Analysis of Dynamic Brain Imaging Data

Modern imaging techniques for probing brain function, including functional Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this paper we develop appropriate techniques of analysis and visualization of such imaging data, in order to separate the signal from the noise, as well as to characterize the signal. The techniques developed fall into the general category of multivariate time series analysis, and in particular we extensively use the multitaper framework of spectral analysis. We develop specific protocols for the analysis of fMRI, optical imaging and MEG data, and illustrate the techniques by applications to real data sets generated by these imaging modalities. In general, the analysis protocols involve two distinct stages: `noise' characterization and suppression, and `signal' characterization and visualization. An important general conclusion of our study is the utility of a frequency-based representation, with short, moving analysis windows to account for non-stationarity in the data. Of particular note are (a) the development of a decomposition technique (`space-frequency singular value decomposition') that is shown to be a useful means of characterizing the image data, and (b) the development of an algorithm, based on multitaper methods, for the removal of approximately periodic physiological artifacts arising from cardiac and respiratory sources.Comment: 40 pages; 26 figures with subparts including 3 figures as .gif files. Originally submitted to the neuro-sys archive which was never publicly announced (was 9804003

Signal Reconstruction From Nonuniform Samples Using Prolate Spheroidal Wave Functions: Theory and Application

Nonuniform sampling occurs in many applications due to imperfect sensors, mismatchedclocks or event-triggered phenomena. Indeed, natural images, biomedical responses andsensor network transmission have bursty structure so in order to obtain samples that correspondto the information content of the signal, one needs to collect more samples when thesignal changes fast and fewer samples otherwise which creates nonuniformly distibuted samples.On the other hand, with the advancements in the integrated circuit technology, smallscale and ultra low-power devices are available for several applications ranging from invasivebiomedical implants to environmental monitoring. However the advancements in the devicetechnologies also require data acquisition methods to be changed from the uniform (clockbased, synchronous) to nonuniform (clockless, asynchronous) processing. An important advancementis in the data reconstruction theorems from sub-Nyquist rate samples which wasrecently introduced as compressive sensing and that redenes the uncertainty principle. Inthis dissertation, we considered the problem of signal reconstruction from nonuniform samples.Our method is based on the Prolate Spheroidal Wave Functions (PSWF) which can beused in the reconstruction of time-limited and essentially band-limited signals from missingsamples, in event-driven sampling and in the case of asynchronous sigma delta modulation.We provide an implementable, general reconstruction framework for the issues relatedto reduction in the number of samples and estimation of nonuniform sample times. We alsoprovide a reconstruction method for level crossing sampling with regularization. Another way is to use projection onto convex sets (POCS) method. In this method we combinea time-frequency approach with the POCS iterative method and use PSWF for the reconstructionwhen there are missing samples. Additionally, we realize time decoding modulationfor an asynchronous sigma delta modulator which has potential applications in low-powerbiomedical implants

Approaching the ultimate capacity limit in deep-space optical communication

The information capacity of an optical channel under power constraints is ultimately limited by the quantum nature of transmitted signals. We discuss currently available and emerging photonic technologies whose combination can be shown theoretically to enable nearly quantum-limited operation of a noisy optical communication link in the photon-starved regime, with the information rate scaling linearly in the detected signal power. The key ingredients are quantum pulse gating to facilitate mode selectivity, photon-number-resolved direct detection, and a photon-efficient high-order modulation format such as pulse position modulation, frequency shift keying, or binary phase shift keyed Hadamard words decoded optically using structured receivers.Comment: 9 pages, 4 figures. Presented at Free-Space Laser Communications XXXI, 4-6 February 2019, San Francisco, C

Non-Gaussian states from continuous-wave Gaussian light sources

We present a general analysis of the state obtained by subjecting the output from a continuous-wave (cw) Gaussian field to non-Gaussian measurements. The generic multimode state of cw Gaussian fields is characterized by an infinite dimensional covariance matrix involving the noise correlations of the source. Our theory extracts the information relevant for detection within specific temporal output modes from these correlation functions . The formalism is applied to schemes for production of non-classical light states from a squeezed beam of light

Processing and Transmission of Information

Contains reports on four research projects.National Aeronautics and Space Administration (Grant NsG-334)Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E

Power Spectrum Estimation for Frequency Domain Ambient Modal Analysis

This paper studies the effect of Power Spectrum Density (PSD) estimation techniques on the accuracy of Fast Frequency Domain Decomposition (FFDD) modal analysis. FFDD utilizes ambient synchrophasor measurements to estimate characteristics of dominant system modes and oscillations by analyzing the PSD estimates from multiple synchrophasor measurements. In this paper, the impact of three different methods for PSD estimation on the accuracy of FFDD modal estimates is investigated: PWelch, MultiTaper Method (MTM) using Slepian Tapers, and MTM using Sine Tapers. Tests are done using synthetic and archived synchrophasor data. All three PSD methods are shown to work well for oscillation detection of sustained oscillations using FFDD. However, for ambient modal analysis, it is shown that FFDD based on MTM with Slepian Tapers has the most reliable modal estimations. FFDD using both MTM with Sine Tapers and PWelch have bias issues in estimating well-damped system modes, requiring more research for them to be suitable for FFDD

