Journal of X-Ray Science and Technology 24 (2016) 221–240 DOI 10.3233/XST-160547 IOS Press 221 Ordered-subset Split-Bregman algorithm for interior tomography Huihua Kong a,b , Rui Liu b,c,d and Hengyong Yu b,∗ a School of Science, North University of China, Taiyuan, Shanxi, China b Department of Electrical and Computer Engineering, University of Massachusetts Lowell, Lowell, MA, USA c Department of Biomedical Engineering, Wake Forest University Health Sciences, Winston-Salem, NC, USA d Virginia Tech-Wake Forest University School of Biomedical Engineering and Sciences, Winston-Salem, NC, USA Received 19 June 2015 Revised 20 November 2015 Accepted 23 November 2015 Abstract. Inspired by the Compressed Sensing (CS) theory, it has been proved that the interior problem of computed tomography (CT) can be accurately and stably solved if a region-of-interest (ROI) is piecewise constant or polynomial, resulting in the CS-based interior tomography. The key is to minimize the total variation (TV) of the ROI under the constraint of the truncated projections. Coincidentally, the Split-Bregman (SB) method has attracted a major attention to solve the TV minimization problem for CT image reconstruction. In this paper, we apply the SB approach to reconstruct an ROI for the CS-based interior tomography assuming a piecewise constant imaging model. Furthermore, the ordered subsets (OS) technique is used to accelerate the convergence of SB algorithm, leading to a new OS-SB algorithm for interior tomography. The conventional OS simultaneous algebraic reconstruction technique (OS-SART) and soft-threshold filtering (STF) based OS-SART are also implemented as references to evaluate the performance of the proposed OS-SB algorithm for interior tomography. Both numerical simulations and clinical applications are performed and the results confirm the advantages of the proposed OS-SB method. Keywords: Ordered subset Split-Bregman, interior tomography, compressive sensing, total variation minimization, piecewise constant imaging model 1. Introduction In the computed tomography (CT) field, the interior problem refers to reconstruct a region of interest (ROI) only from data associated with x-rays through the ROI. It has a great potential to handle large objects, minimize radiation dose, reduce system cost, enhance temporal resolution and increase scanner throughput, etc. Because the interior problem does not have a unique solution in an unconstrained setting, an internal ROI cannot be accurately reconstructed only from the truncated data based on the conventional CT theory. In 2007, it was proved and demonstrated that the interior problem can ∗ Corresponding author: Hengyong Yu, Department of Electrical and Computer Engineering, University of Massachusetts Lowell, Lowell, MA 01854, USA. Tel.: +1 978 934 6756; Fax: +1 978 934 3027; E-mail: hengyong-yu@ieee.org. 0895-3996/16/$35.00 © 2016 – IOS Press and the authors. All rights reserved