Accelerated Computation of Regularized Estimates in Magnetic Resonance Imaging.

Magnetic resonance imaging (MRI) is a non-invasive medical imaging modality that uses magnetic fields. Accurate estimates of these fields are often used to improve the quality of MR imaging techniques. Regularized estimators for such fields are robust and can provide high quality estimates but often at a significant computational cost. In this work, we investigate several of these estimators with a focus on developing novel minimization methods that reduce their computation times. First, we explore regularized receive coil sensitivity estimation by demonstrating the improved performance of regularized methods over existing, heuristic approaches and by presenting several algorithms, based on augmented Lagrangian methods, that minimize the quadratic cost function in half the time required by a preconditioned conjugate gradient (CG) method. Second, we present a general cost function that combines the regularized estimation of the main magnetic field inhomogeneity for both multiple echo time field map estimation and chemical shift based water-fat imaging. We present two methods, both based on optimization transfer principles, that reduce the computation time of this estimator by a factor of 30 compared to the existing separable quadratic surrogates method. We also evaluate the effectiveness of edge preserving regularization for field inhomogeneity estimation near tissue interfaces. Third, we present a novel alternating minimization method that uses augmented Lagrangian methods to accelerate the computation of the compressed sensing based water-fat image reconstruction problem by at least ten times compared to the existing nonlinear CG method. The algorithms presented in this thesis may also be applicable to other MRI topics including B1+ estimation, T1 estimation from variable flip angles, and R2* corrected or parallel imaging extensions of compressed sensing based water-fat imaging.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107096/1/mjalliso_1.pd

Fast Acquisition and Reconstruction Techniques in MRI

The aim of this thesis was to develop fast reconstruction and acquisition techniques for MRI that can support clinical applications where time is a limiting factor. In general, fast acquisition techniques were realized by undersampling k-space, while fast reconstruction techniques were achieved by using efficient numerical algorithms. In particular, undersampled acquisitions were processed in a CS and MRF framework. Preconditioning techniques were used to accelerate CS reconstructions, and a number of challenges encountered in MRF were addressed using appropriate post-processing techniques. European Research Council (ERC) Advanced Grant (670629 NOMA MRI)LUMC / Geneeskund

Controller Design and Experimental Validation for Connected Vehicle Systems Subject to Digital Effects and Stochastic Packet Drops

Vehicle-to-everything (V2X) communication allows vehicles to monitor the nearby traffic environment, including participants that are beyond the line of sight. Equipping conventional vehicles with V2X devices results in connected vehicles (CVs) while incorporating the information provided by V2X devices into the controllers of automated vehicles (AVs) leads to connected automated vehicles (CAVs). CAVs have great potential for improving driving comfort, reducing fuel consumption and advancing active safety for individual vehicles, as well as enhancing traffic efficiency and mobility for human-dominated traffic systems. In this dissertation, we study a class of connected cruise control (CCC) algorithms for longitudinal control of CAVs, where they respond to the motion information of one or multiple connected vehicles ahead. For validation and demonstration purposes, we utilize a scaled connected vehicle testbed consisting of a group of ground robots, which can provide us with insights about the controller design of full-size vehicles. On the one hand, intermittencies in V2X communication combined with the digital implementation of controllers introduce information delays. To ensure the performance of individual CAVs and the overall traffic, a set of methods is proposed for design and analysis of such communication-based controllers. We validate them with the scaled testbed by conducting a series of experiments on two-car predecessor-follower systems, cascaded predecessor-follower systems, and more complex connected vehicle systems. It is demonstrated that CAVs utilizing information about multiple preceding vehicles in the CCC algorithm can improve the system performance even for low penetration levels. This can be beneficial at the early stage of vehicle automation when human-driven vehicles still dominate the traffic system. On the other hand, we study the delay variations caused by stochastic packet drops in V2X communication and derive the stochastic processes describing the dynamics for the predecessor-follower systems. The dynamics of the mean, second moment and covariance are utilized to obtain stability conditions. Then the results of the two-car predecessor-follower system with stochastic delay variations are extended to an open chain as well as to a closed ring of cascaded predecessor-followers where stochastic packet drops lead to heterogeneity among different V2X devices. It is shown that the proposed analytical methods allow CCC design for CAVs that can achieve stability and stochastic disturbance attenuation in the presence of stochastic packet drops in complex connected vehicle systems.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145874/1/wubing_1.pd

