The latest generation of synthetic aperture radar satellites produce measurements of ground deformation at the majority of the world's subaerial active volcanoes and can be used to detect signs of volcanic unrest. We present an automatic detection algorithm that uses these data to automatically warn when deformation at a volcano departs from the background. We demonstrate our approach on synthetic data sets and the unrest leading to the 2018 eruption of Sierra Negra (Galapagos). Our algorithm encompasses spatial independent component analysis and uses a significantly improved version of the ICASO algorithm, which we term ICASAR, to robustly perform spatial independent component analysis. We use ICASAR to isolate signals of geophysical interest from atmospheric signals, before monitoring the evolution of these signals through time in order to detect the onset of a period of volcanic unrest.