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The Spectrometer/Telescope for Imaging X-rays (STIX) on-board the ESA Solar Orbiter mission retrieves the coordinates of solar flare locations by means of a specific sub-collimator, named the Coarse Flare Locator (CFL). When a solar flare occurs on the Sun, the emitted X-ray radiation casts the shadow of a peculiar "H-shaped" tungsten grid over the CFL X-ray detector. From measurements of the areas of the detector that are illuminated by the X-ray radiation, it is possible to retrieve the $(x,y)$ coordinates of the flare location on the solar disk. In this paper, we train a neural network on a dataset of real CFL observations to estimate the coordinates of solar flare locations. Further, we apply a post-training quantization technique specifically tailored to the adopted model architecture. This technique allows all computations to be in integer arithmetic at inference time, making the model compatible with the STIX computational requirements. We show that our model outperforms the currently adopted algorithm for estimating the flare locations from CFL data regarding prediction accuracy while requiring fewer parameters. We finally discuss possible future applications of the proposed model on-board STIX., Comment: Conference paper accepted for an poster presentation to the ESA SPAICE CONFERENCE 17 19 September 2024

Reconstructing an image from sparsely sampled Fourier data is an ill-posed inverse problem that occurs in a variety of subjects within science, including the data analysis for Very Long Baseline Interferometry (VLBI) and the Spectrometer/Telescope for Imaging X-rays (STIX) for solar observations. Despite ongoing parallel developments of novel imaging algorithms, synergies remain unexplored. We study the synergies between the data analysis for the STIX instrument and VLBI, compare the methodologies and evaluate their potential. In this way, we identify key trends in the performance of several algorithmic ideas and draw recommendations for the future. To this end, we organized a semi-blind imaging challenge with data sets and source structures that are typical for sparse VLBI, specifically in the context of the Event Horizon Telescope (EHT), and for STIX observations. 17 different algorithms from both communities, from 6 different imaging frameworks, participated in the challenge, marking this work the largest scale code comparisons for STIX and VLBI to date. Strong synergies between the two communities have been identified, as can be proven by the success of the imaging methods proposed for STIX in imaging VLBI data sets and vice versa. Novel imaging methods outperform the standard CLEAN algorithm significantly in every test-case. Improvements over the performance of CLEAN make deeper updates to the inverse modeling pipeline necessary, or consequently replacing inverse modeling with forward modeling. Entropy-based and Bayesian methods perform best on STIX data. The more complex imaging algorithms utilizing multiple regularization terms (recently proposed for VLBI) add little to no additional improvements for STIX, but outperform the other methods on EHT data. This work demonstrates the great synergy between the STIX and VLBI imaging efforts and the great potential for common developments., Comment: accepted for publication in A&A

AI-FLARES (Artificial Intelligence for the Analysis of Solar Flares Data) is a research project funded by the Agenzia Spaziale Italiana and by the Istituto Nazionale di Astrofisica within the framework of the ``Attivit\`a di Studio per la Comunit\`a Scientifica Nazionale Sole, Sistema Solare ed Esopianeti'' program. The topic addressed by this project was the development and use of computational methods for the analysis of remote sensing space data associated to solar flare emission. This paper overviews the main results obtained by the project, with specific focus on solar flare forecasting, reconstruction of morphologies of the flaring sources, and interpretation of acceleration mechanisms triggered by solar flares.

Regularized imaging spectroscopy was introduced for the construction of electron flux images at different energies from count visibilities recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). In this work we seek to extend this approach to data from the Spectrometer/Telescope for Imaging X-rays (STIX) on-board the Solar Orbiter mission. Our aims are to demonstrate the feasibility of regularized imaging spectroscopy as a method for analysis of STIX data, and also to show how such analysis can lead to insights into the physical processes affecting the nonthermal electrons responsible for the hard X-ray emission observed by STIX. STIX records imaging data in an intrinsically different manner from RHESSI. Rather than sweeping the angular frequency plane in a set of concentric circles (one circle per detector), STIX uses $30$ collimators, each corresponding to a specific angular frequency. In this paper we derive an appropriate modification of the previous computational approach for the analysis of the visibilities observed by STIX. This approach also allows for the observed count data to be placed into non-uniformly-spaced energy bins. We show that the regularized imaging spectroscopy approach is not only feasible for analysis of the visibilities observed by STIX, but also more reliable. Application of the regularized imaging spectroscopy technique to several well-observed flares reveals details of the variation of the electron flux spectrum throughout the flare sources. We conclude that the visibility-based regularized imaging spectroscopy approach is well-suited to analysis of STIX data. We also use STIX electron flux spectral images to track, for the first time, the behavior of the accelerated electrons during their path from the acceleration site in the solar corona toward the chromosphere

