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

Shear-promoted drug encapsulation into red blood cells: a CFD model and μ-PIV analysis

The present work focuses on the main parameters that influence shear-promoted encapsulation of drugs into erythrocytes. A CFD model was built to investigate the fluid dynamics of a suspension of particles flowing in a commercial micro channel. Micro Particle Image Velocimetry (μ-PIV) allowed to take into account for the real properties of the red blood cell (RBC), thus having a deeper understanding of the process. Coupling these results with an analytical diffusion model, suitable working conditions were defined for different values of haematocrit

NASA/ASEE Summer Faculty Fellowship Program, 1990, Volume 1

The 1990 Johnson Space Center (JSC) NASA/American Society for Engineering Education (ASEE) Summer Faculty Fellowship Program was conducted by the University of Houston-University Park and JSC. A compilation of the final reports on the research projects are presented. The topics covered include: the Space Station; the Space Shuttle; exobiology; cell biology; culture techniques; control systems design; laser induced fluorescence; spacecraft reliability analysis; reduced gravity; biotechnology; microgravity applications; regenerative life support systems; imaging techniques; cardiovascular system; physiological effects; extravehicular mobility units; mathematical models; bioreactors; computerized simulation; microgravity simulation; and dynamic structural analysis

Nonlocal smoothing and adaptive morphology for scalar- and matrix-valued images

In this work we deal with two classic degradation processes in image analysis, namely noise contamination and incomplete data. Standard greyscale and colour photographs as well as matrix-valued images, e.g. diffusion-tensor magnetic resonance imaging, may be corrupted by Gaussian or impulse noise, and may suffer from missing data. In this thesis we develop novel reconstruction approaches to image smoothing and image completion that are applicable to both scalar- and matrix-valued images. For the image smoothing problem, we propose discrete variational methods consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures. We obtain edge-preserving filters by the joint use of such measures rich in texture content together with robust non-convex penalisers. For the image completion problem, we introduce adaptive, anisotropic morphological partial differential equations modelling the dilation and erosion processes. They adjust themselves to the local geometry to adaptively fill in missing data, complete broken directional structures and even enhance flow-like patterns in an anisotropic manner. The excellent reconstruction capabilities of the proposed techniques are tested on various synthetic and real-world data sets.In dieser Arbeit beschäftigen wir uns mit zwei klassischen Störungsquellen in der Bildanalyse, nämlich mit Rauschen und unvollständigen Daten. Klassische Grauwert- und Farb-Fotografien wie auch matrixwertige Bilder, zum Beispiel Diffusionstensor-Magnetresonanz-Aufnahmen, können durch Gauß- oder Impulsrauschen gestört werden, oder können durch fehlende Daten gestört sein. In dieser Arbeit entwickeln wir neue Rekonstruktionsverfahren zum zur Bildglättung und zur Bildvervollständigung, die sowohl auf skalar- als auch auf matrixwertige Bilddaten anwendbar sind. Zur Lösung des Bildglättungsproblems schlagen wir diskrete Variationsverfahren vor, die aus nichtlokalen Daten- und Glattheitstermen bestehen und allgemeine auf Bildausschnitten definierte Unähnlichkeitsmaße bestrafen. Kantenerhaltende Filter werden durch die gemeinsame Verwendung solcher Maße in stark texturierten Regionen zusammen mit robusten nichtkonvexen Straffunktionen möglich. Für das Problem der Datenvervollständigung führen wir adaptive anisotrope morphologische partielle Differentialgleichungen ein, die Dilatations- und Erosionsprozesse modellieren. Diese passen sich der lokalen Geometrie an, um adaptiv fehlende Daten aufzufüllen, unterbrochene gerichtet Strukturen zu schließen und sogar flussartige Strukturen anisotrop zu verstärken. Die ausgezeichneten Rekonstruktionseigenschaften der vorgestellten Techniken werden anhand verschiedener synthetischer und realer Datensätze demonstriert

Wavelet and Multiscale Methods

[no abstract available

Foundations, Inference, and Deconvolution in Image Restoration

Image restoration is a critical preprocessing step in computer vision, producing images with reduced noise, blur, and pixel defects. This enables precise higher-level reasoning as to the scene content in later stages of the vision pipeline (e.g., object segmentation, detection, recognition, and tracking). Restoration techniques have found extensive usage in a broad range of applications from industry, medicine, astronomy, biology, and photography. The recovery of high-grade results requires models of the image degradation process, giving rise to a class of often heavily underconstrained, inverse problems. A further challenge specific to the problem of blur removal is noise amplification, which may cause strong distortion by ringing artifacts. This dissertation presents new insights and problem solving procedures for three areas of image restoration, namely (1) model foundations, (2) Bayesian inference for high-order Markov random fields (MRFs), and (3) blind image deblurring (deconvolution). As basic research on model foundations, we contribute to reconciling the perceived differences between probabilistic MRFs on the one hand, and deterministic variational models on the other. To do so, we restrict the variational functional to locally supported finite elements (FE) and integrate over the domain. This yields a sum of terms depending locally on FE basis coefficients, and by identifying the latter with pixels, the terms resolve to MRF potential functions. In contrast with previous literature, we place special emphasis on robust regularizers used commonly in contemporary computer vision. Moreover, we draw samples from the derived models to further demonstrate the probabilistic connection. Another focal issue is a class of high-order Field of Experts MRFs which are learned generatively from natural image data and yield best quantitative results under Bayesian estimation. This involves minimizing an integral expression, which has no closed form solution in general. However, the MRF class under study has Gaussian mixture potentials, permitting expansion by indicator variables as a technical measure. As approximate inference method, we study Gibbs sampling in the context of non-blind deblurring and obtain excellent results, yet at the cost of high computing effort. In reaction to this, we turn to the mean field algorithm, and show that it scales quadratically in the clique size for a standard restoration setting with linear degradation model. An empirical study of mean field over several restoration scenarios confirms advantageous properties with regard to both image quality and computational runtime. This dissertation further examines the problem of blind deconvolution, beginning with localized blur from fast moving objects in the scene, or from camera defocus. Forgoing dedicated hardware or user labels, we rely only on the image as input and introduce a latent variable model to explain the non-uniform blur. The inference procedure estimates freely varying kernels and we demonstrate its generality by extensive experiments. We further present a discriminative method for blind removal of camera shake. In particular, we interleave discriminative non-blind deconvolution steps with kernel estimation and leverage the error cancellation effects of the Regression Tree Field model to attain a deblurring process with tightly linked sequential stages