MEM_GE: A New Maximum Entropy Method for Image Reconstruction from Solar X-Ray Visibilities

Abstract

Maximum Entropy is an image reconstruction method conceived to image a sparsely occupied field of view, therefore it is particularly effective at achieving 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 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 also working properly when that code produces unphysical reconstructions. We also obtain results via 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.

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

“…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].…”

“…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].…”

Imaging from STIX visibility amplitudes

“…For a fully calibrated instrument, the image reconstruction problem for STIX is therefore the linear Fourier inver-sion problem from limited data that can be addressed by means of regularization methods, such as interpolation and extrapolation (Perracchione et al 2020), maximum entropy (Massa et al 2020), or compressed sensing (Duval-Poo et al 2018).…”

Imaging from STIX visibility amplitudes

“…For a fully-calibrated instrument, the image reconstruction problem for STIX is therefore the linear Fourier inversion problem from limited data that can be addressed by means of regularization methods like interpolation/extrapolation (Perracchione et al, 2020), maximum entropy (Massa et al, 2020), or compressed sensing (Duval-Poo et al, 2018).…”