Noisy independent component analysis of auto-correlated components

We present a new method for the separation of superimposed, independent, auto-correlated components from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably, allowing separations even in the high noise regime. Characteristics of the measurement instruments can be included, allowing for application in complex measurement situations. Independent posterior samples can be provided, permitting error estimates on all desired quantities. Using the concept of information field theory, the algorithm is not restricted to any dimensionality of the underlying space or discretization scheme thereof

Metric Gaussian variational inference

One main result of this dissertation is the development of Metric Gaussian Variational Inference (MGVI), a method to perform approximate inference in extremely high dimensions and for complex probabilistic models. The problem with high-dimensional and complex models is twofold. Fist, to capture the true posterior distribution accurately, a sufficiently rich approximation for it is required. Second, the number of parameters to express this richness scales dramatically with the number of model parameters. For example, explicitly expressing the correlation between all model parameters requires their squared number of correlation coefficients. In settings with millions of model parameter, this is unfeasible. MGVI overcomes this limitation by replacing the explicit covariance with an implicit approximation, which does not have to be stored and is accessed via samples. This procedure scales linearly with the problem size and allows to account for the full correlations in even extremely large problems. This makes it also applicable to significantly more complex setups. MGVI enabled a series of ambitious signal reconstructions by me and others, which will be showcased. This involves a time- and frequency-resolved reconstruction of the shadow around the black hole M87* using data provided by the Event Horizon Telescope Collaboration, a three-dimensional tomographic reconstruction of interstellar dust within 300pc around the sun from Gaia starlight-absorption and parallax data, novel medical imaging methods for computed tomography, an all-sky Faraday rotation map, combining distinct data sources, and simultaneous calibration and imaging with a radio-interferometer. The second main result is an an approach to use several, independently trained and deep neural networks to reason on complex tasks. Deep learning allows to capture abstract concepts by extracting them from large amounts of training data, which alleviates the necessity of an explicit mathematical formulation. Here a generative neural network is used as a prior distribution and certain properties are imposed via classification and regression networks. The inference is then performed in terms of the latent variables of the generator, which is done using MGVI and other methods. This allows to flexibly answer novel questions without having to re-train any neural network and to come up with novel answers through Bayesian reasoning. This novel approach of Bayesian reasoning with neural networks can also be combined with conventional measurement data

Bayesian Reasoning with Trained Neural Networks

We showed how to use trained neural networks to perform Bayesian reasoning in order to solve tasks outside their initial scope. Deep generative models provide prior knowledge, and classification/regression networks impose constraints. The tasks at hand were formulated as Bayesian inference problems, which we approximately solved through variational or sampling techniques. The approach built on top of already trained networks, and the addressable questions grew super-exponentially with the number of available networks. In its simplest form, the approach yielded conditional generative models. However, multiple simultaneous constraints constitute elaborate questions. We compared the approach to specifically trained generators, showed how to solve riddles, and demonstrated its compatibility with state-of-the-art architectures

Resolving Horizon-Scale Dynamics of Sagittarius A*

Sagittarius A* (Sgr A*), the supermassive black hole at the heart of our galaxy, provides unique opportunities to study black hole accretion, jet formation, and gravitational physics. The rapid structural changes in Sgr A*'s emission pose a significant challenge for traditional imaging techniques. We present dynamic reconstructions of Sgr A* using Event Horizon Telescope (EHT) data from April 6th and 7th, 2017, analyzed with a one-minute temporal resolution with the Resolve framework. This Bayesian approach employs adaptive Gaussian Processes and Variational Inference for data-driven self-regularization. Our results not only fully confirm the initial findings by the EHT Collaboration for a time-averaged source but also reveal intricate details about the temporal dynamics within the black hole environment. We find an intriguing dynamic feature on April 6th that propagates in a clock-wise direction. Geometric modelling with ray-tracing, although not fully conclusive, indicates compatibility with high-inclination configurations of about $\theta_o = 160^\circ$, as seen in other studies

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

First spatio-spectral Bayesian imaging of SN1006 in X-ray

Supernovae are an important source of energy in the interstellar medium. Young remnants of supernovae have a peak emission in the X-ray region, making them interesting objects for X-ray observations. In particular, the supernova remnant SN1006 is of great interest due to its historical record, proximity and brightness. It has therefore been studied by several X-ray telescopes. Improving the X-ray imaging of this and other remnants is important but challenging as it requires to address a spatially varying instrument response in order to achieve a high signal-to-noise ratio. Here, we use Chandra observations to demonstrate the capabilities of Bayesian image reconstruction using information field theory. Our objective is to reconstruct denoised, deconvolved and spatio-spectral resolved images from X-ray observations and to decompose the emission into different morphologies, namely diffuse and point-like. Further, we aim to fuse data from different detectors and pointings into a mosaic and quantify the uncertainty of our result. Utilizing prior knowledge on the spatial and spectral correlation structure of the two components, diffuse emission and point sources, the presented method allows the effective decomposition of the signal into these. In order to accelerate the imaging process, we introduce a multi-step approach, in which the spatial reconstruction obtained for a single energy range is used to derive an informed starting point for the full spatio-spectral reconstruction. The method is applied to 11 Chandra observations of SN1006 from 2008 and 2012, providing a detailed, denoised and decomposed view of the remnant. In particular, the separated view of the diffuse emission should provide new insights into its complex small-scale structures in the center of the remnant and at the shock front profiles