Aims: To formulate, implement, and validate a user-independent release of CLEAN for Fourier-based image reconstruction of hard X-rays flaring sources. Methods: CLEAN is an iterative deconvolution method for radio and hard X-ray solar imaging. In a specific step of its pipeline, CLEAN requires the convolution between an idealized version of the instrumental Point Spread Function (PSF), and a map collecting point sources located at positions on the solar disk from where most of the flaring radiation is emitted. This convolution step has highly heuristic motivations and the shape of the idealized PSF, which depends on the user's choice, impacts the shape of the overall reconstruction. Here we propose the use of an interpolation/extrapolation process to avoid this user-dependent step, and to realize a completely unbiased version of CLEAN. Results: Applications to observations recorded by the Spectrometer/Telescope for Imaging X-rays (STIX) on-board Solar Orbiter show that this unbiased release of CLEAN outperforms the standard version of the algorithm in terms of both automation and reconstruction reliability, with reconstructions whose accuracy is in line with the one offered by other imaging methods developed in the STIX framework. Conclusions: This unbiased version of CLEAN proposes a feasible solution to a well-known open issue concerning CLEAN, i.e., its low degree of automation. Further, this study provided the first application of an interpolation/extrapolation approach to image reconstruction from STIX experimental visibilities.

Aims. To provide a schematic mathematical description of the imaging concept of the Spectrometer/Telescope for Imaging X-rays (STIX) on board Solar Orbiter. The derived model is the fundamental starting point for both the interpretation of STIX data and the description of the data calibration process. Methods. We describe the STIX indirect imaging technique which is based on spatial modulation of the X-ray photon flux by means of tungsten grids. We show that each of 30 STIX imaging sub-collimators measures a complex Fourier component of the flaring X-ray source corresponding to a specific angular frequency. We also provide details about the count distribution model, which describes the relationship between the photon flux and the measured pixel counts. Results. We define the image reconstruction problem for STIX from both visibilities and photon counts. We provide an overview of the algorithms implemented for the solution of the imaging problem, and a comparison of the results obtained with these different methods in the case of the SOL2022-03-31T18 flaring event.

The Spectrometer and Telescope for Imaging X-rays (STIX) on board Solar Orbiter observes solar X-ray emission in the range of 4 – 150 keV and produces spectra and images of solar flares over a wide range of flare magnitudes. During nominal operation, STIX continuously generates data. A constant data flow requires fully automated data-processing pipelines to process and analyze the data, and a data platform to manage, visualize, and distribute the data products to the scientific community. The STIX Data Center has been built to fulfill these needs. In this paper, we outline its main components to help the community better understand the tools and data it provides. The STIX Data Center is operated at the University of Applied Sciences and Arts Northwestern Switzerland (FHNW) and consists of automated processing pipelines and a data platform. The pipelines process STIX telemetry data, perform common analysis tasks, and generate data products at different processing levels. They have been designed to operate fully automatically with minimal human intervention. The data platform provides web-based user interfaces and application programmable interfaces for searching and downloading STIX data products. The STIX Data Center has been operating successfully for more than two years. The platform facilitates instrument operations and provides vital support to STIX data users., Comment: 18 pages, Accepted by A&A, https://doi.org/10.1051/0004-6361/202346031

