Likelihood Analysis of Power Spectra and Generalized Moment Problems

We develop an approach to spectral estimation that has been advocated by Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance extension problem, by Enqvist and Karlsson. The aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying Gaussian stochastic process to that of a prior. The approach is analogous to the framework of earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a generalization of the classical work by Burg and Jaynes on the maximum entropy method. In the present paper we present a new fast algorithm in the general case (i.e., for general Gaussian priors) and show that for priors with a specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure

Digital Signal Processing

Contains research objectives and reports on sixteen research projects.U.S. Navy - Office of Naval Research (Contract N00014-75-C-0852)National Science Foundation FellowshipNational Science Foundation (Grant ENG76-24117)U.S. Navy - Office of Naval Research (Contract N00014-77-C-0257)U.S. Air Force (Contract F19628-80-C-0002)U.S. Navy - Office of Naval Research (Contract N00014-75-C-0951)Schlumberger-Doll Research Center FellowshipHertz Foundation FellowshipGovernment of Pakistan ScholarshipU.S. Navy - Office of Naval Research (Contract N00014-77-C-0196

Global analysis of coherence and population dynamics in 2D electronic spectroscopy

2D electronic spectroscopy is a widely exploited tool to study excited state dynamics. A high density of information is enclosed in 2D spectra. A crucial challenge is to objectively disentangle all the features of the third order optical signal. We propose a global analysis method based on the variable projection algorithm, which is able to reproduce simultaneously coherence and population dynamics of rephasing and non-rephasing contributions. Test measures at room temperature on a standard dye are used to validate the procedure and to discuss the advantages of the proposed methodology with respect to the currently employed analysis procedures

Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media

The resistive or non-resistive nature of the extracellular space in the brain is still debated, and is an important issue for correctly modeling extracellular potentials. Here, we first show theoretically that if the medium is resistive, the frequency scaling should be the same for electroencephalogram (EEG) and magnetoencephalogram (MEG) signals at low frequencies (<10 Hz). To test this prediction, we analyzed the spectrum of simultaneous EEG and MEG measurements in four human subjects. The frequency scaling of EEG displays coherent variations across the brain, in general between 1/f and 1/f^2, and tends to be smaller in parietal/temporal regions. In a given region, although the variability of the frequency scaling exponent was higher for MEG compared to EEG, both signals consistently scale with a different exponent. In some cases, the scaling was similar, but only when the signal-to-noise ratio of the MEG was low. Several methods of noise correction for environmental and instrumental noise were tested, and they all increased the difference between EEG and MEG scaling. In conclusion, there is a significant difference in frequency scaling between EEG and MEG, which can be explained if the extracellular medium (including other layers such as dura matter and skull) is globally non-resistive.Comment: Submitted to Journal of Computational Neuroscienc