Multivariate nonparametric regression using lifting

Summary For regularly spaced one-dimensional data wavelet shrinkage has proven to be a compelling method for nonparametric function estimation. We argue that this is not the case for irregularly spaced data in two or higher dimensions. This article develops three methods for the multiscale analysis of irregularly spaced data based on the recently developed lifting paradigm by "lifting one coefficient at a time". The concept of scale still exists within these transforms but as a continuous quantity rather than dyadic levels. We develop empirical Bayes methods that take account of the continuous nature of the scale. We apply our new methods to the problems of estimation of krill density and rail arrival delays. We demonstrate good performance in a simulation study on new two-dimensional analogues of the well-known Blocks, Bumps, Doppler and Heavisine and a new piecewise linear function called maartenfunc

Time series forecasting using wavelet and support vector machine

Master'sMASTER OF ENGINEERIN

Hardware-accelerated algorithms in visual computing

This thesis presents new parallel algorithms which accelerate computer vision methods by the use of graphics processors (GPUs) and evaluates them with respect to their speed, scalability, and the quality of their results. It covers the fields of homogeneous and anisotropic diffusion processes, diffusion image inpainting, optic flow, and halftoning. In this turn, it compares different solvers for homogeneous diffusion and presents a novel \u27extended\u27 box filter. Moreover, it suggests to use the fast explicit diffusion scheme (FED) as an efficient and flexible solver for nonlinear and in particular for anisotropic parabolic diffusion problems on graphics hardware. For elliptic diffusion-like processes, it recommends to use cascadic FED or Fast Jacobi schemes. The presented optic flow algorithm represents one of the fastest yet very accurate techniques. Finally, it presents a novel halftoning scheme which yields state-of-the-art results for many applications in image processing and computer graphics.Diese Arbeit präsentiert neue parallele Algorithmen zur Beschleunigung von Methoden in der Bildinformatik mittels Grafikprozessoren (GPUs), und evaluiert diese im Hinblick auf Geschwindigkeit, Skalierungsverhalten, und Qualität der Resultate. Sie behandelt dabei die Gebiete der homogenen und anisotropen Diffusionsprozesse, Inpainting (Bildvervollständigung) mittels Diffusion, die Bestimmung des optischen Flusses, sowie Halbtonverfahren. Dabei werden verschiedene Löser für homogene Diffusion verglichen und ein neuer \u27erweiterter\u27 Mittelwertfilter präsentiert. Ferner wird vorgeschlagen, das schnelle explizite Diffusionsschema (FED) als effizienten und flexiblen Löser für parabolische nichtlineare und speziell anisotrope Diffusionsprozesse auf Grafikprozessoren einzusetzen. Für elliptische diffusionsartige Prozesse wird hingegen empfohlen, kaskadierte FED- oder schnelle Jacobi-Verfahren einzusetzen. Der vorgestellte Algorithmus zur Berechnung des optischen Flusses stellt eines der schnellsten und dennoch äußerst genauen Verfahren dar. Schließlich wird ein neues Halbtonverfahren präsentiert, das in vielen Bereichen der Bildverarbeitung und Computergrafik Ergebnisse produziert, die den Stand der Technik repräsentieren

Atomic-scale and three-dimensional transmission electron microscopy of nanoparticle morphology

The burgeoning field of nanotechnology motivates comprehensive elucidation of nanoscale materials. This thesis addresses transmission electron microscope characterisation of nanoparticle morphology, concerning specifically the crystal- lographic status of novel intermetallic GaPd2 nanocatalysts and advancement of electron tomographic methods for high-fidelity three-dimensional analysis. Going beyond preceding analyses, high-resolution annular dark-field imaging is used to verify successful nano-sizing of the intermetallic compound GaPd2. It also reveals catalytically significant and crystallographically intriguing deviations from the bulk crystal structure. So-called ‘non-crystallographic’ five-fold twinned nanoparticles are observed, adding a new perspective in the long standing debate over how such morphologies may be achieved. The morphological complexity of the GaPd2 nanocatalysts, and many cognate nanoparticle systems, demands fully three-dimensional analysis. It is illustrated how image processing techniques applied to electron tomography reconstructions can facilitate more facile and objective quantitative analysis (‘nano-metrology’). However, the fidelity of the analysis is limited ultimately by artefacts in the tomographic reconstruction. Compressed sensing, a new sampling theory, asserts that many signals can be recovered from far fewer measurements than traditional theories dictate are necessary. Compressed sensing is applied here to electron tomographic reconstruction, and is shown to yield far higher fidelity reconstructions than conventional algorithms. Reconstruction from extremely limited data, more robust quantitative analysis and novel three-dimensional imaging are demon- strated, including the first three-dimensional imaging of localised surface plasmon resonances. Many aspects of transmission electron microscopy characterisation may be enhanced using a compressed sensing approach

