Spatial priors for tomographic reconstructions from limited data

Tomografie is het reconstrueren van het inwendige van een object a.d.h.v externe metingen, b.v. beelden verkregen met X-stralen of microgolven. Deze thesis bekijkt de specifieke aspecten van microgolftomografie en magnetische resonantie beeldvorming (Magnetic Resonance Imaging – MRI); beide technieken zijn onschadelijk voor de mens. Terwijl het gebruik van MRI wijdverspreid is voor veel klinische toepassingen, is microgolftomografie nog niet in klinisch gebruik ondanks zijn potentiële voordelen. Door de lage kost en draagbaarheid van de toestellen is het een waardevolle aanvulling aan het assortiment

Analysis and Modeling of Passive Stereo and Time-of-Flight Imaging

This thesis is concerned with the analysis and modeling of effects which cause errors in passive stereo and Time-of-Flight imaging systems. The main topics are covered in four chapters: I commence with a treatment of a system combining Time-of-Flight imaging with passive stereo and show how commonly used fusion models relate to the measurements of the individual modalities. In addition, I present novel fusion techniques capable of improving the depth reconstruction over those obtained separately by either modality. Next, I present a pipeline and uncertainty analysis for the generation of large amounts of reference data for quantitative stereo evaluation. The resulting datasets not only contain reference geometry, but also per pixel measures of reference data uncertainty. The next two parts deal with individual effects observed: Time-of-Flight cameras suffer from range ambiguity if the scene extends beyond a certain distance. I show that it is possible to extend the valid range by changing design parameters of the underlying measurement system. Finally, I present methods that make it possible to amend model violation errors in stereo due to reflections. This is done by means of modeling a limited level of light transport and material properties in the scene

Software model with verification of the imaging chamber in microwave tomography

Микроталасна томографија је метода за снимање објекта путем микроталаса. Након мерења објекта системом антена у комори решава се инверзни проблем нумеричком симулацијом и оптимизацијом. У овом раду се решава проблем верности моделовања антенског система у симулацији. Избегавањем апроксимација у моделовању антенског система, добија се вернији софтверски модел. Ради постизавања тог циља  жичана квадратна спирална антена је одабрана за коришћење у комори за снимање. Употреба предложене антене у микроталасној томографији је новитет. Реализован је софтверски симулациони модел коморе са предложеном антеном.  У симулацијама је извршено поређење са другим антенама често коришћеним у литератури за дату сврху. Израђен је прототип коморе са предложеним антенама. Извршена су мерења и поређења са предложеним моделом, како би се потврдила веродостојсност модела.Mikrotalasna tomografija je metoda za snimanje objekta putem mikrotalasa. Nakon merenja objekta sistemom antena u komori rešava se inverzni problem numeričkom simulacijom i optimizacijom. U ovom radu se rešava problem vernosti modelovanja antenskog sistema u simulaciji. Izbegavanjem aproksimacija u modelovanju antenskog sistema, dobija se verniji softverski model. Radi postizavanja tog cilja  žičana kvadratna spiralna antena je odabrana za korišćenje u komori za snimanje. Upotreba predložene antene u mikrotalasnoj tomografiji je novitet. Realizovan je softverski simulacioni model komore sa predloženom antenom.  U simulacijama je izvršeno poređenje sa drugim antenama često korišćenim u literaturi za datu svrhu. Izrađen je prototip komore sa predloženim antenama. Izvršena su merenja i poređenja sa predloženim modelom, kako bi se potvrdila verodostojsnost modela.Microwave tomography is method of object imaging by means of microwaves. After object measurement by system of antennas in chamber inverse problem is solved by numeric simulation and optimization. This thesis focuses on problem of trueness in modeling antenna system in simulation. Avoding approximations while modeling antenna system yield better trueness of software model. To achieve this target wire square spiral antenna is utilized in imaging chamber. Usage of proposed antenna in microwave tomography is novelty. Software simulation model of chamber with proposed antenna is designed and evaluated. Comparison with other antennas often used in literature for this purpose is done in simulation. Chamber with antennas is realized at the prototype level. Measurement and comparison with proposed model are done in order to verify its trueness

Large Scale Inverse Problems

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation &amp Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

New insights in huber and TV-like regularizers in microwave imaging

In this paper we give new insights into quantitative microwave tomography with robust Huber regularizer and Gauss-Newton optimization. Firstly, we validate this approach for the first time on real electromagnetic measurements. Secondly, we extend the framework with a modified Huber function, which behaves like TV regularization. This is interesting for reconstructing piece-wise constant permittivities that appear in non-destructive testing of installations and other man-made objects