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Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
Multiline techniques assuming similar line profiles have become a standard tool in stellar astronomy for increasing the signal-to-noise ratio (SNR) of spectropolarimetric measurements. However, due to the widely-used weak field…
Context. The numerical modeling of the generation and transfer of polarized radiation is a key task in solar and stellar physics research and has led to a relevant class of discrete problems that can be reframed as linear systems. In order…
In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…
Scattering polarization signals offer a unique diagnostics of the physical conditions in the solar atmosphere, in particular magnetic fields via the Hanle effect. However, their spatial structure remains poorly constrained due to the…
Chromospheric magnetic fields are notoriously diffcult to measure. The chromospheric lines are broad, while the fields are producing a minuscule Zeeman-effect polarization. A promising diagnostic alternative is provided by the…
Context. High-contrast exoplanet imaging is a rapidly growing field as can be seen through the significant resources invested. In fact, the detection and characterization of exoplanets through direct imaging is featured at all major…
Partial differential equations (PDEs) are widely used for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identification of optimal parameters or the solution of the…
Context: State of the art quantitative spectroscopy of OB-stars compares synthetic spectra (calculated by means of 1D, spherically symmetric computer codes) with observations. Certain stellar atmospheres, however, show strong deviations…
Cross-domain few-shot learning (CD-FSL) requires models to generalize from limited labeled samples under significant distribution shifts. While recent methods enhance adaptability through lightweight task-specific modules, they operate…
This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame…
This paper introduces a novel technique to preserve spectral features in lossy compression based on a novel fast Fourier correction algorithm\added{ for regular-grid data}. Preserving both spatial and frequency representations of data is…
We study recovery from incomplete random spatial samples for discretized fields arising as fixed-time snapshots of partial differential equations. The organizing parameter is the Fourier ratio $$ FR(g)=\frac{\|\widehat g\|_1}{\|\widehat…
The process of wide-field synthesis imaging is explored, with the aim of understanding the implications of variable, polarised primary beams for forthcoming Epoch of Reionisation experiments. These experiments seek to detect weak signatures…
Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…
An approach for measuring linear X-ray polarization over a broad-band using conventional spectroscopic optics is described. A set of multilayer-coated flats reflect the dispersed X-rays to the instrument detectors. The intensity variation…
In this paper we explain how to use the Fast Fourier Transform (FFT) to solve partial differential equations (PDEs). We start by defining appropriate discrete domains in coordinate and frequency domains. Then describe the main limitation of…
Observations of scattering polarization and the Hanle effect in various spectral lines are increasingly used to complement traditional solar magnetic field determination techniques. One of the strongest scattering polarization signals in…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…