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Jakob Knollmüller

Publications and source records attributed to Jakob Knollmüller.

At least 19 recordsLinked to original sources
arXiv2025

aim-resolve: Automatic Identification and Modeling for Bayesian Radio Interferometric Imaging

Modern radio interferometers deliver large volumes of data containing high-sensitivity sky maps over wide fields-of-view. These large area observations can contain various and superposed structures such as point sources, extended objects, and large-scale diffuse emission. To fully realize the potential of these observations, it is crucial to build appropriate sky emission models which separate and reconstruct the underlying astrophysical components. We introduce aim-resolve, an automatic and iterative method that combines the Bayesian imaging algorithm resolve with deep learning and clustering algorithms in order to jointly solve the reconstruction and source extraction problem. The method identifies and models different astrophysical components in radio observations while providing uncertainty quantification of the results. By using different model descriptions for point sources, extended objects, and diffuse background emission, the method efficiently separates the individual components and improves the overall reconstruction. We demonstrate the effectiveness of this method on synthetic image data containing multiple different sources. We further show the application of aim-resolve to an L-band (856 - 1712 MHz) MeerKAT observation of the radio galaxy ESO 137-006 and other radio galaxies in that environment. We observe a reasonable object identification for both applications, yielding a clean separation of the individual components and precise reconstructions of point sources and extended objects along with detailed uncertainty quantification. In particular, the method enables the creation of catalogs containing source positions and brightnesses and the corresponding uncertainties. The full decoupling of sky emission model and instrument response makes the method applicable to a wide variety of instruments or wavelength bands.

astro-ph.IM↗
arXiv2024

Bias-Free Estimation of Signals on Top of Unknown Backgrounds

We present a method for obtaining unbiased signal estimates in the presence of a significant unknown background, eliminating the need for a parametric model for the background itself. Our approach is based on a minimal set of conditions for observation and background estimators, which are typically satisfied in practical scenarios. To showcase the effectiveness of our method, we apply it to simulated data from the planned dielectric axion haloscope MADMAX.

astro-ph.IM↗
arXiv2023

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.

astro-ph.HE↗
arXiv2023

Multi-Component Imaging of the Fermi Gamma-ray Sky in the Spatio-spectral Domain

We perform two distinct spatio-spectral reconstructions of the gamma-ray sky in the range of 0.56-316 GeV based on Fermi Large Area Telescope (LAT) data. Both describe the sky brightness to be composed of a diffuse-emission and a point-source component. The first model requires minimal assumptions and provides a template-free reconstruction as a reference. It makes use of spatial and spectral correlations to distinguish between the different components. The second model is physics-informed and further differentiates between diffuse emission of hadronic and leptonic origin. For this, we assume parametric, but spatially varying energy spectra to distinguish between the processes and use thermal Galactic dust observations to indicate the preferred sites of hadronic interactions. To account for instrumental effects we model the point-spread, the energy dispersion, and the exposure of the telescope throughout the observation. The reconstruction problem is formulated as a Bayesian inference task, that is solved by variational inference. We show decompositions of the Gamma-ray flux into diffuse and point-like emissions, and of the diffuse emissions into multiple physically motivated components. The diffuse decomposition provides an unprecedented view of the Galactic leptonic diffuse emission. It shows the Fermi bubbles and their spectral variations in high fidelity and other areas exhibiting strong cosmic ray electron contents, such as a thick disk in the inner Galaxy and outflow regions. Furthermore, we report a hard spectrum gamma ray arc in the northern outer bubble co-spatial with the reported X-ray arc by the eROSITA collaboration. All our spatio-spectral sky reconstructions and their uncertainty quantification are publicly available.

astro-ph.HE↗
arXiv2023

Progress in the Partial-Wave Analysis Methods at COMPASS

We study the excitation spectrum of light and strange mesons in diffractive scattering. We identify different hadron resonances through partial wave analysis, which inherently relies on analysis models. Besides statistical uncertainties, the model dependence of the analysis introduces dominant systematic uncertainties. We discuss several of their sources for the $π^-π^-π^+$ and $K^0_S K^-$ final states and present methods to reduce them. We have developed a new approach exploiting a-priori knowledge of signal continuity over adjacent final-state-mass bins to stably fit a large pool of partial-waves to our data, allowing a clean identification of very small signals in our large data sets. For two-body final states of scalar particles, such as $K^0_S K^-$, mathematical ambiguities in the partial-wave decomposition lead to the same intensity distribution for different combinations of amplitude values. We will discuss these ambiguities and present solutions to resolve or at least reduce the number of possible solutions. Resolving these issues will allow for a complementary analysis of the $a_J$-like resonance sector in these two final states.

