  We investigate the reconstruction problem of limited angle tomography. Such
problems arise naturally in applications like digital breast tomosynthesis,
dental tomography, electron microscopy etc. Since the acquired tomographic data
is highly incomplete, the reconstruction problem is severely ill-posed and the
traditional reconstruction methods, such as filtered backprojection (FBP), do
not perform well in such situations. To stabilize the reconstruction procedure
additional prior knowledge about the unknown object has to be integrated into
the reconstruction process. In this work, we propose the use of the sparse
regularization technique in combination with curvelets. We argue that this
technique gives rise to an edge-preserving reconstruction. Moreover, we show
that the dimension of the problem can be significantly reduced in the curvelet
domain. To this end, we give a characterization of the kernel of limited angle
Radon transform in terms of curvelets and derive a characterization of
solutions obtained through curvelet sparse regularization. In numerical
experiments, we will present the practical relevance of these results.
