  When it comes to computed tomography (CT), the possibility to reconstruct a
small region-of-interest (ROI) using truncated projection data is particularly
appealing due to its potential to lower radiation exposure and reduce the
scanning time. However, ROI reconstruction from truncated projections is an
ill-posed inverse problem, with the ill-posedness becoming more severe when the
ROI size is getting smaller. To address this problem, both ad hoc analytic
formulas and iterative numerical schemes have been proposed in the literature.
In this paper, we introduce a novel approach for ROI CT reconstruction,
formulated as a convex optimization problem with a regularized term based on
shearlets. Our numerical implementation consists of an iterative scheme based
on the scaled gradient projection (SGP) method and is tested in the context of
fan beam CT. Our results show that this approach is essentially insensitive to
the location of the ROI and remains very stable also when the ROI size is
rather small.
