arXiv subjects
Publications and source records attributed to Michele Piana.
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).
We describe here the application of a machine learning method for flare forecasting using vectors of properties extracted from images provided by the Helioseismic and Magnetic Imager in the Solar Dynamics Observatory (SDO/HMI). We also discuss how the method can be used to quantitatively assess the impact of such properties on the prediction process.
Background: Magneto- and Electro-encephalography record the electromagnetic field generated by neural currents with high temporal frequency and good spatial resolution, and are therefore well suited for source localization in the time and in the frequency domain. In particular, localization of the generators of neural oscillations is very important in the study of cognitive processes in the healthy and in the pathological brain. New method: We introduce the use of a Bayesian multi-dipole localization method in the frequency domain. Given the Fourier Transform of the data at one or multiple frequencies and/or trials, the algorithm approximates numerically the posterior distribution with Monte Carlo techniques. Results: We use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios and correlated sources. We use dipole clusters to mimic the effect of extended sources. In addition, we test the algorithm on real MEG data to confirm its feasibility. Comparison with existing method(s): Throughout the whole study, DICS (Dynamic Imaging of Coherent Sources) is used systematically as a benchmark. The two methods provide similar general pictures; the posterior distributions of the Bayesian approach contain much richer information at the price of a higher computational cost. Conclusions: The Bayesian method described in this paper represents a reliable approach for localization of multiple dipoles in the frequency domain.
This paper reports on the re-analysis of solar flares in which the hard X-rays (HXRs) come predominantly from the corona rather than from the more usual chromospheric footpoints. All of the 26 previously analyzed event time intervals, over 13 flares, are re-examined for consistency with a flare model in which electrons are accelerated near the top of a magnetic loop that has a sufficiently high density to stop most of the electrons by Coulomb collisions before they can reach the footpoints. Of particular importance in the previous analysis was the finding that the length of the coronal HXR source increased with energy in the 20 - 30 keV range. However, after allowing for the possibility that footpoint emission at the higher energies affects the inferred length of the coronal HXR source, and using analysis techniques that suppress the possible influence of such footpoint emission, we conclude that there is no longer evidence that the length of the HXR coronal sources increase with increasing energy. In fact, for the 6 flares and 12 time intervals that satisfied our selection criteria, the loop lengths decreased on average by 1.0 +/- 0.2 arcsec between 20 and 30 keV, with a standard deviation of 3.5 arcsec. We find strong evidence that the peak of the coronal HXR source increases in altitude with increasing energy. For the thermal component of the emission, this is consistent with the standard CHSKP flare model in which magnetic reconnection in a coronal current sheet results in new hot loops being formed at progressively higher altitudes. The explanation for the nonthermal emission is not so clear.
'Flare Likelihood and Region Eruption Forecasting (FLARECAST)' is a Horizon 2020 project, which realized a technological platform for machine learning algorithms, with the objective of providing the space weather community with a prediction service for solar flares. This paper describes the FLARECAST service and shows how the methods implemented in the platform allow both flare prediction and a quantitative assessment of how the information contained in the space data utilized in the analysis may impact the forecasting process.
The hard X-ray emission in a solar flare is typically characterized by a number of discrete sources, each with its own spectral, temporal, and spatial variability. Establishing the relationship amongst these sources is critical to determine the role of each in the energy release and transport processes that occur within the flare. In this paper we present a novel method to identify and characterize each source of hard X-ray emission. The method permits a quantitative determination of the most likely number of subsources present, and of the relative probabilities that the hard X-ray emission in a given subregion of the flare is represented by a complicated multiple source structure or by a simpler single source. We apply the method to a well-studied flare on 2002~February~20 in order to assess competing claims as to the number of chromospheric footpoint sources present, and hence to the complexity of the underlying magnetic geometry/toplogy. Contrary to previous claims of the need for multiple sources to account for the chromospheric hard X-ray emission at different locations and times, we find that a simple two-footpoint-plus-coronal-source model is the most probable explanation for the data. We also find that one of the footpoint sources moves quite rapidly throughout the event, a factor that presumably complicated previous analyses. The inferred velocity of the footpoint corresponds to a very high induced electric field, compatible with those in thin reconnecting current sheets.
