Penalized least-squares for imaging with hypertelescopes

Practical considerations such as cost constrain the aperture size of conventional telescopes, which, combined with atmospheric turbulence effects, even in the presence of adaptive optics, limit achievable angular resolution. Sparse aperture telescopes represent a viable alternative for achieving improved angular resolution by combining light collected from small apertures distributed over a wide spatial area either using amplitude interferometry or a direct imaging approach to beam-combining. The so-called densified hypertelescope imaging concept in particular provides a methodology for direct image formation from large sparse aperture arrays. The densification system suppresses wide-angle side lobes and concentrates that energy in the center of the focal plane, significantly improving the signal-to-noise ratio of the measurement. Even with densification, an inevitable consequence of sparse aperture sampling is that the point-spread function associated with the direct image contains an additional structure not present in full aperture imaging systems. Postdetection image reconstruction is performed here to compute a high-fidelity estimate of the measured object in the presence of noise. In this paper, we describe a penalized least-squares object-estimation approach and compare the results with the classical Richardson–Lucy deconvolution algorithm as it is applied to hypertelescope image formation. The parameters of the algorithm are selected based on a comprehensive simulation study using the structure similarity metric to assess reconstruction performance. We find that the penalized least-squares formulation with optimized parameters provides significantly improved reconstructions compared with the conventional Richardson–Lucy algorithm