Image reconstruction methods for Solar Orbiter STIX

The Spectrometer/Telescope for Imaging X-rays (STIX) is the instrument of the Solar Orbiter mission conceived for the observation of the X-ray radiation emitted during solar flares. STIX adopts an indirect imaging technique based on the use of modulation collimators, i.e., pairs of grids mounted in front of detectors. By measuring the modulated X-ray photon flux, the telescope provides the complex values of 30 Fourier components of the angular distribution of the X-ray source, named visibilities. Hence, the imaging problem for STIX is the inverse problem of reconstructing the image of the flaring X-ray source from a sparse sampling of its Fourier transform. In this thesis, we describe the STIX imaging concept and the image reconstruction problem both from visibilities and from photon count measurements. We present different image reconstruction techniques: the count-based Expectation Maximization (EM) algorithm, the visibility-based maximum entropy method MEM_GE and a neural network approach for parametric image reconstruction. We test these methods on synthetic STIX data and, in the case of MEM_GE, on real data provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). We propose a stopping rule for EM based on a predictive risk estimator. This estimator is derived by using a Poisson counterpart of Stein’s lemma for Gaussian variates. We validate the performance of the stopping rule in the case of the STIX imaging problem from synthetic data and in the case of a deconvolution inverse problem. Finally, we present the results of the STIX imaging problem from real data. We describe the first approaches of image reconstruction from semi-calibrated data, i.e., visibility amplitudes only. Then, we provide an overview of the visibility phase calibration, and we show the reconstructions from fully-calibrated visibilities obtained by using several methods, including MEM_GE and EM. The STIX reconstructions are validated by comparison with maps of the same events provided by the Atmospheric Imaging Assembly on board the Solar Dynamic Observatory (SDO/AIA) in UV wavelengths.