Parametric imaging is a compartmental approach that processes nuclear imaging data to estimate the spatial distribution of the kinetic parameters governing tracer flow. The present paper proposes a novel and efficient computational method for parametric imaging which is potentially applicable to several compartmental models of diverse complexity and which is effective in the determination of the parametric maps of all kinetic coefficients. We consider applications to [{18}F]-fluorodeoxyglucose Positron Emission Tomography (FDG-PET) data and analyze the two-compartment catenary model describing the standard FDG metabolization by an homogeneous tissue and the three-compartment non-catenary model representing the renal physiology. We show uniqueness theorems for both models. The proposed imaging method starts from the reconstructed FDG-PET images of tracer concentration and preliminarily applies image processing algorithms for noise reduction and image segmentation. The optimization procedure solves pixelwise the non-linear inverse problem of determining the kinetic parameters from dynamic concentration data through a regularized Gauss-Newton iterative algorithm. The reliability of the method is validated against synthetic data, for the two-compartment system, and experimental real data of murine models, for the renal three-compartment system.
In this work we use numerical simulation to investigate how the temporal length of the data affects the reliability of the estimates of brain connectivity from EEG time--series. We assume that the neural sources follow a stable MultiVariate AutoRegressive model, and consider three connectivity metrics: Imaginary part of Coherency (IC), generalized Partial Directed Coherence (gPDC) and frequency--domain Granger Causality (fGC). In order to assess the statistical significance of the estimated values, we use the surrogate data test by generating phase--randomized and autoregressive surrogate data. We first consider the ideal case where we know the source time courses exactly. Here we show how, expectedly, even exact knowledge of the source time courses is not sufficient to provide reliable estimates of the connectivity when the number of samples gets small; however, while gPDC and fGC tend to provide a larger number of false positives, the IC becomes less sensitive to the presence of connectivity. Then we proceed with more realistic simulations, where the source time courses are estimated using eLORETA, and the EEG signal is affected by biological noise of increasing intensity. Using the ideal case as a reference, we show that the impact of biological noise on IC estimates is qualitatively different from the impact on gPDC and fGC.
We introduce a hybrid approach to solar flare prediction, whereby a supervised regularization method is used to realize feature importance and an unsupervised clustering method is used to realize the binary flare/no-flare decision. The approach is validated against NOAA SWPC data.
The present paper proposes a novel computational method for parametric imaging of nuclear medicine data. The mathematical procedure is general enough to work for compartmental models of diverse complexity and is effective in the determination of the parametric maps of all kinetic parameters governing tracer flow. We consider applications to [18F]-fluorodeoxyglucose Positron Emission Tomography (FDG-PET) data and analyze the two-compartment catenary model describing the standard FDG metabolization by an homogeneous tissue, e.g. the liver, and the three-compartment non-catenary model representing the renal physiology. The proposed imaging method starts from the reconstructed FDG-PET images of tracer concentration and preliminarily applies image processing algorithms for noise reduction and image segmentation processes for selecting the region enclosing the organ of physiologic interest. The optimization scheme solves pixelwise the non-linear inverse problem of determining the kinetic parameters from dynamic concentration data through a Gauss-Newton iterative algorithm with a penalty term accounting for the ill-posedness of the problem. We tested our imaging approach on FDG-PET data of murine models obtained by means of a dedicated microPET system, and we analyzed different PET slices containing axial sections of the liver and axial sections of the kidneys. The reconstructed parametric images proved to be reliable and qualitatively effective in the description of the local FDG metabolism with respect to the different physiologies.