QUANTUM ALGORITHMS FOR DIFFERENTIAL EQUATIONS

This thesis describes quantum algorithms for Hamiltonian simulation, ordinary differential equations (ODEs), and partial differential equations (PDEs). Product formulas are used to simulate Hamiltonians which can be expressed as a sum of terms which can each be simulated individually. By simulating each of these terms in sequence, the net effect approximately simulates the total Hamiltonian. We find that the error of product formulas can be improved by randomizing over the order in which the Hamiltonian terms are simulated. We prove that this approach is asymptotically better than ordinary product formulas and present numerical comparisons for small numbers of qubits. The ODE algorithm applies to the initial value problem for time-independent first order linear ODEs. We approximate the propagator of the ODE by a truncated Taylor series, and we encode the initial value problem in a large linear system. We solve this linear system with a quantum linear system algorithm (QLSA) whose output we perform a post-selective measurement on. The resulting state encodes the solution to the initial value problem. We prove that our algorithm is asymptotically optimal with respect to several system parameters. The PDE algorithms apply the finite difference method (FDM) to Poisson's equation, the wave equation, and the Klein-Gordon equation. We use high order FDM approximations of the Laplacian operator to develop linear systems for Poisson's equation in cubic volumes under periodic, Neumann, and Dirichlet boundary conditions. Using QLSAs, we output states encoding solutions to Poisson's equation. We prove that our algorithm is exponentially faster with respect to the spatial dimension than analogous classical algorithms. We also consider how high order Laplacian approximations can be used for simulating the wave and Klein-Gordon equations. We consider under what conditions it suffices to use Hamiltonian simulation for time evolution, and we propose an algorithm for these cases that uses QLSAs for state preparation and post-processing

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Space programs summary no. 37-61, volume 3 for the period 1 December 1969 - 31 January 1970. Supporting research and advanced development

Planetary atmospheres, space communications, and spacecraft power, control, antennas, materials, and propulsion system

Systematic Design of Multiport Antennas for MIMO-enabled Mobile Wireless Terminals

