The process of data formation for the Spectrometer/Telescope for Imaging X-rays (STIX) in Solar Orbiter

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.Comment: submitted to SIAM Journal on Imaging Science

A new semi-blind deconvolution approach for Fourier-based image restoration: an application in astronomy

The aim of this paper is to develop a new optimization algorithm for the restoration of an image starting from samples of its Fourier Transform, when only partial information about the data frequencies is provided. The corresponding constrained optimization problem is approached with a cyclic block alternating scheme, in which projected gradient methods are used to find a regularized solution. Our algorithm is then applied to the imaging of high-energy radiation emitted during a solar flare through the analysis of the photon counts collected by the NASA RHESSI satellite. Numerical experiments on simulated data show that, both in presence and in absence of statistical noise, the proposed approach provides some improvements in the reconstructions

A regularized visibility-based approach to astronomical imaging spectroscopy

We develop a formal procedure for the analysis of imaging spectroscopy data, i.e., remote sensing observations of the structure of a radiation source as a function of an observed parameter (e.g., radiation wavelength, frequency, or energy) and two-dimensional location in the observation plane of the instrument used. In general, imaging spectroscopy involves inversions of both spatial and spectral information. “Traditional” approaches typically proceed by performing the spatial inversion first, and then applying spectral deconvolution algorithms on a “pixel-by-pixel” basis across the source to deduce the (line-of-sight-weighted) form of the “source function” (a function involving only physical properties of the source itself) at each location in the observation plane. However, in the special case where spatial information is encoded in the form of visibilities (two-dimensional spatial Fourier transforms of the source structure), it is advantageous, both conceptually and computationally, to reverse the order of the steps in this procedure. In such an alternative approach, the spectral inversion is performed first, yielding visibilities of the unknown source function, and then these source function visibilities are spatially transformed to yield in situ information on the source, as a function of both energy and position. We illustrate the power and fidelity of this method using simulated data and apply it to hard X-ray observations of a solar flare on April 15, 2002. We also discuss briefly its broader applicability