Tetrahedron beam computed tomography (TBCT) performs volumetric imaging using a stack of fan beams generated by a multiple pixel X-ray source. While the TBCT system was designed to overcome the scatter and detector issues faced by cone beam computed tomography (CBCT), it still suffers the same large cone angle artifacts as CBCT due to the use of approximate reconstruction algorithms. It has been shown that iterative reconstruction algorithms are better able to model irregular system geometries and that algebraic iterative algorithms in particular have been able to reduce cone artifacts appearing at large cone angles. In this paper, the SART algorithm is modified for the use with the different TBCT geometries and is tested using both simulated projection data and data acquired using the TBCT benchtop system. The modified SART reconstruction algorithms were able to mitigate the effects of using data generated at large cone angles and were also able to reconstruct CT images without the introduction of artifacts due to either the longitudinal or transverse truncation in the data sets. Algebraic iterative reconstruction can be especially useful for dual-source dual-detector TBCT, wherein the cone angle is the largest in the center of the field of view. 1. Introduction Image-guided radiation therapy (IGRT) is essential to ensure proper dose delivery to the target while sparing the surrounding tissue [1, 2]. Cone beam CT (CBCT) is a popular online imaging modality used for LINAC-based IGRT [3, 4]. Although CBCT is convenient to use, the performance of CBCT systems is less than ideal. The image quality for the CBCT is significantly degraded due to excessive scattered photons [5–8] as well as suboptimal performance of the flat panel detector [9]. These issues limit the use of CBCT for certain advanced radiation therapy techniques such as online adaptive radiotherapy [8, 10]. It is also well known that at large cone angles, there are artifacts caused by using approximate reconstruction methods that appear in CBCT reconstructions [11], but this issue has largely been ignored in IGRT because the scatter and detector issues are the dominant factors in the degradation of CBCT image quality. Tetrahedron beam computed tomography (TBCT) is a novel volumetric CT modality that overcomes the scatter and detector problems of CBCT [12, 13]. A TBCT system is composed of a minimum of one linear source array with one linear detector array positioned opposite and orthogonal to it. In TBCT, scattered photons are largely rejected due to the fan-beam geometry of the system. A TBCT
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