Mobile wireless communication systems have undergone a tremendous development in the past decade. One of the major advancements is the widespread use of MIMO transmission schemes beginning with the introduction of the 3rd Generation Partnership Project (3GPP) standard LTE and being extended in LTE Advanced. So as to support MIMO transmission schemes mobile terminals must be equipped with multiport antenna systems. The term refers to an arrangement of two or more antenna elements operating in the same frequency range and mounted on the same mobile wireless platform. Reduced volume per antenna element and strong interaction between all antenna elements are major design challenges and require for new systematic design approaches beyond classical single antenna design. The ongoing miniaturization of mobile terminals, the extension of the mobile spectrum and in particular the opening of new mobile communication bands at the lower end of the spectrum exacerbate these challenges. Design and characterization of multiport antennas have therefore become subject of high interest and of numerous research projects in both academia and industry. This dissertation contributes to the development of systematic design procedures for multiport antennas with emphasis on accounting for the restrictions and side conditions which apply when designing multiport antennas for actual consumer equipment. The dissertation has developed along an industry funded research project, with a focus on electrically small devices where antenna design is constantly faced with fundamental physical limits. Chapter 1 gives an overview of the state of the art in antenna characterization and design techniques applicable to multiport antennas for MIMO. Chapter 2 introduces into the analysis of multiport antennas in terms of their radiation modes. Modal analysis, based on spectrum of the radiation matrix, allows for unambiguous characterization of a multiport antenna by means of invariant properties. Modal descriptive quantities are defined which are basic to the design approach followed in this dissertation. Analyzing a multiport antenna with respect to its radiation modes is possible only after a design concept has been conceived. More fundamental from a design point of view is the question for the space of feasible radiation modes and their realization under the constraint of a given chassis form factor. Chapter 3 addresses this question based on the theory of characteristic modes for conducting bodies. The relevant properties of characteristic modes on the chassis of mobile terminals are reviewed. The excitation of characteristic modes by means of capacitive and inductive coupling elements is investigated in detail. Finally, a systematic design approach for multiport antennas is presented in which the antenna’s radiation modes are constructively derived from the usable characteristic chassis modes. Chapter 4 deals with design of matching networks for N-port antennas. Starting from the general expression for the scattering matrix of an ideal 2N-port matching network different topologies and alternative implementations are discussed. As a solution of particular interest in cases where some radiation modes feature insufficient bandwidths, special attention is given to systematic design of MDN which maps radiation modes to external ports of the antenna system. Chapter 5 focuses on the particular problems encountered in the design of antenna systems for extremely small mobile wireless terminals. After a review of applicable fundamental limits bandwidth estimation and approaches to maintain a decent total efficiency are discussed. The combination of electrical switching in the antenna structure with electrical tuning in an external matching network is suggested in this context. The DL-MIMO concept is introduced as a system level measure to cope with insufficient bandwidth. The different aspects are exemplified with the design of a 2-port MIMO antenna for a USB dongle. Chapter 6 describes in detail design, fabrication and measurement of four antenna prototypes. The validity of the design approach described in the previous chapters is confirmed. In conclusion, a systematic design approach, which combines the theory of characteristic chassis modes for conducting bodies with modal analysis of a multiport antenna, i.e. considers the spectrum of its radiation matrix is presented. The approach is successfully applied to a number of practically relevant design problems. The design technique permits identification of near optimum antenna solutions which approach the fundamental limits of attainable bandwidth and total efficiency.Systematischen Entwurf von Multiport-Antennen für MIMO-fähigen Mobilfunkendgeräte Die Mobilkommunikation hat in den letzten Jahren eine enorme Entwicklung durchlaufen. Eine der wesentlichen technischen Weiterentwicklungen