Nonlinear multiple regression methods for spectroscopic analysis: application to NIR calibration

Chemometrics has been applied to analyse near-infrared (NIR) spectra for decades. Linear regression methods such as partial least squares (PLS) regression and principal component regression (PCR) are simple and widely used solutions for spectroscopic calibration. My dissertation connects spectroscopic calibration with nonlinear machine learning techniques. It explores the feasibility of applying nonlinear methods for NIR calibration. Investigated nonlinear regression methods include least squares support vec- tor machine (LS-SVM), Gaussian process regression (GPR), Bayesian hierarchical mixture of linear regressions (HMLR) and convolutional neural networks (CNN). Our study focuses on the discussion of various design choices, interpretation of nonlinear models and providing novel recommendations and insights for the con- struction nonlinear regression models for NIR data. Performances of investigated nonlinear methods were benchmarked against traditional methods on multiple real-world NIR datasets. The datasets have differ- ent sizes (varying from 400 samples to 7000 samples) and are from various sources. Hypothesis tests on separate, independent test sets indicated that nonlinear methods give significant improvements in most practical NIR calibrations

Computational Imaging with Limited Photon Budget

The capability of retrieving the image/signal of interest from extremely low photon flux is attractive in scientific, industrial, and medical imaging applications. Conventional imaging modalities and reconstruction algorithms rely on hundreds to thousands of photons per pixel (or per measurement) to ensure enough signal-to-noise (SNR) ratio for extracting the image/signal of interest. Unfortunately, the potential of radiation or photon damage prohibits high SNR measurements in dose-sensitive diagnosis scenarios. In addition, imaging systems utilizing inherently weak signals as contrast mechanism, such as X-ray scattering-based tomography, or attosecond pulse retrieval from the streaking trace, entail prolonged integration time to acquire hundreds of photons, thus rendering high SNR measurement impractical. This dissertation addresses the problem of imaging from limited photon budget when high SNR measurements are either prohibitive or impractical. A statistical image reconstruction framework based on the knowledge of the image-formation process and the noise model of the measurement system has been constructed and successfully demonstrated on two imaging platforms – photon-counting X-ray imaging, and attosecond pulse retrieval. For photon-counting X-ray imaging, the statistical image reconstruction framework achieves high-fidelity X-ray projection and tomographic image reconstruction from as low as 16 photons per pixel on average. The capability of our framework in modeling the reconstruction error opens the opportunity of designing the optimal strategies to distribute a fixed photon budget for region-of-interest (ROI) reconstruction, paving the way for radiation dose management in an imaging-specific task. For attosecond pulse retrieval, a learning-based framework has been incorporated into the statistical image reconstruction to retrieve the attosecond pulses from the noisy streaking traces. Quantitative study on the required signal-to-noise ratio for satisfactory pulse retrieval enabled by our framework provides a guideline to future attosecond streaking experiments. In addition, resolving the ambiguities in the streaking process due to the carrier envelop phase has also been demonstrated with our statistical reconstruction framework

Image Diversification via Deep Learning based Generative Models

Machine learning driven pattern recognition from imagery such as object detection has been prevalenting among society due to the high demand for autonomy and the recent remarkable advances in such technology. The machine learning technologies acquire the abstraction of the existing data and enable inference of the pattern of the future inputs. However, such technologies require a sheer amount of images as a training dataset which well covers the distribution of the future inputs in order to predict the proper patterns whereas it is impracticable to prepare enough variety of images in many cases. To address this problem, this thesis pursues to discover the method to diversify image datasets for fully enabling the capability of machine learning driven applications. Focusing on the plausible image synthesis ability of generative models, we investigate a number of approaches to expand the variety of the output images using image-to-image translation, mixup and diffusion models along with the technique to enable a computation and training dataset efficient diffusion approach. First, we propose the combined use of unpaired image-to-image translation and mixup for data augmentation on limited non-visible imagery. Second, we propose diffusion image-to-image translation that generates greater quality images than other previous adversarial training based translation methods. Third, we propose a patch-wise and discrete conditional training of diffusion method enabling the reduction of the computation and the robustness on small training datasets. Subsequently, we discuss a remaining open challenge about evaluation and the direction of future work. Lastly, we make an overall conclusion after stating social impact of this research field

Galactic dust and dynamics

Physics is about building a model of the world. Building a model can have two different interpretations. On the one hand, it can refer to the construction of a model that mimics the behavior of a system, i.e. in the form of a simulation. On the other hand it can denote the process of building something that has properties of the original, i.e. a map. This dissertation contributes to modeling the world in both meanings of the word, and also connects them. We regard a map as a conditional probability, the map has degrees of freedom that constrain the mapped system. Maps of time variable systems have to be updated as the system evolves. Given only the information that a map contains about a system at a previous point in time, and the time evolution of the system, the degrees of freedom of an updated map should be selected such that the least amount of information about the system is lost. Iterating this procedure, one obtains a simulation scheme, as the time evolution of the system is imprinted in the sequence of maps. In this thesis, simulation schemes for a simple fluid dynamic equation are constructed this way from first principles. Of paramount importance is the conditional probability of the system given the map data, as it is the only way to influence the resulting simulation scheme. The second part of this thesis focuses on constructing three dimensional maps of the Galactic dust. In this application one has to specify as well, which statements the map degrees of freedom make about the actual distribution of Galactic dust. We choose to model dust as a correlated field, where the degree of correlation is an additional parameter of the map. To infer the parameters of the map, data about dust in three dimensions is needed. To this end, data from stellar surveys are used, which reflects dust density through the extinction towards millions of sources; sources of which also the distance is known to a limited precision. Three dust maps are presented, one using simulated data through which we verify the validity of our approach, one using data from the most recent and precise stellar survey obtained by the Gaia satellite, and a final map using data from a combination of many larger stellar surveys that are available. Our final result is a map showing the extinction due to Galactic dust up to a distance of about $1000$ light years in three dimensions. The map is of importance for observers, to whom dust extinction comprises a foreground to observations, as well as for astrophysicists interested in the composition and structure of the interstellar medium. Also parameters of simulations of the interstellar medium can be constrained using our derived statistical properties. In conclusion, this thesis demonstrates the importance of models and how they constrain reality, as well as the impact of statistical analyses that are derived from first principles.Physik befasst sich mit der Modellierung der Welt. Ein Modell zu bauen kann zwei Bedeutungen haben: Einerseits kann man damit die Konstruktion eines Modells bezeichnen, das das Verhalten eines Systems imitiert, eine Simulation. Andererseits kann ein Modell etwas bezeichnen, das Aspekte des Originals zeigt, nur nicht so groß ist, z.B. eine Karte. Diese Dissertation beschäftigt sich mit der Modellierung der Welt in beiderlei Bedeutungen, und verbindet diese auch. Wir betrachten eine Karte als bedingte Wahrscheinlichkeit, denn die Karte hat Freiheitsgrade, die Aussagen über das System ermöglichen. Kartografiert man ein zeitveränderliches System, so muss man Karten erneuern wenn das System sich verändert. Kennt man die Zeitevolution des Systems, so kann man Aussagen einer Karte in die Zukunft extrapolieren. Die Freiheitsgrade einer erneuerten Karte sollte man dann so wählen, dass man möglichst wenig Informationen über das System verliert. Folgt man diesem Paradigma wiederholt, so erhält man eine Simulation des Systems, abgebildet durch die Serie an Karten. Auf diese Art und Weise leiten wir Simulationen eines einfachen fluiddynamischen Systems von Grund auf her. Dabei ist die durch die Karte induzierte bedingte Wahrscheinlichkeit entscheidend, da sie die einzige Stellschraube für das resultierende Simulationsschema ist. Der zweite Teil dieser Arbeit behandelt das Erstellen von dreidimensionalen Karten von galaktischem Staub. Auch hierbei spielt die Wahl der bedingten Wahrscheinlichkeit, die von der Karte induziert wird, eine zentrale Rolle. Wir modellieren Staub als ein korreliertes Feld, wobei der Grad der Korrelation ein zusätzlicher Parameter der Karte ist. Um die Parameter der Karte zu inferieren werden Daten über Staub in drei Dimensionen benötigt. Diese beziehen wir aus Sternenkatalogen, die Informationen über die Staubdichte durch Abdunklungswerte von Sternen enthält; Sternen von welchen auch die Positionen zu gewissem Grad bekannt sind. Drei Staubkarten werden hier präsentiert. Die erste Staubkarte verwendete synthetische Daten und dient der Validierung unseres Ansatzes. Der zweiten Staubkarte liegt der neuste und präziseste Katalog von Sternen, durchgeführt von dem Gaia Satelliten, zu Grunde. Die finale Staubkarte benutzt Daten von allen größeren öffentlichen Katalogen von Sternen zusammen. Diese Karte zeigt die Abdunklung durch Staub bis zu einer Distanz von 1000 Lichtjahren in drei Dimensionen. Sie ist sowohl für Beobachter zur Korrektur von Staubabsorption relevant, als auch für Astrophysiker, die sich für die Zusammensetzung des interstellaren Mediums interessieren. Auch Parameter von Simulationen des interstellaren Mediums können durch die hergeleiteten statistischen Eigenschaften eingeschränkt werden. Zusammenfassend demonstriert diese Arbeit die Wichtigkeit von Modellen und deren Aussagen über die Realität, sowie die Bedeutung statistischer Analysen, die von Grund auf hergeleitet werden

The Nature and Impact of Active Galactic Nuclei

The gravitational interaction around the event horizon of black holes presents theoretical challenges. With the advent of the Event Horizon Telescope (EHT), we are now entering an era in physics where we can probe the structure of spacetime on horizon scales. The EHT presents the first opportunity to directly image the supermassive black holes at the center of the Milky Way and M 87. By imaging the central black hole, we can directly learn about the nature of spacetime and plasma physics on horizon scales. The black hole images produced by the EHT are dominated by a bright ring. The ellipticity of the ring could potentially signal deviations from general relativity. However, whether the EHT imaging techniques can robustly detect ellipticity has not been fully explored. Chapters 2–5 analyze the EHT’s ability to measure ellipticity in four parts. First, in Chapter 2, we develop a method to extract image features (e.g., ring ellipticity) called variational image domain analysis. Second, in Chapter 3, we apply variational image domain analysis to the M 87 image reconstruction pipeline and demonstrate that it is unable to measure ellipticity. The core reason for this failure is that traditional radio imaging techniques cannot quantify image uncertainty. To solve this issue, in Chapters 4 and 5 we use Themis, a Bayesian parameter estimation framework for the EHT, to robustly measure the ellipticity of M 87. To apply Themis to the problem of Bayesian imaging, we developed a new sampler interface in Chapter 4. In Chapter 5 we apply Themis to M 87 and construct the first Bayesian estimates of its ellipticity. Furthermore, we demonstrate that the measured ellipticity is consistent with the expected ellipticity from an accretion disk around a Kerr black hole. In Chapter 6 we describe a novel method to measure spacetime around Sgr A∗ using hot spots. While M 87 is static over an observation, Sgr A∗ is dynamic, changing on minute timescales. Furthermore, Sgr A∗ flares 1–3 times a day in sub-mm, infrared, and X-ray. The Gravity Collaboration recently demonstrated that hot spots near the innermost stable circular orbit explain Sgr A∗ flares. Using Themis, we construct an efficient semi- analytical model of hotspots and fit simulated Sgr A∗ data from the 2017 EHT observations. We demonstrate that the EHT could potentially make a sub-percent spin measurement of Sgr A∗ by tracking the evolution of these flares. Furthermore, by observing multiple flares, we can tomographically map spacetime around Sgr A∗ , providing a test of general relativity in the strong-field regime