A visibility-based approach using regularization for imaging-spectroscopy in solar X-ray astronomy

The Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) is a nine-collimators satellite detecting X-rays and $\gamma$-rays emitted by the Sun during flares. As thespacecraft rotates, imaging information is encoded as rapid time-variations of the detected flux. We recently proposed a method for the construction of electron flux maps at different electron energies from sets of count visibilities (i.e., direct, calibrated measurements of specific Fourier components of the source spatial structure) measured by RHESSI. The method requires the application of regularized inversion for the synthesis of electron visibility spectra and of imaging techniques for the reconstruction of two-dimensional electron flux maps. The method, already tested on real events registered by RHESSI, is validated in this paper by means of simulated realistic data.