Extreme-ultraviolet (EUV) observations provide considerable insight into evolving physical conditions in the active solar atmosphere. For a prescribed density and temperature structure, it is straightforward to construct the corresponding differential emission measure profile $\xi(T)$, such that $\xi(T) \, dT$ is proportional to the emissivity from plasma in the temperature range $[T, T + dT]$. Here we study the inverse problem of obtaining a valid $\xi(T)$ profile from a set of EUV spectral line intensities observed at a pixel within a solar image. Our goal is to introduce and develop a regularized maximum likelihood (RML) algorithm designed to address the mathematically ill-posed problem of constructing differential emission measure profiles from a discrete set of EUV intensities in specified wavelength bands, specifically those observed by the Atmospheric Imaging Assembly (AIA) on the NASA Solar Dynamics Observatory. The RML method combines features of maximum likelihood and regularized approaches used by other authors. It is also guaranteed to produce a positive definite differential emission measure profile. We evaluate and compare the effectiveness of the method against other published algorithms, using both simulated data generated from parametric differential emission profile forms, and AIA data from a solar eruptive event on 2010 November 3. Similarities and differences between the differential emission measure profiles and maps reconstructed by the various algorithms are discussed. The RML inversion method is mathematically rigorous, computationally efficient, and produces acceptable measures of performance in the following three key areas: fidelity to the data, accuracy in the reconstruction, and robustness in the presence of data noise. As such, it shows considerable promise for computing differential emission measure profiles from datasets of discrete spectral lines.

Context. We present an analysis of a GOES M1.8 flare with excellent observational coverage in UV, EUV, and X-ray, including observations from the instruments IRIS, SDO with AIA, Hinode/EIS, Hinode/XRT, and Solar Orbiter with the Spectrometer/Telescope for Imaging X-rays (STIX). Hard X-ray emission is often observed at the footpoints of flare loops and is occasionally observed in the corona. In this flare, four nonthermal hard X-ray sources are seen. Aim. Our aim is to understand why we can observe four individual nonthermal sources in this flare and how we can characterize the physical properties of these four sources. Methods. We used the multiwavelength approach to analyze the flare and characterize the four sources. To do this, we combined imaging at different wavelengths and spectroscopic fitting in the EUV and X-ray range. Results. The flare is eruptive with an associated coronal mass ejection, and it shows the classical flare picture of a heated flare loop seen in EUV and X-rays, and two nonthermal hard X-ray footpoints at the loop ends. In addition to the main flare sources, we observed two outer sources in the UV, EUV, and nonthermal X-ray range located away from the main flare loop to the east and west. The two outer sources are clearly correlated in time, and they are only seen during the first two minutes of the impulsive phase, which lasts a total of about four minutes. Conclusions. Based on the analysis, we determine that the outer sources are the anchor points of an erupting filament. The hard X-ray emission is interpreted as flare-accelerated electrons that are injected upward into the filament and then precipitate along the filament toward the chromosphere, producing Bremsstrahlung. While sources like this have been speculated to exist, this is the first report of their detection., Comment: 12 pages, 10 figures, accepted for publication in A&A

Aima. To determine to what extent the problem of forward fitting visibilities measured by the Spectrometer/Telescope Imaging X-rays (STIX) on-board Solar Orbiter is more challenging with respect to the same problem in the case of previous hard X-ray solar imaging missions; to identify an effective optimization scheme for parametric imaging for STIX. Methods. This paper introduces a Particle Swarm Optimization (PSO) algorithm for forward fitting STIX visibilities and compares its effectiveness with respect to the standard simplex-based optimization algorithm used so far for the analysis of visibilities measured by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). This comparison is made by considering experimental visibilities measured by both RHESSI and STIX, and synthetic visibilities generated by accounting for the STIX signal formation model. Results. We found out that the parametric imaging approach based on PSO is as reliable as the one based on the simplex method in the case of RHESSI visibilities. However, PSO is significantly more robust when applied to STIX simulated and experimental visibilities. Conclusions. Standard deterministic optimization is not effective enough for forward-fitting the few visibilities sampled by STIX in the angular frequency plane. Therefore a more sofisticated optimization scheme must be introduced for parametric imaging in the case of the Solar Orbiter X-ray telescope. The forward-fitting routine based on PSO we introduced in this paper proved to be significantly robust and reliable, and could be considered as an effective candidate tool for parametric imaging in the STIX context.

