Top: image of the ring with the star represented in red (model), the (u,v)-plan used in the simulation, and the simulated dataset. Bottom: image reconstructions with the four cases discussed in Sect. 3.2 : 1) classical gray image reconstruction; 2) and d_env = d_star; 3) and d_star = − 4 and d_env = 1 with MiRA/SPARCO; 4) idem with MACIM/SPARCO.