The ROI CT problem: a shearlet-based regularization approach

The possibility to significantly reduce the X-ray radiation dose and shorten the scanning time is particularly appealing, especially for the medical imaging community. Region- of-interest Computed Tomography (ROI CT) has this potential and, for this reason, is currently receiving increasing attention. Due to the truncation of projection images, ROI CT is a rather challenging problem. Indeed, the ROI reconstruction problem is severely ill-posed in general and naive local reconstruction algorithms tend to be very unstable. To obtain a stable and reliable reconstruction, under suitable noise circumstances, we formulate the ROI CT problem as a convex optimization problem with a regularization term based on shearlets, and possibly nonsmooth. For the solution, we propose and analyze an iterative approach based on the variable metric inexact line-search algorithm (VMILA). The reconstruction performance of VMILA is compared against different regularization conditions, in the case of fan-beam CT simulated data. The numerical tests show that our approach is insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.