We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and recently proposed regularization methods, as well as Monte Carlo techniques for Bayesian inference. We classify the inverse methods based on the underlying source model, and discuss advantages and disadvantages. Finally we describe an application to the pre-surgical evaluation of epileptic patients.
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.
We consider the problem of retrieving the aerosol extinction coefficient from Raman lidar measurements. This is an ill--posed inverse problem that needs regularization, and we propose to use the Expectation--Maximization (EM) algorithm to provide stable solutions. Indeed, EM is an iterative algorithm that imposes a positivity constraint on the solution, and provides regularization if iterations are stopped early enough. We describe the algorithm and propose a stopping criterion inspired by a statistical principle. We then discuss its properties concerning the spatial resolution. Finally, we validate the proposed approach by using both synthetic data and experimental measurements; we compare the reconstructions obtained by EM with those obtained by the Tikhonov method, by the Levenberg-Marquardt method, as well as those obtained by combining data smoothing and numerical derivation.
The Radon transform is a linear integral transform that mimics the data formation process in medical imaging modalities like X-ray Computerized Tomography and Positron Emission Tomography. The Hough transform is a pattern recognition technique, which is mainly used to detect straight lines in digital images and which has been recently extended to the automatic recognition of algebraic plane curves. Although defined in very different ways, in numerical applications both transforms ultimately take an image as an input and provide, as an output, a function defined on a parameter space. The parameters in this space describe a family of curves, which represent either the integration domains considered in the (generalized) Radon transform, or the curves to be detected by means of the Hough transform. In both cases, the 2D plot of the intensity values of the output function is the so-called (Radon or Hough) sinogram. While the Hough sinogram is produced by an algorithm whose implementation requires that the parameter space be discretized in cells, the Radon sinogram is mathematically defined on a continuous parameter space, which in turn may need to be discretized just for physical or numerical reasons. In this paper, by considering a more general and n-dimensional setting, we prove that, whether the input image is described as a set of points (possibly with different intensity values) or as a piecewise constant function, its (rescaled) Hough sinogram converges to the corresponding Radon sinogram as the discretization step in the parameter space tends to zero. We also show that this result may have a notable impact on the image reconstruction problem of inverting the Radon sinogram recorded by a medical imaging scanner, and that the description of the Hough transform problem within the framework of regularization theory for inverse problems is worth investigating.
Saturation affects a significant rate of images recorded by the Atmospheric Imaging Assembly on the Solar Dynamics Observatory. This paper describes a computational method and a technological pipeline for the de-saturation of such images, based on several mathematical ingredients like Expectation Maximization, image correlation and interpolation. An analysis of the computational properties and demands of the pipeline, together with an assessment of its reliability are performed against a set of data recorded from the Feburary 25 2014 flaring event.
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).
The Spectrometer/Telescope for Imaging X-rays (STIX) is a hard X-ray imaging spectroscopy device to be mounted in the Solar Orbiter cluster with the aim of providing images and spectra of solar flaring regions at different photon energies in the range from a few keV to around 150 keV. The imaging modality of this telescope is based on the Moire pattern concept and utilizes 30 sub-collimators, each one containing a pair of co-axial grids. This paper applies Fourier analysis to provide the first rigorous description of the data formation process in STIX. Specifically, we show that, under first harmonic approximation, the integrated counts measured by STIX sub-collimators can be interpreted as specific spatial Fourier components of the incoming photon flux, named visibilities. Fourier analysis also allows the quantitative assessment of the reliability of such interpretation. The description of STIX data in terms of visibilities has a notable impact on the image reconstruction process, since it fosters the application of Fourier-based imaging algorithms.
EUV images of solar flares provided by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory (SDO/AIA) are often affected by saturation effects in their core, physically most interesting region. We introduce an image reconstruction procedure that allows recovering information in the primary saturation domain using the secondary images produced by the diffraction fringes as input data. Such a procedure is based on standard image-processing tools like correlation, convolution, and back-projection. Its effectiveness is tested in the case of SDO/AIA observations of the July 8 2013 flaring event.