  Solar rotational tomography (SRT) applied to white-light coronal images
observed at multiple aspect angles has been the preferred approach for
determining the three-dimensional (3D) electron density structure of the solar
corona. However, it is seriously hampered by the restrictive assumption that
the corona is time-invariant which introduces significant errors in the
reconstruction. We first explore several methods to mitigate the temporal
variation of the corona by decoupling the "fast-varying" inner corona from the
"slow-moving" outer corona using multiple masking (either by juxtaposition or
recursive combination) and radial weighting. Weighting with a radial
exponential profile provides some improvement over a classical reconstruction
but only beyond 3 Rsun. We next consider a full time-dependent tomographic
reconstruction involving spatio-temporal regularization and further introduce a
co-rotating regularization aimed at preventing concentration of reconstructed
density in the plane of the sky. Crucial to testing our procedure and properly
tuning the regularization parameters is the introduction of a time-dependent
MHD model of the corona based on observed magnetograms to build a time-series
of synthetic images of the corona. Our procedure, which successfully reproduces
the time-varying model corona, is finally applied to a set of of 53 LASCO-C2 pB
images roughly evenly spaced in time from 15 to 29 March 2009. Our procedure
paves the way to a time-dependent tomographic reconstruction of the coronal
electron density to the whole set of LASCO-C2 images presently spanning 20
years.
