  We present a novel approach for analysing radial velocity data that combines
two features: all the planets are searched at once and the algorithm is fast.
This is achieved by utilizing compressed sensing techniques, which are modified
to be compatible with the Gaussian processes framework. The resulting tool can
be used like a Lomb-Scargle periodogram and has the same aspect but with much
fewer peaks due to aliasing. The method is applied to five systems with
published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a
simulated very active star. The results are fully compatible with previous
analysis, though obtained more straightforwardly. We further show that 55 Cnc e
and f could have been respectively detected and suspected in early measurements
from the Lick observatory and Hobby-Eberly Telescope available in 2004, and
that frequencies due to dynamical interactions in GJ 876 can be seen.
