Reconstructing Video from Interferometric Measurements of Time-Varying Sources

Very long baseline interferometry (VLBI) makes it possible to recover images of astronomical sources with extremely high angular resolution. Most recently, the Event Horizon Telescope (EHT) has extended VLBI to short millimeter wavelengths with a goal of achieving angular resolution sufficient for imaging the event horizons of nearby supermassive black holes. VLBI provides measurements related to the underlying source image through a sparse set spatial frequencies. An image can then be recovered from these measurements by making assumptions about the underlying image. One of the most important assumptions made by conventional imaging methods is that over the course of a night's observation the image is static. However, for quickly evolving sources, such as the galactic center's supermassive black hole (Sgr A*) targeted by the EHT, this assumption is violated and these conventional imaging approaches fail. In this work we propose a new way to model VLBI measurements that allows us to recover both the appearance and dynamics of an evolving source by reconstructing a video rather than a static image. By modeling VLBI measurements using a Gaussian Markov Model, we are able to propagate information across observations in time to reconstruct a video, while simultaneously learning about the dynamics of the source's emission region. We demonstrate our proposed Expectation-Maximization (EM) algorithm, StarWarps, on realistic synthetic observations of black holes, and show how it substantially improves results compared to conventional imaging algorithms. Additionally, we demonstrate StarWarps on real VLBI data of the M87 Jet from the VLBA

Interferometry concepts

This paper serves as an introduction to the current book. It provides the basic notions of long-baseline optical/infrared interferome-try prior to reading all the subsequent chapters, and is not an extended introduction to the field.Comment: 35 pages, 13 figure

M87* in space, time, and frequency

Observing the dynamics of compact astrophysical objects provides insights into their inner workings, thereby probing physics under extreme conditions. The immediate vicinity of an active supermassive black hole with its event horizon, photon ring, accretion disk, and relativistic jets is a perfect pace to study general relativity, magneto-hydrodynamics, and high energy plasma physics. The recent observations of the black hole shadow of M87* with Very Long Baseline Interferometry (VLBI) by the Event Horizon Telescope (EHT) open the possibility to investigate its dynamical processes on time scales of days. In this regime, radio astronomical imaging algorithms are brought to their limits. Compared to regular radio interferometers, VLBI networks typically have fewer antennas and low signal to noise ratios (SNRs). If the source is variable during the observational period, one cannot co-add data on the sky brightness distribution from different time frames to increase the SNR. Here, we present an imaging algorithm that copes with the data scarcity and the source's temporal evolution, while simultaneously providing uncertainty quantification on all results. Our algorithm views the imaging task as a Bayesian inference problem of a time-varying brightness, exploits the correlation structure between time frames, and reconstructs an entire, $\mathbf{2+1+1}$ dimensional time-variable and spectrally resolved image at once. The degree of correlation in the spatial and the temporal domains is inferred from the data and no form of correlation is excluded a priori. We apply this method to the EHT observation of M87* and validate our approach on synthetic data. The time- and frequency-resolved reconstruction of M87* confirms variable structures on the emission ring on a time scale of days. The reconstruction indicates extended and time-variable emission structures outside the ring itself.Comment: 43 pages, 15 figures, 6 table

The quantitative analysis of transonic flows by holographic interferometry

This thesis explores the feasibility of routine transonic flow analysis by holographic interferometry. Holography is potentially an important quantitative flow diagnostic, because whole-field data is acquired non-intrusively without the use of particle seeding. Holographic recording geometries are assessed and an image plane specular illumination configuration is shown to reduce speckle noise and maximise the depth-of-field of the reconstructed images. Initially, a NACA 0012 aerofoil is wind tunnel tested to investigate the analysis of two-dimensional flows. A method is developed for extracting whole-field density data from the reconstructed interferograms. Fringe analysis errors axe quantified using a combination of experimental and computer generated imagery. The results are compared quantitatively with a laminar boundary layer Navier-Stokes computational fluid dynamics (CFD) prediction. Agreement of the data is excellent, except in the separated wake where the experimental boundary layer has undergone turbulent transition. A second wind tunnel test, on a cone-cylinder model, demonstrates the feasibility of recording multi-directional interferometric projections using holographic optical elements (HOE’s). The prototype system is highly compact and combines the versatility of diffractive elements with the efficiency of refractive components. The processed interferograms are compared to an integrated Euler CFD prediction and it is shown that the experimental shock cone is elliptical due to flow confinement. Tomographic reconstruction algorithms are reviewed for analysing density projections of a three-dimensional flow. Algebraic reconstruction methods are studied in greater detail, because they produce accurate results when the data is ill-posed. The performance of these algorithms is assessed using CFD input data and it is shown that a reconstruction accuracy of approximately 1% may be obtained when sixteen projections are recorded over a viewing angle of ±58°. The effect of noise on the data is also quantified and methods are suggested for visualising and reconstructing obstructed flow regions

An appraisal and developments of laser holography for interferometric engineering measurement