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 04. bis 06.07. 2012, Bauhaus-Universität Weimar

The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Methods in wave propagation and scattering

Supervised by Jin A. Kong.Also issued as Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 195-213).by Henning Braunisch

Methods in wave propagation and scattering

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Vita.Includes bibliographical references (p. 195-213).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Aspects of wave propagation and scattering with an emphasis on specific applications in engineering and physics are examined. Frequency-domain methods prevail. Both forward and inverse problems are considered. Typical applications of the method of moments to rough surface three-dimensional (3-D) electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave. It is shown how such wave can be constructed as a superposition of plane waves, avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence. The proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a wave that is optimal in a least squared error sense. Issues in the application to 3-D scattering from an object over a rough surface are discussed. Approximate 3-D scalar and vector tapered waves are derived which can be evaluated without resorting to any numerical integrations. Important limitations to the accuracy and applicability of these approximations are pointed out. An analytical solution is presented for the electromagnetic induction problem of magnetic diffusion into and scattering from a permeable, highly but not perfectly conducting prolate spheroid under axial excitation, expressed in terms of an infinite matrix equation. The spheroid is assumed to be embedded in a homogeneous non-conducting medium as appropriate for low-frequency, high-contrast scattering governed by magnetoquasistatics. The solution is based on separation of variables and matching boundary conditions where the prolate spheroidal wavefunctions with complex wavenumber parameter are expanded in terms of spherical harmonics. For small skin depths, an approximate solution is constructed, which avoids any reference to the spheroidal wavefunctions. The problem of long spheroids and long circular cylinders is solved by using an infinite cylinder approximation. In some cases, our ability to evaluate the spheroidal wavefunctions breaks down at intermediate frequencies. To deal with this, a general broadband rational function approximation technique is developed and demonstrated. We treat special cases and provide numerical reference data for the induced magnetic dipole moment or, equivalently, the magnetic polarizability factor. The magnetoquasistatic response of a distribution of an arbitrary number of interacting small conducting and permeable objects is also investigated. Useful formulations are provided for expressing the magnetic dipole moment of conducting and permeable objects of general shape. An alternative to Tikhonov regularization for deblurring and inverse diffraction, based on a local extrapolation scheme, is described, analyzed, and illustrated numerically for the cases of continuation of fields obeying Laplace and Helmholtz equations. At the outset of the development, a special deconvolution problem, where a parameter describes the degree of additive blurring, is considered. No a priori knowledge on the unblurred data is assumed. A standard solution based on an output least squares formulation includes a regularization parameter into a linear, shift-invariant filter. The proposed alternative approach takes advantage of the analyticity of the smoothing process with respect to the blurring parameter. Here a simple local extrapolation scheme is employed. The problem is encountered in applications involving potential theories dealing with magnetostatics, electrostatics, and gravity data. As a generalization to the dynamic case, inverse diffraction of scalar waves is considered. Examples are presented and the two methods compared numerically. The problem of inferring unknown geometry and material parameters of a waveguide model from noisy samples of the associated modal dispersion curves is considered. In a significant reduction of the complexity of a common inversion methodology, the inner of two nested iterations is eliminated: The approach described does not employ explicit fitting of the data to computed dispersion curves. Instead, the unknown parameters are adjusted to minimize a cost function derived directly from the determinant of the boundary condition system matrix. This results in a very efficient inversion scheme that, in the case of noise-free data, yields exact results. Multi-mode data can be simultaneously processed without extra complications. Furthermore, the inversion scheme can accommodate an arbitrary number of unknown parameters, provided that the data have sufficient sensitivity to these parameters. As an important application, the sonic guidance condition for a fluid-filled borehole in an elastic, homogeneous, and isotropic rock formation is considered for numerical forward and inverse dispersion analysis. The parametric inversion with uncertain model parameters and the influence of bandwidth and noise are investigated numerically. The cases of multi-frequency and multi-mode data are examined. Finally, the borehole leaky-wave modes are classified according to the location of the roots of the characteristic equation on a multi-sheeted Riemann surface. A comprehensive set of dipole leaky-wave modal dispersions is computed. In an independent numerical experiment the excitation of some of these modes is demonstrated. The utilization of leaky-wave dispersion data for inversion is discussed.by Henning Braunisch.Ph.D

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 04. bis 06.07. 2012, Bauhaus-Universität Weimar

The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference