Research database

Given a set of highly sparse data in the Fourier domain, the inversion of the Fourier transform from limited data is a challenging numerical issue whose success strongly depends on the samples' number and location. On the other hand, in real applications, the number and locations of such samples are often constrained by the hardware of the instrument. Hence, the project ambition is to develop numerical schemes based on greedy approaches for an optimal choice of these samples. Such a theoretical study finds a natural application in the field of astronomical imaging. Specifically, space telescopes for solar hard X-ray imaging principally aim at observing big explosions on the solar surface (called solar flares) and providing indirect observations (called visibilities) made of sampled Fourier components of the incoming photon flux. Motivated by the growing interests in the construction of more compact and possibly cheaper satellites (for a general overview, refer e.g. to the European Space Agency - ESA website), the scientific community is currently investigating new technologies for solar nano X-ray telescopes, allowing a continuous flare monitoring. The small shape constraint implies that the telescope would return only a few discrete indirect measurements of the observed flaring events. To ensure reliable scientific results, the number and locations of such samples need to be accurately selected. The Greedy Optimal Sampling for Solar Inverse Problems (GOSSIP) project will thus investigate optimal and highly sparse plausible visibility sampling sets, compatible with the implementation in small satellites. To reach this goal, the GOSSIP researchers will take advantage of the so-called greedy numerical algorithms, properly tailored for the Fourier inversion task, and able to return optimal sampling sets. Hence, having in mind this specific application, the scientific products and expected results consist in: 1) Developing a greedy approach taking into account how the uncertainties on the sample locations propagate into the process of regularized inversion and image reconstruction 2) Simulating plausible sampling sets for miniature telescopes that, with a few optimal observed visibilities in the Fourier space, are able to provide informative reconstructions of the sought flaring sources. Due to concrete technological constraints on the telescope devices, the sampling in the Fourier space will not be totally free in practice. Therefore, the validation of the so-constructed flare-driven greedy approach will be carried out by considering both synthetic and experimental visibilities as sampled by the ESA telescope Spectrometer/Telescope for Imaging X-rays (STIX) or as observed by the NASA imaging system Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The GOSSIP project will thus produce a versatile tool that identifies optimal sparse sampling sets for inverse problems following concrete instrument designs.