Holography is a two-stage method of imagery in which both amplitude and phase information characterizing a wavefront are recorded, and subsequently reconstructed. Only with the advent of laser light sources in the early 1960s did the method become practical, motivating research into applications. One of these, holographic interferometry, was based on the fact that a reconstructed wavefront from a hologram could be used as a reference for interferometric comparison. This enabled interferometry to be extended to objects having scattering surfaces of any shape, and the potential of the method in engineering measurement was considered to be high. A literature survey carried out at the start of this project (1967 to 1968), and reported in Chapter 2, revealed that many potential applications in the fields of stress analysis, vibration analysis, fault detection in materials and structures, and dimensional inspection, had been proposed but were not quickly materializing. This was seen to be partly due to practical difficulties necessitating laboratory procedures, and partly due to difficulties in analysing interferograms to obtain specific measurements. Accordingly, the aims of this project were: (i) to develop apparatus and methods that would simplify and improve the practice of holographic interferometry and the interpretation of results; (ii) to investigate fringe interpretation, and to assess the accuracy and general feasibility, in relation to practical measurements of surface deformation. [Continues.

Holography: A survey

The development of holography and the state of the art in recording and displaying information, microscopy, motion, pictures, and television applications are discussed. In addition to optical holography, information is presented on microwave, acoustic, ultrasonic, and seismic holography. Other subjects include data processing, data storage, pattern recognition, and computer-generated holography. Diagrams of holographic installations are provided. Photographs of typical holographic applications are used to support the theoretical aspects

New measuring techniques using holographic and speckle interferometric recording

Electronic and photographic interferometric recording, and their combination, result in several novel optical measuring techniques. The interferometric properties of holographic and speckle processes in these techniques encompass fields such as lapse time, real time and time average holographic interferometry, two-wavelength and multiple-index speckle contouring, figure (moire) interference, photographic bleach processes and electronic processing. Each of these fields is analysed and conclusions are drawn in their interaction with the proposed techniques. A clear and simple approach to optical wave theory is intended with emphasis in scalar wave theory. [Continues.

Regularisierte Optimierungsverfahren für Rekonstruktion und Modellierung in der Computergraphik

The field of computer graphics deals with virtual representations of the real world. These can be obtained either through reconstruction of a model from measurements, or by directly modeling a virtual object, often on a real-world example. The former is often formalized as a regularized optimization problem, in which a data term ensures consistency between model and data and a regularization term promotes solutions that have high a priori probability. In this dissertation, different reconstruction problems in computer graphics are shown to be instances of a common class of optimization problems which can be solved using a uniform algorithmic framework. Moreover, it is shown that similar optimization methods can also be used to solve data-based modeling problems, where the amount of information that can be obtained from measurements is insufficient for accurate reconstruction. As real-world examples of reconstruction problems, sparsity and group sparsity methods are presented for radio interferometric image reconstruction in static and time-dependent settings. As a modeling example, analogous approaches are investigated to automatically create volumetric models of astronomical nebulae from single images based on symmetry assumptions.Das Feld der Computergraphik beschäftigt sich mit virtuellen Abbildern der realen Welt. Diese können erlangt werden durch Rekonstruktion eines Modells aus Messdaten, oder durch direkte Modellierung eines virtuellen Objekts, oft nach einem realen Vorbild. Ersteres wird oft als regularisiertes Optimierungsproblem dargestellt, in dem ein Datenterm die Konsistenz zwischen Modell und Daten sicherstellt, während ein Regularisierungsterm Lösungen fördert, die eine hohe A-priori-Wahrscheinlichkeit aufweisen. In dieser Arbeit wird gezeigt, dass verschiedene Rekonstruktionsprobleme der Computergraphik Instanzen einer gemeinsamen Klasse von Optimierungsproblemen sind, die mit einem einheitlichen algorithmischen Framework gelöst werden können. Darüber hinaus wird gezeigt, dass vergleichbare Optimierungsverfahren auch genutzt werden können, um Probleme der datenbasierten Modellierung zu lösen, bei denen die aus Messungen verfügbaren Daten nicht für eine genaue Rekonstruktion ausreichen. Als praxisrelevante Beispiele für Rekonstruktionsprobleme werden Sparsity- und Group-Sparsity-Methoden für die radiointerferometrische Bildrekonstruktion im statischen und zeitabhängigen Fall vorgestellt. Als Beispiel für Modellierung werden analoge Verfahren untersucht, um basierend auf Symmetrieannahmen automatisch volumetrische Modelle astronomischer Nebel aus Einzelbildern zu erzeugen

Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging

Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically focus on recovering a point estimate. This is a serious limitation when working with underdetermined imaging systems, where it is conceivable that multiple image modes would be consistent with the measured data. Characterizing the space of probable images that explain the observational data is therefore crucial. In this paper, we propose a variational deep probabilistic imaging approach to quantify reconstruction uncertainty. Deep Probabilistic Imaging (DPI) employs an untrained deep generative model to estimate a posterior distribution of an unobserved image. This approach does not require any training data; instead, it optimizes the weights of a neural network to generate image samples that fit a particular measurement dataset. Once the network weights have been learned, the posterior distribution can be efficiently sampled. We demonstrate this approach in the context of interferometric radio imaging, which is used for black hole imaging with the Event Horizon Telescope, and compressed sensing Magnetic Resonance Imaging (MRI).Comment: This paper has been accepted to AAAI 2021. Keywords: Computational Imaging, Normalizing Flow, Uncertainty Quantification, Interferometry, MR