Signal analysis of impulse response functions in MR- and CT-measurements of cerebral blood flow

The impulse response function (IRF) of a localized bolus in cerebral blood flow codes important information on the tissue type. It is indirectly accessible both from MR- and CT-imaging methods, at least in principle. In practice, however, noise and limited signal resolution render standard deconvolution techniques almost useless. Parametric signal descriptions look more promising, and it is the aim of this contribution to develop some improvements along this line.Comment: 15 pages, 6 figure

Guidance, flight mechanics and trajectory optimization. Volume 11 - Guidance equations for orbital operations

Mathematical formulation of guidance equations and solutions for orbital space mission

Comparative study on the application of evolutionary optimization techniques to orbit transfer maneuvers

Orbit transfer maneuvers are here considered as benchmark cases for comparing performance of different optimization techniques in the framework of direct methods. Two different classes of evolutionary algorithms, a conventional genetic algorithm and an estimation of distribution method, are compared in terms of performance indices statistically evaluated over a prescribed number of runs. At the same time, two different types of problem representations are considered, a first one based on orbit propagation and a second one based on the solution of Lambert’s problem for direct transfers. In this way it is possible to highlight how problem representation affects the capabilities of the considered numerical approaches

Bregman Cost for Non-Gaussian Noise

One of the tasks of the Bayesian inverse problem is to find a good estimate based on the posterior probability density. The most common point estimators are the conditional mean (CM) and maximum a posteriori (MAP) estimates, which correspond to the mean and the mode of the posterior, respectively. From a theoretical point of view it has been argued that the MAP estimate is only in an asymptotic sense a Bayes estimator for the uniform cost function, while the CM estimate is a Bayes estimator for the means squared cost function. Recently, it has been proven that the MAP estimate is a proper Bayes estimator for the Bregman cost if the image is corrupted by Gaussian noise. In this work we extend this result to other noise models with log-concave likelihood density, by introducing two related Bregman cost functions for which the CM and the MAP estimates are proper Bayes estimators. Moreover, we also prove that the CM estimate outperforms the MAP estimate, when the error is measured in a certain Bregman distance, a result previously unknown also in the case of additive Gaussian noise

Characterization of causes of signal phase and frequency instability Final report

Characteristic instabilities in phase and frequency errors of reference oscillator

Reconstructing the primordial power spectrum from the CMB

We propose a straightforward and model independent methodology for characterizing the sensitivity of CMB and other experiments to wiggles, irregularities, and features in the primordial power spectrum. Assuming that the primordial cosmological perturbations are adiabatic, we present a function space generalization of the usual Fisher matrix formalism, applied to a CMB experiment resembling Planck with and without ancillary data. This work is closely related to other work on recovering the inflationary potential and exploring specific models of non-minimal, or perhaps baroque, primordial power spectra. The approach adopted here, however, most directly expresses what the data is really telling us. We explore in detail the structure of the available information and quantify exactly what features can be reconstructed and at what statistical significance.Comment: 43 pages Revtex, 23 figure

Maximum likelihood parameter estimation for linear systems with singular observations

It is shown that maximum likelihood estimation of unknown parameters of a linear system with singular observations in general results in the maximization of a likelihood function subject to equality constraints