  Assuming linearity of the perturbations at the time of decoupling, we
reconstruct the primordial scalar potential from the temperature and
polarization anisotropies in the cosmic microwave background radiation. In
doing so we derive an optimal linear filter which, when operated on the
spherical harmonic coefficients of the anisotropy maps, returns an estimate of
the primordial scalar potential fluctuations in a spherical slice. The
reconstruction is best in a thick shell around the decoupling epoch; the
quality of the reconstruction depends on the redshift of the slice within this
shell. With high quality maps of the temperature and polarization anisotropies
it will be possible to obtain a reconstruction of potential fluctuation on
scales between l=2 and l ~ 300 at the redshift of decoupling, with some
information about the three-dimensional shapes of the perturbations in a shell
of width 250Mpc.