Context. The Spectrometer/Telescope for Imaging X-rays (STIX) is one of 6 remote sensing instruments on-board Solar Orbiter. It provides hard X-ray imaging spectroscopy of solar flares by sampling the Fourier transform of the incoming flux. Aims. To show that the visibility amplitude and phase calibration of 24 out of 30 STIX sub-collimators is well advanced and that a set of imaging methods is able to provide the first hard X-ray images of the flaring Sun from Solar Orbiter. Methods. We applied four visibility-based image reconstruction methods and a count-based one to calibrated STIX observations. The resulting reconstructions are compared to those provided by an optimization algorithm used for fitting the amplitudes of STIX visibilities. Results. When applied to six flares with GOES class between C4 and M4 which occurred in May 2021, the five imaging methods produce results morphologically consistent with the ones provided by the Atmospheric Imaging Assembly on-board the Solar Dynamic Observatory (SDO/AIA) in UV wavelengths. The $\chi^2$ values and the parameters of the reconstructed sources are comparable between methods, thus confirming their robustness. Conclusions. This paper shows that the current calibration of the main part of STIX sub-collimators has reached a satisfactory level for scientific data exploitation, and that the imaging algorithms already available in the STIX data analysis software provide reliable and robust reconstructions of the morphology of solar flares.

In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a regularizing inverse operator by using a dataset of input-output pairs of the forward model rely on deep learning techniques. In these approaches, a neural network is trained to predict the value of the sought parameters directly from the data. In this paper, we show that these methods provide suboptimal results when the topology of the parameter space is strictly coarser than the Euclidean one. To overcome this issue, we propose a two-step strategy for approximating a regularizing inverse operator by means of a neural network, which works under general topological conditions. First, we embed the parameters into a subspace of a low-dimensional Euclidean space; second, we use a neural network to approximate a homeomorphism between the subspace and the image of the parameter space through the forward operator. The parameters are then retrieved by applying the inverse of the embedding to the network predictions. The results are shown for the problem of X-ray imaging of solar flares with data from the Spectrometer/Telescope for Imaging X-rays. In this case, the parameter space is a family of Moebius strips that collapse into a point. Our simulation studies show that the use of a neural network for predicting the parameters directly from the data yields systematic errors due to the non-Euclidean topology of the parameter space. The proposed strategy overcomes the topological issues and furnishes stable and accurate reconstructions.

Aims: To provide the first demonstration of STIX Fourier-transform X-ray imaging using semi-calibrated (amplitude-only) visibility data acquired during the Solar Orbiter's cruise phase. Methods: We use a parametric imaging approach by which STIX visibility amplitudes are fitted by means of two non-linear optimization methods: a fast meta-heuristic technique inspired by social behavior, and a Bayesian Monte Carlo sampling method, which, although slower, provides better quantification of uncertainties. Results: When applied to a set of solar flare visibility amplitudes recorded by STIX on November 18, 2020 the two parametric methods provide very coherent results. The analysis also demonstrates the ability of STIX to reconstruct high time resolution information and, from a spectral viewpoint, shows the reliability of a double-source scenario consistent with a thermal versus nonthermal interpretation. Conclusions: In this preliminary analysis of STIX imaging based only on visibility amplitudes, we formulate the imaging problem as a non-linear parametric issue we addressed by means of two high-performance optimization techniques that both showed the ability to sample the parametric space in an effective fashion, thus avoiding local minima.

The Spectrometer/Telescope for Imaging X-rays (STIX) is the HXR instrument onboard Solar Orbiter designed to observe solar flares over a broad range of flare sizes, between 4-150 keV. We report the first STIX observations of microflares recorded during the instrument commissioning phase in order to investigate the STIX performance at its detection limit. This first result paper focuses on the temporal and spectral evolution of STIX microflares occuring in the AR12765 in June 2020, and compares the STIX measurements with GOES/XRS, SDO/AIA, and Hinode/XRT. For the observed microflares of the GOES A and B class, the STIX peak time at lowest energies is located in the impulsive phase of the flares, well before the GOES peak time. Such a behavior can either be explained by the higher sensitivity of STIX to higher temperatures compared to GOES, or due to the existence of a nonthermal component reaching down to low energies. The interpretation is inconclusive due to limited counting statistics for all but the largest flare in our sample. For this largest flare, the low-energy peak time is clearly due to thermal emission, and the nonthermal component seen at higher energies occurs even earlier. This suggests that the classic thermal explanation might also be favored for the majority of the smaller flares. In combination with EUV and SXR observations, STIX corroborates earlier findings that an isothermal assumption is of limited validity. Future diagnostic efforts should focus on multi-wavelength studies to derive differential emission measure distributions over a wide range of temperatures to accurately describe the energetics of solar flares. Commissioning observations confirm that STIX is working as designed. As a rule of thumb, STIX detects flares as small as the GOES A class. For flares above the GOES B class, detailed spectral and imaging analyses can be performed., Comment: 19 pages, 11 figures

