A Compressed Sensing-based Image Reconstruction Algorithm for Solar Flare X-Ray Observations

Felix, S.; Bolzern, Roman; Battaglia, Marina

doi:10.3847/1538-4357/aa8d1e

Cited by 24 publications

(18 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present study we focused on solar hard X-ray imaging and, specifically, we cast our interpolation-based reconstruction scheme into the framework of the NASA RHESSI and the ESA STIX missions. RHESSI had its nominal phase between February 2002 and August 2018 and many inversion methods have been formulated to express its observations as images [36][37][38][39][40][41][42]. Instead, STIX will begin its nominal phase in September 2021 and the few studies devoted to its imaging process involve just synthetic data [40].…”

Section: Applications To Astronomical Imagingmentioning

confidence: 99%

Feature augmentation for the inversion of the Fourier transform with limited data

Perracchione,

Massone,

Piana

2021

Preprint

View full text Add to dashboard Cite

We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shapedriven 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.

show abstract

Section: Applications To Astronomical Imagingmentioning

confidence: 99%

Feature augmentation for the inversion of the Fourier transform with limited data

Perracchione,

Massone,

Piana

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Image reconstruction methods in solar hard X-ray astronomy rely on procedures that allow some sort of interpolation/extrapolation in the (u, v)-space in order to recover information in between the sampled frequencies, for reducing the imaging artifacts and, outside the sampling domain, for obtaining super-resolution effects. Most methods accomplish these objectives by imposing constraints in the image domain, either by optimizing parameters associated to predefined image shapes via comparison with observations (Aschwanden et al, 2002;Sciacchitano et al, 2018), or by minimizing regularization functionals that combine a fitting term with a stability term (Felix et al, 2017;Duval-Poo et al, 2018;Massa et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Visibility Interpolation in Solar Hard X-ray Imaging: Application to RHESSI and STIX

Perracchione,

Massa,

Massone

et al. 2020

Preprint

View full text Add to dashboard Cite

Aims. 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. 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. 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. 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.

show abstract

“…calibrated samples of the Fourier transform of the incoming photon flux, generated via a data stacking process. Among count-based methods, SSW includes Back Projection (Hurford et al 2002), Clean (Högbom 1974), Forward Fit (Aschwanden et al 2002), Pixon (Metcalf et al 1996), and Expectation Maximization (Benvenuto et al 2013); among visibility-based methods, SSW includes MEM NJIT (Bong et al 2006;Schmahl et al 2007), a Maximum Entropy method; VIS FWDFIT (Schmahl et al 2007), which selects pre-defined source shapes based on their best fitting of visibilities; uv smooth (Massone et al 2009), an interpolation/extrapolation method in the Fourier domain; VIS CS (Felix et al 2017), a catalogue-based compressed sensing algorithm; and VIS WV (Duval-Poo et al 2018), a wavelet-based compressed sensing algorithm. Although each one of these algorithms combines specific values with applicability limitations and specific flaws, a critical comparison of the maps of a given flaring event obtained by the application of all (or most) of these algorithms provides a good picture of what a reliable image of the event could be.…”

mentioning

confidence: 99%

MEM_GE: a new maximum entropy method for image reconstruction from solar X-ray visibilities

Massa,

Schwartz,

Tolbert

et al. 2020

Preprint

View full text Add to dashboard Cite

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 HESSI folder of the Solar SoftWare (SSW) tree.

show abstract

A Compressed Sensing-based Image Reconstruction Algorithm for Solar Flare X-Ray Observations

Cited by 24 publications

References 34 publications

Feature augmentation for the inversion of the Fourier transform with limited data

Feature augmentation for the inversion of the Fourier transform with limited data

Visibility Interpolation in Solar Hard X-ray Imaging: Application to RHESSI and STIX

MEM_GE: a new maximum entropy method for image reconstruction from solar X-ray visibilities

Contact Info

Product

Resources

About