  Throughout the last decades, Zeeman-Doppler Imaging (ZDI) has been
intensively used to reconstruct large-scale magnetic topologies of active stars
from time series of circularly polarized (Stokes $V$) profiles. ZDI being based
on the assumption that the topology to be reconstructed is constant with time
(apart from being sheared by differential rotation), it fails at describing
stellar magnetic fields that evolve on timescales similar to the observing
period. We present a new approach, called TIMeS (for Time-dependent Imaging of
Magnetic Stars), to derive the time-dependent large-scale magnetic topologies
of active stars, from time series of high-resolution Stokes $V$ spectra. This
new method uses the combined concepts of sparse approximation and Gaussian
process regression to derive the simplest time-dependent magnetic topology
consistent with the data. Assuming a linear relation between the Stokes $V$
data and the reconstructed magnetic image, TIMeS is currently applicable to
cases in which the magnetic field is not too strong (with an upper limit
depending on $v\sin{i}$). We applied TIMeS to several simulated data sets to
investigate its ability to retrieve the poloidal and toroidal components of
large-scale magnetic topologies. We find that the proposed method works best in
conditions similar to those needed for ZDI, reconstructing reliable topologies
with minor discrepancies at very low latitudes whose contribution to the data
is small. We however note that TIMeS can fail at reconstructing the input
topology when the field evolves on a timescale much shorter than the stellar
rotation cycle
