Tomographic reconstruction from incomplete data is required
in many fields, including medical imaging, sonar, and radar. In this paper,
we present a new reconstruction algorithm for limited-angle tomography,
a problem that occurs when projections are missing over a range of angles.
The approach uses a variational formulation that incorporates the Ludwig-
Helgason consistency conditions, measurement noise statistics, and a sinogram
smoothness condition. Optimal restored sinograms, therefore, satisfy
an associated Euler-Lagrange partial differential equation, which we
solve on a lattice using a primal-dual optimization procedure. Object estimates
are then reconstructed using convolution backprojection applied
to the restored sinogram. We present results of simulations that illustrate
the performance of the algorithm and discuss directions for further research.