliasing conveys also valuable information on the signal above the Nyquist frequency. Hence, an effective processing of the samples, based on a model of the input signal, would allow to virtually increase the sampling frequency using slower and cheaper converters. In this paper, we present such an algorithm for bandlimited signals that are sampled below twice the maximum signal frequency. Using a subspace method in the frequency domain, we show that these signals can be reconstructed from multiple sets of samples. The offset between the sets is unknown and can have arbitrary values. This approach can be applied to the creation of super-resolution images from sets of low resolution images. In this application, registration parameters have to be computed from aliased images. We show that parameters and high resolution images can be computed precisely, even when high levels of aliasing are present on the low resolution images.