A nonsmooth regularization approach based on shearlets for Poisson noise removal in ROI tomography

Due to its potential to lower exposure to X-ray radiation and reduce the scanning time, region-of-interest (ROI) computed tomography (CT) is particularly appealing for a wide range of biomedical applications. To overcome the severe ill-posedness caused by the truncation of projection measurements, ad hoc strategies are required, since traditional CT reconstruction algorithms result in instability to noise, and may give inaccurate results for small ROI. To handle this difficulty, we propose a nonsmooth convex optimization model based on ℓ1 shearlet regularization, whose solution is addressed by means of the variable metric inexact line search algorithm (VMILA), a proximal-gradient method that enables the inexact computation of the proximal point defining the descent direction. We compare the reconstruction performance of our strategy against a smooth total variation (sTV) approach, by using both Poisson noisy simulated data and real data from fan-beam CT geometry. The results show that, while for synthetic data both shearets and sTV perform well, for real data, the proposed nonsmooth shearlet-based approach outperforms sTV, since the localization and directional properties of shearlets allow to detect finer structures of a textured image. Finally, our approach appears to be insensitive to the ROI size and location.