Related papers: Full Resolution Deconvolution of Complex Faraday S…
The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions,…
Fourier imaging is an indirect imaging method which records the diffraction pattern of the object scene coherently in the focal plane of the imaging system and reconstructs the image using computational resources. The spatial resolution,…
Radio polarimetry at decimetre wavelengths is the principal source of information on the Galactic magnetic field. The diffuse polarized emission is strongly influenced by Faraday rotation in the magneto-ionic medium and rotation measure is…
We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is…
When interpreting spectropolarimetric observations of the solar atmosphere, wavelength variations of the emergent intensity and polarization translate into information on the depth stratification of physical parameters. We aim to quantify…
X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of…
We investigate whether the method of wavelet-based Faraday rotation measure (RM) Synthesis can help us to identify structures of regular and turbulent magnetic fields in extended magnetized objects, such as galaxies and galaxy clusters.…
This paper considers the problem of recovering a one or two dimensional discrete signal which is approximately sparse in its discrete gradient from an incomplete subset of its discrete Fourier coefficients which have been corrupted with…
We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Coherent X-ray beams with energies $\geq 50$ keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction…
Diffraction limit is manifested in the loss of high spatial frequency information that results from decay of evanescent waves. As a result, conventional far-field optics yields no information about an object's subwavelength features. Here…
The autocorrelation function and similarly the Fourier-power spectrum of a rotation measure (RM) map of an extended background radio source can be used to measure components of the magnetic autocorrelation and power-spectrum tensor within a…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum…
We present a broadband spectro-polarimetric analysis of 1,565 polarized radio sources from the LOFAR Two-Metre Sky Survey Data Release 2 (LoTSS-DR2) RM Grid catalogue. This study uses frequency-dependent Stokes Q and U spectra across the…
Understanding origin and evolution of cosmological magnetic fields requires knowledge of magnetic fields in different extragalactic environments. In this context, a powerful tool is the statistical analysis of the Faraday effect on the…
A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides,…
We extend the rotation measure work of Burn (1966) to the cases of limited sampling of lambda squared space and non-constant emission spectra. We introduce the rotation measure transfer function (RMTF), which is an excellent predictor of…
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…