A new framework for sparse regularization in limited angle x-ray tomography

We propose a new framework for limited angle tomographic reconstruction. Our approach is based on the observation that for a given acquisition geometry only a few (visible) structures of the object can be reconstructed reliably using a limited angle data set. By formulating this problem in the curvelet domain, we can characterize those curvelet coefficients which correspond to visible structures in the image domain. The integration of this information into the formulation of the reconstruction problem leads to a considerable dimensionality reduction and yields a speedup of the corresponding reconstruction algorithms.