  An important issue in the tomographic reconstruction of the solar poles is
the relatively rapid evolution of the polar plumes. We demonstrate that it is
possible to take into account this temporal evolution in the reconstruction.
The difficulty of this problem comes from the fact that we want a 4D
reconstruction (three spatial dimensions plus time) while we only have 3D data
(2D images plus time). To overcome this difficulty, we introduce a model that
describes polar plumes as stationary objects whose intensity varies
homogeneously with time. This assumption can be physically justified if one
accepts the stability of the magnetic structure. This model leads to a bilinear
inverse problem. We describe how to extend linear inversion methods to these
kinds of problems. Studies of simulations show the reliability of our method.
Results for SOHO/EIT data show that we are able to estimate the temporal
evolution of polar plumes in order to improve the reconstruction of the solar
poles from only one point of view. We expect further improvements from
STEREO/EUVI data when the two probes will be separated by about 60 degrees.