hep-ph↗
arXiv2023

Progress in the partial-wave analysis methods at COMPASS

We study the excitation spectrum of light and strange mesons in diffractive scattering. We identify different hadron resonances through partial wave analysis, which inherently relies on analysis models. Besides statistical uncertainties, the model dependence of the analysis introduces dominant systematic uncertainties. We discuss several of their sources for the $π^-π^-π^+$ and $K^0_S K^-$ final states and present methods to reduce them. We have developed a new approach exploiting a-priori knowledge of signal continuity over adjacent final-state-mass bins to stably fit a large pool of partial-waves to our data, allowing a clean identification of very small signals in our large data sets. For two-body final states of scalar particles, such as $K^0_S K^-$, mathematical ambiguities in the partial-wave decomposition lead to the same intensity distribution for different combinations of amplitude values. We will discuss these ambiguities and present solutions to resolve or at least reduce the number of possible solutions. Resolving these issues will allow for a complementary analysis of the $a_J$-like resonance sector in these two final states.

hep-ex↗
arXiv2023

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 $θ_o = 160^\circ$, as seen in other studies.

astro-ph.HE↗
arXiv2023

Classification and Uncertainty Quantification of Corrupted Data using Semi-Supervised Autoencoders

Parametric and non-parametric classifiers often have to deal with real-world data, where corruptions like noise, occlusions, and blur are unavoidable - posing significant challenges. We present a probabilistic approach to classify strongly corrupted data and quantify uncertainty, despite the model only having been trained with uncorrupted data. A semi-supervised autoencoder trained on uncorrupted data is the underlying architecture. We use the decoding part as a generative model for realistic data and extend it by convolutions, masking, and additive Gaussian noise to describe imperfections. This constitutes a statistical inference task in terms of the optimal latent space activations of the underlying uncorrupted datum. We solve this problem approximately with Metric Gaussian Variational Inference (MGVI). The supervision of the autoencoder's latent space allows us to classify corrupted data directly under uncertainty with the statistically inferred latent space activations. Furthermore, we demonstrate that the model uncertainty strongly depends on whether the classification is correct or wrong, setting a basis for a statistical "lie detector" of the classification. Independent of that, we show that the generative model can optimally restore the uncorrupted datum by decoding the inferred latent space activations.

cs.LG↗
arXiv2023

Accretion Flow Morphology in Numerical Simulations of Black Holes from the ngEHT Model Library: The Impact of Radiation Physics

In the past few years, the Event Horizon Telescope (EHT) has provided the first-ever event horizon-scale images of the supermassive black holes (BHs) (M87*) and Sagittarius A$^*$ (Sgr A*). The next-generation EHT project is an extension of the EHT array that promises larger angular resolution and higher sensitivity to the dim, extended flux around the central ring-like structure, possibly connecting the accretion flow and the jet. The ngEHT Analysis Challenges aim to understand the science extractability from synthetic images and movies to inform the ngEHT array design and analysis algorithm development. In this work, we compare the accretion flow structure and dynamics in numerical fluid simulations that specifically target M87* and Sgr A*, and were used to construct the source models in the challenge set. We consider (1) a steady-state axisymmetric radiatively inefficient accretion flow model with a time-dependent shearing hotspot, (2) two time-dependent single fluid general relativistic magnetohydrodynamic (GRMHD) simulations from the H-AMR code, (3) a two-temperature GRMHD simulation from the BHAC code, and (4) a two-temperature radiative GRMHD simulation from the KORAL code. We find that the different models exhibit remarkably similar temporal and spatial properties, except for the electron temperature, since radiative losses substantially cool down electrons near the BH and the jet sheath, signaling the importance of radiative cooling even for slowly accreting BHs such as M87*. We restrict ourselves to standard torus accretion flows, and leave larger explorations of alternate accretion models to future work.

astro-ph.HE↗
arXiv2022

Variable structures in M87* from space, time and frequency resolved interferometry

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 place to study general relativity and magneto-hydrodynamics. The observations of M87* with Very Long Baseline Interferometry (VLBI) by the Event Horizon Telescope (EHT) allows to investigate its dynamical processes on time scales of days. Compared to regular radio interferometers, VLBI networks typically have fewer antennas and low signal to noise ratios (SNRs). Furthermore, the source is variable, prohibiting integration over time to improve SNR. Here, we present an imaging algorithm that copes with the data scarcity and temporal evolution, while providing uncertainty quantification. Our algorithm views the imaging task as a Bayesian inference problem of a time-varying brightness, exploits the correlation structure in time, and reconstructs a ${2+1+1}$ dimensional time-variable and spectrally resolved image at once. 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. The reconstruction indicates extended and time-variable emission structures outside the ring itself.

astro-ph.IM↗
arXiv2021

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.