Scalable Bayesian methods for the analysis of neuroimaging data

The recent surge in large-scale population health datasets, such as the UK Biobank or the Adolescent Brain Cognitive Development (ABCD) study, requires the development of scalable statistical methods that are capable of analysing the rich multitude of data sources. This thesis focuses on the scalable analysis of Magnetic Resonance Imaging (MRI) neuroimaging data, such as binary lesion masks and task-based functional Magnetic Resonance Imaging (fMRI). In particular, we introduce two Bayesian spatial models with sparsity priors on the spatially varying coefficients and extend our work to suit the large sample sizes found in population health studies. Firstly, we propose a scalable hierarchical Bayesian image-on-scalar regression model, called BLESS, capable of handling binary responses and of placing continuous spike-and-slab mixture priors on spatially varying parameters. Thereby, enforcing spatial dependency on the parameter dictating the amount of sparsity within the probability of inclusion. The use of mean-field variational inference with dynamic posterior exploration, which is an annealing-like strategy that improves optimisation, allows our method to scale to large sample sizes. We validate our results via simulation studies and an application to binary lesion masks from the UK Biobank. Secondly, we extend our method to account for underestimation of posterior variance due to variational inference by providing an approximate posterior sampling approach inspired by Bayesian bootstrap ideas and spike-and-slab priors with random shrinkage targets. Besides accurate uncertainty quantification, this approach is capable of producing novel cluster size-based imaging statistics, such as credible intervals of cluster size, and measures of reliability of cluster occurrence. Thirdly, we develop a Bayesian nonparametric scalar-on-image regression model with a relaxed-thresholded Gaussian process prior on the spatially varying coefficients in order to introduce sparsity and smoothness into the model. Our main contribution is the improved scalability, allowing for larger sample sizes and bigger image dimensions, which is made possible by replacing posterior sampling with a variational approximation. We validate our results via simulation studies and an application to cortical surface task-based fMRI data from the ABCD study

Characterisation of the unsteady wake of a square-back road vehicle

Square-back shapes are popular in the automotive market for their high level of practicality. These geometries, however, are usually characterised by high aerodynamic drag and their wake flow dynamics present many aspects, such as the coexistence of long- and short-time unsteady modes, whose full comprehension is still far from being achieved. The present work aims to provide some contributions to this field. An extensive experimental campaign consisting of balance, pressure tapping, particle image velocimetry and single point velocity measurements has been carried out in order to characterise the dynamic behaviour of the wake developing downstream of a simplified square-back geometry. Tests have been performed considering the Windsor body, at a Reynolds number (based on the model height) of ReH = 7.7 × 10^5. New insights on how the long-time instability develops are provided. The instability is shown to stem from the mutual interactions between the four shear layers bounding the wake rather than being the result of the state of perturbation of a single shear layer. Changes in the level of interaction between two or more shear layers are also reported to affect the short-time unsteady modes. A drag reduction is reported every time the symmetry of the wake is restored, as a consequence of the increased amount of reverse flow impinging on the base of the model. This seems to be true regardless of the configuration considered (with or without wheels) and the type of optimisation strategy adopted, although it does not necessarily imply the complete suppression of the long-time instability. In fact, a certain level of mobility in the flow reversal seems to be inevitable every time the symmetry of the wake is restored. Several elements that can alter this behaviour are also identified. A change in the curvature of at least one of the four shear layers is shown to increase the frequency of the switches between bi-stable states, until eventually the long-time instability disappears replaced by low frequency flapping or swinging motions. Such changes can be triggered by applying perturbations on either a global scale or a more local scale. Overall, the results presented in this work help to bridge the gap between simplified geometries and more realistic automotive shapes, as far as the characterisation of the time averaged and main unsteady features of the wake is concerned, and provide insights that may allow in the future the design of more effective flow control systems for drag reduction

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions