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

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. The interpolation-based method is applied to 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, in the context of inverse problems. When compared to an interpolation-based reconstruction algorithm previously introduced for RHESSI, VSKs offer significantly better performance, 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 the flaring sources are either characterized by narrow, ribbon-like shapes or high-resolution detectors are utilized for observations. The use of VSKs for interpolating hard X-ray visibilities allows remarkable 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