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When it comes to computed tomography (CT), the possibility to reconstruct asmall region-of-interest (ROI) using truncated projection data is particularlyappealing due to its potential to lower radiation exposure and reduce thescanning time. However, ROI reconstruction from truncated projections is anill-posed inverse problem, with the ill-posedness becoming more severe when theROI size is getting smaller. To address this problem, both ad hoc analyticformulas 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 onshearlets. Our numerical implementation consists of an iterative scheme basedon the scaled gradient projection (SGP) method and is tested in the context offan beam CT. Our results show that this approach is essentially insensitive tothe location of the ROI and remains very stable also when the ROI size israther small.

Numerical assessment of shearlet-based regularization in ROI tomography