  We study the scenery reconstruction problem on the $d$-dimensional torus,
proving that a criterion on Fourier coefficients obtained by Matzinger and
Lember (2006) for discrete cycles applies also in continuous spaces. In
particular, with the right drift, Brownian motion can be used to reconstruct
any scenery. To this end, we prove an injectivity property of an infinite
Vandermonde matrix.
