Shearlet-based regularized reconstruction in region-of-interest computed tomography

¹ Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2B, Helsinki 00014, Finland
² Department of Mathematics, University of Houston, 651 Phillip G. Hoffman, Houston, TX 77204-3008, USA
³ Deptartment of Mathematics and Computer Science, University of Ferrara, and INdAM-GNCS, via G. Saragat 1, Ferrara 44122, Italy
⁴ Department of Physics, Computer Science and Mathematics, University of Modena and Reggio Emilia, and INdAM-GNCS, via G. Campi 213/B, Modena 41125, Italy

^* Corresponding author: tatiana.bubba@helsinki.fi

Received: 30 November 2017
Accepted: 17 January 2018

Abstract

Region of interest (ROI) tomography has gained increasing attention in recent years due to its potential to reducing radiation exposure and shortening the scanning time. However, tomographic reconstruction from ROI-focused illumination involves truncated projection data and typically results in higher numerical instability even when the reconstruction problem has unique solution. 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 tomographic 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 method and it is tested in the context of fan-beam CT. Our results show that our approach is essentially insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.