The sky at MeV energies is currently poorly explored. Here we present an innovative mission concept that builds upon the heritage of past and current missions improving the sensitivity and, very importantly, the angular resolution. This consists in combining a Compton telescope and a coded-mask telescope. We delineate the motivation for such a concept and we define the scientific goals for such a mission. The Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO) is a novel concept for a next-generation telescope covering hard X-ray and soft gamma-ray energies. The potential and importance of this approach that bridges the observational gap in the MeV energy range are presented. With the unprecedented angular resolution of the coded mask telescope combined with the sensitive Compton telescope, a mission such as GECCO can disentangle the discrete sources from the truly diffuse emission. Individual Galactic and extragalactic sources are detected. This also allows to understand the gamma-ray Galactic center excess and the Fermi Bubbles, and to trace the low-energy cosmic rays, and their propagation in the Galaxy. Nuclear and annihilation lines are spatially and spectrally resolved from the continuum emission and from sources, addressing the role of low-energy cosmic rays in star formation and galaxy evolution, the origin of the 511 keV positron line, fundamental physics, and the chemical enrichment in the Galaxy. Such an instrument also detects explosive transient gamma-ray sources, which, in turn, enables identifying and studying the astrophysical objects that produce gravitational waves and neutrinos in a multi-messenger context. By looking at a poorly explored energy band it also allows discoveries of new astrophysical phenomena.

Bayesian imaging algorithms are becoming increasingly important in, e.g., astronomy, medicine and biology. Given that many of these algorithms compute iterative solutions to high-dimensional inverse problems, the efficiency and accuracy of the instrument response representation are of high importance for the imaging process. For efficiency reasons, point spread functions, which make up a large fraction of the response functions of telescopes and microscopes, are usually assumed to be spatially invariant in a given field of view and can thus be represented by a convolution. For many instruments, this assumption does not hold and degrades the accuracy of the instrument representation. Here, we discuss the application of butterfly transforms, which are linear neural network structures whose sizes scale sub-quadratically with the number of data points. Butterfly transforms are efficient by design, since they are inspired by the structure of the Cooley–Tukey fast Fourier transform. In this work, we combine them in several ways into butterfly networks, compare the different architectures with respect to their performance and identify a representation that is suitable for the efficient representation of a synthetic spatially variant point spread function up to a 1% error. Furthermore, we show its application in a short synthetic example.

Results from different methods searching for Quasi periodic oscillations (QPOs) in blazars will be shown, indicating no significant evidence for periodic signals beyond the noise level. Blazars are a subclass of active galactic nuclei (AGN), and are highly variable objects. QPOs, which might originate from a binary black hole located at the AGN core, have been found in some blazar light curves. For the blazars Mrk 421 and Mrk 501, we test the possible QPO behaviour using a variety of methods (generalized Lomb-Scargle Periodogram, CARMA, Wavepal and A-T plane), studying in detail systematic effects. We use gamma-ray light curves from FACT, a ground-based imaging air Cherenkov telescope and Fermi-LAT, a gamma-ray satellite. Furthermore, we explore the possibility to search for periodicities with the information field theory.