ist der Übergang zu MIMO Übertragungsverfahren, in großem Maßstab beginnend mit der Einführung des 3GPP Standards LTE und in grÖßerem Umfang noch im zukünftigen LTE-Advanced. Mobile Endgeräte müssen dazu mit Mehrtorantennen ausgestattet sein. Der Begriff Mehrtorantenne bezeichnet eine Anordnung von zwei oder mehr Antennenelementen, die im gleichen Fequenzbereich betrieben werden und auf einer gemeinsamen Plattform angeordnet sind. Die Verringerung des je Antennenelement zur Verfügung stehenden Volumens und die starke Kopplung zwischen den Antennenelementen führen auf neue Herausforderungen für den Entwurf. Neue, systematische Entwurfsmethoden jenseits der klassischen Methoden für den Entwurf von Einzelantennen sind gefordert. Die fortschreitende Miniaturisierung mobiler Endgeräte, die Erweiterung des für den Mobilfunk genutzten Spektrums und insbesondere die Öffnung neuer Bander am unteren Ende des Spektrums für den Mobilfunk verschärfen die Anforderung an die Entwurfsmethodik. Entwurf und Charakterisierung von Mehrtorantennen sind deswegen heute Themen von großem Interesse und Gegenstand zahlreicher industrieller und akademischer Forschungsprojekte. Die vorliegende Dissertation liefert einen Beitrag zur Entwicklung systematischer Entwurfsverfahren für Mehrtorantennen unter besonderer Berücksichtigung der Einschränkungen und Randbedingungen die beim Entwurf von kommerziellen Endgeräten vorliegen. Zahlreiche Fragestellungen ergaben sich aus einem vom Verfasser bearbeiteten industriellen Forschungs- und Entwicklungsprojekt mit Schwerpunkt auf elektrisch kleinen Endgeräten, bei denen der Entwurf stets mit fundamentalen physikalischen Schranken konfrontiert ist. Kapitel 1 gibt einen Überblick über den Stand der Technik auf dem Gebiet des Entwurfs und der Charakterisierung von Mehrtorantennen für MIMO Anwendungen. Kapitel 2 führt in die Analyse von Mehrtorantennen mit Hilfe ihrer Strahlungsmoden ein. Die modale Betrachtung auf Grundlage des Spektrums der Strahlungsmatrix gestattet es, Mehtorantennen mit Hilfe ihrer invarianten Eigenschaften eindeutig zu charakterisieren. Es werden die modalen Beschreibungsgrössen definiert auf denen der in dieser Arbeit verfolgte Entwurfsansatz basiert. Die Strahlungsmoden einer Mehtorantenne können jedoch erst betrachtet werden, wenn ein Entwurf bereits vorliegt. Die vom Standpunkt der Entwurfsmethodik wichtigere Frage ist die nach Raum der unter den Einschränkungen eines gegebenen Geräte-Formfaktors realisierbaren Strahlungsmoden. Sie wird in Kapitel 3 auf Grundlage der Theorie Charakteristischer Moden leitender Körper behandelt. Die relevanten Eigenschaften charakteristischer Moden auf dem Gehäuse elektrisch kleiner mobiler Endgeräte werden betrachtet. Die Anregung charakteristischer Moden mit Hilfe von kapazitiven und induktiven Koppelelementen wird ausführlich untersucht. Abschließend wird ein Entwurfsansatz für Mehtorantennen beschrieben, in welchem die Strahlungsmoden der Antenne konstruktiv aus den nutzbaren charakteristischen Moden des Gehäuses abgeleitet werden. In Kapitel 4 werden Anpassnetzwerke für N-Tor Antennen behandelt. Ausgehend von der allgemeinen Formulierung für die Streumatrix des benötigten 2N-Tor Netzwerkes werden verschiedene Topologien und Realisierungsalternativen diskutiert. Gesondert betrachtet werden noch einmal MDNs, welche die Strahlungsmoden einer Mehtorantenne unmittelbar auf die Speisetore abbilden, da sie in Falle unzureichender modaler Bandbreiten, von besonderem Interesse sind. Kapitel 5 fokussiert auf die besonderen Probleme bei beim Entwurf extrem kleiner Antennensysteme. Nach Betrachtung in die maßgeblichen physikalischen Beschränkungen werden die Abschätzung erreichbarer Bandbreiten und Maßnahmen zur Sicherstellung eines akzeptablen Wirkungsgrades diskutiert. Vorgeschlagen wird in diesem Zusammenhang die Kombination von elektrisch rekonfigurierbaren Antennenstrukturen mit elektrisch abstimmbaren Anpass-Netzwerken. Die verschiedenen Aspekte werden am Beispiel des Entwurfs eines 2-Tor MIMO Antennensystems für einen USB Dongle erläutert. pKapitel 6 beschreibt im Detail den Entwurf, die Herstellung und die messtechnische Charakterisierung vier unterschiedlicher Prototypen von Mehrtorantennen. Anhand der Beispiele wird der in den vorherigen Kapiteln entwickelte Entwurfsansatz validiert. Insgesamt wird mit dieser Arbeit ein systematischer Entwurfsansatz vorgeschlagen, der auf der Kombination der Theorie charakteristische Moden leitender Körper mit der modalen Analyse von Mehrtorantennen, d.h. der Betrachtung des Spektrums der Strahlungsmatrix aufbaut. Der Ansatz wird erfolgreich auf eine Reihe praktisch relevanter Entwurfsaufgaben angewandt. Er führt auf ein systematisches Entwurfsverfahren, das es gestattet, Lösungen in der Nähe der physikalischen Grenzen für die erreichbare Bandbreite und den Wirkungsgrad aufzufinden