Space telescopes for solar hard X-ray imaging provide observations made of sampled Fourier components of the incoming photon flux. The aim of this study is to design an image reconstruction method relying on enhanced visibility interpolation in the Fourier domain. % methods heading (mandatory) The interpolation-based method is applied on synthetic visibilities generated by means of the simulation software implemented within the framework of the Spectrometer/Telescope for Imaging X-rays (STIX) mission on board Solar Orbiter. An application to experimental visibilities observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is also considered. In order to interpolate these visibility data we have utilized an approach based on Variably Scaled Kernels (VSKs), which are able to realize feature augmentation by exploiting prior information on the flaring source and which are used here, for the first time, for image reconstruction purposes.} % results heading (mandatory) When compared to an interpolation-based reconstruction algorithm previously introduced for RHESSI, VSKs offer significantly better performances, particularly in the case of STIX imaging, which is characterized by a notably sparse sampling of the Fourier domain. In the case of RHESSI data, this novel approach is particularly reliable when either the flaring sources are characterized by narrow, ribbon-like shapes or high-resolution detectors are utilized for observations. % conclusions heading (optional), leave it empty if necessary The use of VSKs for interpolating hard X-ray visibilities allows a notable image reconstruction accuracy when the information on the flaring source is encoded by a small set of scattered Fourier data and when the visibility surface is affected by significant oscillations in the frequency domain.

In this work, we introduce a novel estimator of the predictive risk with Poisson data, when the loss function is the Kullback-Leibler divergence, in order to define a regularization parameter's choice rule for the Expectation Maximization (EM) algorithm. To this aim, we prove a Poisson counterpart of the Stein's Lemma for Gaussian variables, and from this result we derive the proposed estimator showing its analogies with the well-known Stein's Unbiased Risk Estimator valid for a quadratic loss. We prove that the proposed estimator is asymptotically unbiased with increasing number of measured counts, under certain mild conditions on the regularization method. We show that these conditions are satisfied by the EM algorithm and then we apply this estimator to select its optimal reconstruction. We present some numerical tests in the case of image deconvolution, comparing the performances of the proposed estimator with other methods available in the literature, both in the inverse crime and non-inverse crime setting.

Maximum Entropy is an image reconstruction method conceived to image a sparsely occupied field of view and therefore particularly appropriate to achieve super-resolution effects. Although widely used in image deconvolution, this method has been formulated in radio astronomy for the analysis of observations in the spatial frequency domain, and an Interactive Data Language (IDL) code has been implemented for image reconstruction from solar X-ray Fourier data. However, this code relies on a non-convex formulation of the constrained optimization problem addressed by the Maximum Entropy approach and this sometimes results in unreliable reconstructions characterized by unphysical shrinking effects. This paper introduces a new approach to Maximum Entropy based on the constrained minimization of a convex functional. In the case of observations recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), the resulting code provides the same super-resolution effects of the previous algorithm, while working properly also when that code produces unphysical reconstructions. Results are also provided of testing the algorithm with synthetic data simulating observations of the Spectrometer/Telescope for Imaging X-rays (STIX) in Solar Orbiter. The new code is available in the {\em{HESSI}} folder of the Solar SoftWare (SSW)tree.

The Spectrometer/Telescope for Imaging X-rays (STIX) will look at 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, which will ask for Fourier-based image reconstruction methods. However, in this paper we show that, as for RHESSI, also for STIX count-based imaging is possible. Specifically, here 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 made of 120 count components. Then we test the reliability of Expectation Maximization for image reconstruction in the case of several simulated configurations typical of flare morphology., Comment: submitted to A&A