cs.LG↗
arXiv2020

Metric Gaussian Variational Inference

Solving Bayesian inference problems approximately with variational approaches can provide fast and accurate results. Capturing correlation within the approximation requires an explicit parametrization. This intrinsically limits this approach to either moderately dimensional problems, or requiring the strongly simplifying mean-field approach. We propose Metric Gaussian Variational Inference (MGVI) as a method that goes beyond mean-field. Here correlations between all model parameters are taken into account, while still scaling linearly in computational time and memory. With this method we achieve higher accuracy and in many cases a significant speedup compared to traditional methods. MGVI is an iterative method that performs a series of Gaussian approximations to the posterior. We alternate between approximating the covariance with the inverse Fisher information metric evaluated at an intermediate mean estimate and optimizing the KL-divergence for the given covariance with respect to the mean. This procedure is iterated until the uncertainty estimate is self-consistent with the mean parameter. We achieve linear scaling by avoiding to store the covariance explicitly at any time. Instead we draw samples from the approximating distribution relying on an implicit representation and numerical schemes to approximately solve linear equations. Those samples are used to approximate the KL-divergence and its gradient. The usage of natural gradient descent allows for rapid convergence. Formulating the Bayesian model in standardized coordinates makes MGVI applicable to any inference problem with continuous parameters. We demonstrate the high accuracy of MGVI by comparing it to HMC and its fast convergence relative to other established methods in several examples. We investigate real-data applications, as well as synthetic examples of varying size and complexity and up to a million model parameters.

stat.ML↗
arXiv2018

Encoding prior knowledge in the structure of the likelihood

The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This transformation is a special form of the reparametrization trick, flattens the hierarchy and leads to a standard Gaussian prior on all resulting parameters. The transformation also transfers all the prior information into the structure of the likelihood, hereby decoupling the transformed parameters a priori from each other. A variational Gaussian approximation in this standardized space will be excellent in situations of relatively uninformative data. Additionally, the curvature of the log-posterior is well-conditioned in directions that are weakly constrained by the data, allowing for fast inference in such a scenario. In an example we perform the transformation explicitly for Gaussian process regression with a priori unknown correlation structure. Deep models are inferred rapidly in highly and slowly in poorly informed situations. The flat model show exactly the opposite performance pattern. A synthesis of both, the deep and the flat perspective, provides their combined advantages and overcomes the individual limitations, leading to a faster inference.

stat.ML↗
arXiv2018

Separating diffuse from point-like sources - a Bayesian approach

We present the starblade algorithm, a method to separate superimposed point sources from auto-correlated, diffuse flux using a Bayesian model. Point sources are assumed to be independent from each other and to follow a power-law brightness distribution. The diffuse emission is described as a non-parametric log-normal model with a priori unknown correlation structure. This model enforces positivity of the underlying emission and allows for variation in the order of magnitudes. The correlation structure is recovered non-parametrically in addition to the diffuse flux and is used for the separation of the point sources. Additionally many measurement artifacts appear as point-like or quasi-point-like effects, not compatible with superimposed diffuse emission. An estimate of the separation uncertainty can be provided as well. We demonstrate the capabilities of the derived method on synthetic data and data obtained by the Hubble Space Telescope, emphasizing its effect on instrumental artifacts as well as physical sources. The performance of this method is compared to the background estimation of the SExtractor method, as well as to a denoising auto-encoder.

astro-ph.IM↗
arXiv2018

Radio Imaging With Information Field Theory

Data from radio interferometers provide a substantial challenge for statisticians. It is incomplete, noise-dominated and originates from a non-trivial measurement process. The signal is not only corrupted by imperfect measurement devices but also from effects like fluctuations in the ionosphere that act as a distortion screen. In this paper we focus on the imaging part of data reduction in radio astronomy and present RESOLVE, a Bayesian imaging algorithm for radio interferometry in its new incarnation. It is formulated in the language of information field theory. Solely by algorithmic advances the inference could be sped up significantly and behaves noticeably more stable now. This is one more step towards a fully user-friendly version of RESOLVE which can be applied routinely by astronomers.

astro-ph.IM↗
arXiv2018

Inference of signals with unknown correlation structure from nonlinear measurements

We present a method to reconstruct autocorrelated signals together with their autocorrelation structure from nonlinear, noisy measurements for arbitrary monotonous nonlinear instrument response. In the presented formulation the algorithm provides a significant speedup compared to prior implementations, allowing for a wider range of application. The nonlinearity can be used to model instrument characteristics or to enforce properties on the underlying signal, such as positivity. Uncertainties on any posterior quantities can be provided due to independent samples from an approximate posterior distribution. We demonstrate the methods applicability via simulated and real measurements, using different measurement instruments, nonlinearities and dimensionality.

stat.ME↗
arXiv2017

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.

stat.ME↗
arXiv2017

NIFTy 3 - Numerical Information Field Theory - A Python framework for multicomponent signal inference on HPC clusters

NIFTy, "Numerical Information Field Theory", is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high-dimensional real-world problems. This paper introduces NIFTy 3, a major upgrade to the original NIFTy framework. NIFTy 3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n-dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy 3 is able to treat non-scalar fields. The functionality and performance of the software package is demonstrated with example code, which implements a real inference algorithm from the realm of information field theory. NIFTy 3 is open-source software available under the GNU General Public License v3 (GPL-3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/

astro-ph.IM↗