Title: Directional-TV Algorithm for Image Reconstruction from Limited-Angular-Range Data Show Chinese title

Title: 有限角度范围数据的定向-TV算法图像重建

Abstract: Investigation of image reconstruction from data collected over a limited angular range in X-ray CT remains a topic of active research because it may yield insight into the development of imaging workflow of practical significance. This reconstruction problem is well-known to be challenging, however, because it is highly ill-conditioned. In the work, we investigate optimization-based image reconstruction from data acquired over a limited-angular range that is considerably smaller than the angular range in short-scan CT. We first formulate the reconstruction problem as a convex optimization program with directional total-variation (TV) constraints applied to the image, and then develop an iterative algorithm, referred to as the directional-TV (DTV) algorithm for image reconstruction through solving the optimization program. We use the DTV algorithm to reconstruct images from data collected over a variety of limited-angular ranges for breast and bar phantoms of clinical- and industrial-application relevance. The study demonstrates that the DTV algorithm accurately recovers the phantoms from data generated over a significantly reduced angular range, and that it considerably diminishes artifacts observed otherwise in reconstructions of existing algorithms. We have also obtained empirical conditions on minimal angular ranges sufficient for numerically accurate image reconstruction with the DTV algorithm. Show Chinese abstract

Abstract: 对在X射线CT中从有限角度范围的数据中进行图像重建的研究仍然是活跃的研究课题，因为它可能为实际有重要意义的成像工作流程的发展提供见解。 这种重建问题众所周知是具有挑战性的，然而，因为它是高度病态的。 在本工作中，我们研究了从获取的有限角度范围数据中进行基于优化的图像重建，该角度范围远小于短扫描CT中的角度范围。我们首先将重建问题公式化为一个带有方向总变分（TV）约束的凸优化程序，并开发了一种迭代算法，称为方向-TV（DTV）算法，通过求解优化程序来进行图像重建。 我们使用DTV算法从各种有限角度范围的数据中重建临床和工业应用相关的乳腺和棒体幻影的图像。 该研究表明，DTV算法能够准确地从显著减少的角度范围内生成的数据中恢复幻影，并且能够大大减少现有算法重建中观察到的伪影。 我们还获得了使用DTV算法进行数值准确图像重建的最小角度范围的经验条件。