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This paper focuses on the polarized profiles of resonance scattering lines that form in magnetized disks. Optically thin lines from Keplerian planar disks are considered. Model line profiles are calculated for simple field topologies of…
Phase Measuring Deflectometry (PMD) acquires the two components of the local surface gradient via a sequence of two orthogonal sinusoidal fringe patterns that have to be displayed and captured separately. We will demonstrate that the…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
Low-dose computed tomography (LDCT) plays a vital role in clinical applications by mitigating radiation risks. Nevertheless, reducing radiation doses significantly degrades image quality. Concurrently, common deep learning methods demand…
Purpose: The radial k-space trajectory is a well-established sampling trajectory used in conjunction with magnetic resonance imaging. However, the radial k-space trajectory requires a large number of radial lines for high-resolution…
Astronomical imaging using aperture synthesis telescopes requires deconvolution of the point spread function as well as calibration of instrumental and atmospheric effects. In general, such effects are time-variable and vary across the…
Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary…
This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…
Four different applications of spectral proper orthogonal decomposition (SPOD): low-rank reconstruction, denoising, frequency-time analysis, and prewhitening are demonstrated on large-eddy simulation data of a turbulent jet. SPOD-based…
Faraday rotation measure synthesis is a method for analyzing multichannel polarized radio emissions, and it has emerged as an important tool in the study of galactic and extra-galactic magnetic fields. The method requires the recovery of…
The Mg II k resonance line is commonly used for diagnosing the solar chromosphere. We theoretically investigated its intensity and polarization in solar prominences, taking 3D radiative transfer and Hanle and Zeeman effects into account. We…
The complex spectropolarimetric patterns around strong chromospheric lines, the result of subtle spectroscopic and transport mechanisms, are sensitive, sometimes in unexpected ways, to the presence of magnetic fields in the chromosphere,…
The near-Earth space weather is driven by the quick release of magnetic free energy in the solar corona. Probing this extremely hot and rarified region of the extended solar atmosphere requires modeling the polarization of forbidden and…
Radiative transfer is essential in astronomy, both for interpreting observations and simulating various astrophysical phenomena. However, self-consistent line radiative transfer is computationally expensive, especially in 3D. To reduce the…
An angle-resolved x-ray spectroscopic scheme is presented for determining the hyperfine splitting of highly charged ions. For helium-like ions, in particular, we propose to measure either the angular distribution or polarization of the…
We present a new method for the generation of atmospheric turbulence phase screens based on the frequency shift property of the Fourier transform. This method produces low spatial frequency distortions without additional computation time…
A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…
The Zeeman effect is of limited utility for probing the magnetism of the quiet solar chromosphere. The Hanle effect in some spectral lines is sensitive to such magnetism, but the interpretation of the scattering polarization signals…
An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…
When using Laguerre and Hermite spectral methods to numerically solve PDEs in unbounded domains, the number of collocation points assigned inside the region of interest is often insufficient, particularly when the region is expanded or…