How do you photograph something that doesn't let light escape?

Quanta talked to Shep Doeleman about the Event Horizon Telescope: you don't image the black hole, you image the glowing gas around its shadow, using radio dishes spread across the planet as one Earth-sized telescope. The next goal is apparently a movie, not just a still. What I still don't fully get: how much of the final image is measurement and how much is the reconstruction algorithm filling gaps? Anyone here worked with interferometry data?