  Compressive sensing is considered a huge breakthrough in signal acquisition.
It allows recording an image consisting of $N^2$ pixels using much fewer than
$N^2$ measurements if it can be transformed to a basis where most pixels take
on negligibly small values. Standard compressive sensing techniques suffer from
the computational overhead needed to reconstruct an image with typical
computation times between hours and days and are thus not optimal for
applications in physics and spectroscopy. We demonstrate an adaptive
compressive sampling technique that performs measurements directly in a sparse
basis. It needs much fewer than $N^2$ measurements without any computational
overhead, so the result is available instantly.
