673 research outputs found
Solar hard X-ray imaging by means of Compressed Sensing and Finite Isotropic Wavelet Transform
This paper shows that compressed sensing realized by means of regularized
deconvolution and the Finite Isotropic Wavelet Transform is effective and
reliable in hard X-ray solar imaging.
The method utilizes the Finite Isotropic Wavelet Transform with Meyer
function as the mother wavelet. Further, compressed sensing is realized by
optimizing a sparsity-promoting regularized objective function by means of the
Fast Iterative Shrinkage-Thresholding Algorithm. Eventually, the regularization
parameter is selected by means of the Miller criterion.
The method is applied against both synthetic data mimicking the
Spectrometer/Telescope Imaging X-rays (STIX) measurements and experimental
observations provided by the Reuven Ramaty High Energy Solar Spectroscopic
Imager (RHESSI). The performances of the method are compared with the results
provided by standard visibility-based reconstruction methods.
The results show that the application of the sparsity constraint and the use
of a continuous, isotropic framework for the wavelet transform provide a
notable spatial accuracy and significantly reduce the ringing effects due to
the instrument point spread functions
Properties of the Acceleration Regions in Several Loop-structured Solar Flares
Using {\em RHESSI} hard X-ray imaging spectroscopy observations, we analyze
electron flux maps for a number of extended coronal loop flares. For each
event, we fit a collisional model with an extended acceleration region to the
observed variation of loop length with electron energy , resulting in
estimates of the plasma density in, and longitudinal extent of, the
acceleration region. These quantities in turn allow inference of the number of
particles within the acceleration region and hence the filling factor --
the ratio of the emitting volume to the volume that encompasses the emitting
region(s). We obtain values of that lie mostly between 0.1 and 1.0; the
(geometric) mean value is , somewhat less than, but
nevertheless consistent with, unity. Further, coupling information on the
number of particles in the acceleration region with information on the total
rate of acceleration of particles above a certain reference energy (obtained
from spatially-integrated hard X-ray data) also allows inference of the
specific acceleration rate (electron s per ambient electron above the
chosen reference energy). We obtain a (geometric) mean value of the specific
acceleration rate keV)
electrons s per ambient electron; this value has implications both for
the global electrodynamics associated with replenishment of the acceleration
region and for the nature of the particle acceleration process
Inverse diffraction for the Atmospheric Imaging Assembly in the Solar Dynamics Observatory
The Atmospheric Imaging Assembly in the Solar Dynamics Observatory provides
full Sun images every 1 seconds in each of 7 Extreme Ultraviolet passbands.
However, for a significant amount of these images, saturation affects their
most intense core, preventing scientists from a full exploitation of their
physical meaning. In this paper we describe a mathematical and automatic
procedure for the recovery of information in the primary saturation region
based on a correlation/inversion analysis of the diffraction pattern associated
to the telescope observations. Further, we suggest an interpolation-based
method for determining the image background that allows the recovery of
information also in the region of secondary saturation (blooming)
Fast spectral fitting of hard X-ray bremsstrahlung from truncated power-law electron spectra
<p><b>Context:</b> Hard X-ray bremsstrahlung continuum spectra, such as from solar flares, are commonly described in terms of power-law fits, either to the photon spectra themselves or to the electron spectra responsible for them. In applications various approximate relations between electron and photon spectral indices are often used for energies both above and below electron low-energy cutoffs.</p>
<p><b>Aims:</b> We examine the form of the exact relationships in various situations, and for various cross-sections, showing that empirical relations sometimes used can be highly misleading especially at energies below the low-energy cutoff, and consider how to improve fitting procedures.</p>
<p><b>Methods:</b> We obtain expressions for photon spectra from single, double and truncated power-law electron spectra for a variety of cross-sections and for the thin and thick target models and simple analytic expressions for the non-relativistic Bethe-Heitler case.</p>
<p><b>Results:</b> We show that below the low-energy cutoff Kramers and other constant spectral index forms commonly used are very poor approximations to accurate results, but that our analytical forms are a good match; and that above a low-energy cutoff, the Kramers and non-relativistic Bethe-Heitler results match reasonably well with results for up to energies around 100 keV.</p>
<p><b>Conclusions:</b> Analytical forms of the non-relativistic Bethe-Heitler photon spectra from general power-law electron spectra are good match to exact results for both thin and thick targets and they enable much faster spectral fitting than evaluation of the full spectral integrations.</p>
Feature augmentation for the inversion of the Fourier transform with limited data
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modeling the available data via a shape-driven interpolation based on variably scaled Kernels (VSKs), whose implementation is here tailored for inverse problems. The so-constructed interpolants are used as inputs for a standard iterative inversion scheme. After providing theoretical results concerning the spectrum of the VSK collocation matrix, we test the method on astrophysical imaging benchmarks
Determination of the Acceleration Region Size in a Loop-structured Solar Flare
In order to study the acceleration and propagation of
bremsstrahlung-producing electrons in solar flares, we analyze the evolution of
the flare loop size with respect to energy at a variety of times. A GOES M3.7
loop-structured flare starting around 23:55 on 2002 April 14 is studied in
detail using \textit{Ramaty High Energy Solar Spectroscopic Imager}
(\textit{RHESSI}) observations. We construct photon and mean-electron-flux maps
in 2-keV energy bins by processing observationally-deduced photon and electron
visibilities, respectively, through several image-processing methods: a
visibility-based forward-fit (FWD) algorithm, a maximum entropy (MEM) procedure
and the uv-smooth (UVS) approach. We estimate the sizes of elongated flares
(i.e., the length and width of flaring loops) by calculating the second
normalized moments of the intensity in any given map. Employing a collisional
model with an extended acceleration region, we fit the loop lengths as a
function of energy in both the photon and electron domains. The resulting
fitting parameters allow us to estimate the extent of the acceleration region
which is between and . Both
forward-fit and uv-smooth algorithms provide substantially similar results with
a systematically better fit in the electron domain.The consistency of the
estimates from these methods provides strong support that the model can
reliably determine geometric parameters of the acceleration region. The
acceleration region is estimated to be a substantial fraction () of
the loop extent, indicating that this dense flaring loop incorporates both
acceleration and transport of electrons, with concurrent thick-target
bremsstrahlung emission.Comment: 8 pages, 5 figures, accepted to Astronomy and Astrophysics journa
Count-based imaging model for the Spectrometer/Telescope for Imaging X-rays (STIX) in Solar Orbiter
The Spectrometer/Telescope for Imaging X-rays (STIX) will study solar flares across the hard X-ray window provided by the Solar Orbiter cluster. Similarly to the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), STIX is a visibility-based imaging instrument that will require Fourier-based image reconstruction methods. However, in this paper we show that as for RHESSI, count-based imaging is also possible for STIX. Specifically, we introduce and illustrate a mathematical model that mimics the STIX data formation process as a projection from the incoming photon flux into a vector consisting of 120 count components. Then we test the reliability of expectation maximization for image reconstruction in the case of several simulated configurations that are typical of flare morphology
Verrucous Melanoma Simulating Melanoacanthoma: Dermoscopic, Reflectance Confocal Microscopic and High-Definition Optical Coherence Tomography Presentation of a Rare Melanoma Variant
info:eu-repo/semantics/publishedVersio
- …