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Register a new userCompressed sensing and Sequential Monte Carlo for solar hard X-ray imaging
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We describe two inversion methods for the reconstruction of hard X-ray solar images. The methods are tested against experimental visibilities recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and synthetic visibilities based on the design of the Spectrometer/Telescope for Imaging X-rays (STIX).
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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.
Sequential Monte Carlo (SMC), also known as particle filters, has been widely accepted as a powerful computational tool for making inference with dynamical systems. A key step in SMC is resampling, which plays the role of steering the algorithm towards the future dynamics. Several strategies have been proposed and used in practice, including multinomial resampling, residual resampling (Liu and Chen 1998), optimal resampling (Fearnhead and Clifford 2003), stratified resampling (Kitagawa 1996), and optimal transport resampling (Reich 2013). We show that, in the one dimensional case, optimal transport resampling is equivalent to stratified resampling on the sorted particles, and they both minimize the resampling variance as well as the expected squared energy distance between the original and resampled empirical distributions; in the multidimensional case, the variance of stratified resampling after sorting particles using Hilbert curve (Gerber et al. 2019) in $mathbb{R}^d$ is $O(m^{-(1+2/d)})$, an improved rate compared to the original $O(m^{-(1+1/d)})$, where $m$ is the number of resampled particles. This improved rate is the lowest for ordered stratified resampling schemes, as conjectured in Gerber et al. (2019). We also present an almost sure bound on the Wasserstein distance between the original and Hilbert-curve-resampled empirical distributions. In light of these theoretical results, we propose the stratified multiple-descendant growth (SMG) algorithm, which allows us to explore the sample space more efficiently compared to the standard i.i.d. multiple-descendant sampling-resampling approach as measured by the Wasserstein metric. Numerical evidence is provided to demonstrate the effectiveness of our proposed method.
One way of imaging X-ray emission from solar flares is to measure Fourier components of the spatial X-ray source distribution. We present a new Compressed Sensing-based algorithm named VIS_CS, which reconstructs the spatial distribution from such Fourier components. We demonstrate the application of the algorithm on synthetic and observed solar flare X-ray data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite and compare its performance with existing algorithms. VIS_CS produces competitive results with accurate photometry and morphology, without requiring any algorithm- and X-ray source-specific parameter tuning. Its robustness and performance make this algorithm ideally suited for generation of quicklook images or large image cubes without user intervention, such as for imaging spectroscopy analysis.
We study the nature of energy release and transfer for two sub-A class solar microflares observed during the second flight of the Focusing Optics X-ray Solar Imager (FOXSI-2) sounding rocket experiment on 2014 December 11. FOXSI is the first solar-dedicated instrument to utilize focusing optics to image the Sun in the hard X-ray (HXR) regime, sensitive to the energy range 4-20 keV. Through spectral analysis of the two microflares using an optically thin isothermal plasma model, we find evidence for plasma heated to temperatures of ~10 MK and emissions measures down to ~$10^{44}~$cm$^{-3}$. Though nonthermal emission was not detected for the FOXSI-2 microflares, a study of the parameter space for possible hidden nonthermal components shows that there could be enough energy in nonthermal electrons to account for the thermal energy in microflare 1, indicating that this flare is plausibly consistent with the standard thick-target model. With a solar-optimized design and improvements in HXR focusing optics, FOXSI-2 offers approximately five times greater sensitivity at 10 keV than the Nuclear Spectroscopic Telescope Array (NuSTAR) for typical microflare observations and allows for the first direct imaging spectroscopy of solar HXRs with an angular resolution at scales relevant for microflares. Harnessing these improved capabilities to study the evolution of small-scale events, we find evidence for spatial and temporal complexity during a sub-A class flare. These studies in combination with contemporanous observations by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory (SDO/AIA) indicate that the evolution of these small microflares is more similar to that of large flares than to the single burst of energy expected for a nanoflare.
How impulsive magnetic energy release leads to solar eruptions and how those eruptions are energized and evolve are vital unsolved problems in Heliophysics. The standard model for solar eruptions summarizes our current understanding of these events. Magnetic energy in the corona is released through drastic restructuring of the magnetic field via reconnection. Electrons and ions are then accelerated by poorly understood processes. Theories include contracting loops, merging magnetic islands, stochastic acceleration, and turbulence at shocks, among others. Although this basic model is well established, the fundamental physics is poorly understood. HXR observations using grazing-incidence focusing optics can now probe all of the key regions of the standard model. These include two above-the-looptop (ALT) sources which bookend the reconnection region and are likely the sites of particle acceleration and direct heating. The science achievable by a direct HXR imaging instrument can be summarized by the following science questions and objectives which are some of the most outstanding issues in solar physics (1) How are particles accelerated at the Sun? (1a) Where are electrons accelerated and on what time scales? (1b) What fraction of electrons is accelerated out of the ambient medium? (2) How does magnetic energy release on the Sun lead to flares and eruptions? A Focusing Optics X-ray Solar Imager (FOXSI) instrument, which can be built now using proven technology and at modest cost, would enable revolutionary advancements in our understanding of impulsive magnetic energy release and particle acceleration, a process which is known to occur at the Sun but also throughout the Universe.
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