  In geophysics, volcanoes are particularly difficult to image because of the
multi-scale heterogeneities of fluids and rocks that compose them and their
complex non-linear dynamics. By exploiting seismic noise recorded by a sparse
array of geophones, we are able to reveal the magmatic and hydrothermal
plumbing system of La Soufri\`ere volcano in Guadeloupe. Spatio-temporal
cross-correlation of seismic noise actually provides the impulse responses
between virtual geophones located inside the volcano. The resulting reflection
matrix can be exploited to numerically perform an auto-focus of seismic waves
on any reflector of the underground. An unprecedented view on the volcano's
inner structure is obtained at a half-wavelength resolution. This innovative
observable provides fundamental information for the conceptual modeling and
high-resolution monitoring of volcanoes.
