  (shortened for arXiv) We aim to progress towards more efficient exoplanet
detection around active stars by optimizing the use of Doppler Imaging in
radial velocity measurements. We propose a simple method to simultaneously
extract a brightness map and a set of orbital parameters through a tomographic
inversion technique derived from classical Doppler mapping. Based on the
maximum entropy principle, the underlying idea is to determine the set of
orbital parameters that minimizes the information content of the resulting
Doppler map. We carry out a set of numerical simulations to perform a
preliminary assessment of the robustness of our method, using an actual Doppler
map of the very active star HR 1099 to produce a realistic synthetic data set
for various sets of orbital parameters of a single planet in a circular orbit.
Using a simulated time-series of 50 line profiles affected by a peak-to-peak
activity jitter of 2.5 km/s, we are able in most cases to recover the radial
velocity amplitude, orbital phase and orbital period of an artificial planet
down to a radial velocity semi-amplitude of the order of the radial velocity
scatter due to the photon noise alone (about 50 m/s in our case). One
noticeable exception occurs when the planetary orbit is close to co-rotation,
in which case significant biases are observed in the reconstructed radial
velocity amplitude, while the orbital period and phase remain robustly
recovered. The present method constitutes a very simple way to extract orbital
parameters from heavily distorted line profiles of active stars, when more
classical radial velocity detection methods generally fail. It is easily
adaptable to most existing Doppler Imaging codes, paving the way towards a
systematic search for close-in planets orbiting young, rapidly-rotating stars.
