Despite major advances in x-ray sources, detector arrays, gantry mechanical design and especially computer performance, one component of computed tomography (CT) scanners has remained virtually constant for the past 25 years-the reconstruction algorithm. Fundamental advances have been made in the solution of inverse problems, especially tomographic reconstruction, but these works have not been translated into clinical and related practice. The reasons are not obvious and seldom discussed. This review seeks to examine the reasons for this discrepancy and provides recommendations on how it can be resolved. We take the example of field of compressive sensing (CS), summarizing this new area of research from the eyes of practical medical physicists and explaining the disconnection between theoretical and application-oriented research. Using a few issues specific to CT, which engineers have addressed in very specific ways, we try to distill the mathematical problem underlying each of these issues with the hope of demonstrating that there are interesting mathematical problems of general importance that can result from in depth analysis of specific issues. We then sketch some unconventional CT-imaging designs that have the potential to impact on CT applications, if the link between applied mathematicians and engineers/physicists were stronger. Finally, we close with some observations on how the link could be strengthened. There is, we believe, an important opportunity to rapidly improve the performance of CT and related tomographic imaging techniques by addressing these issues.

中文翻译：

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为什么商用 CT 扫描仪仍然采用传统的滤波背投影进行图像重建？


尽管 X 射线源、探测器阵列、龙门机械设计，尤其是计算机性能取得了重大进步，但计算机断层扫描 (CT) 扫描仪的一个组件在过去 25 年里几乎保持不变，那就是重建算法。在反问题的解决，特别是断层扫描重建方面已经取得了根本性的进展，但这些工作尚未转化为临床和相关实践。原因并不明显，也很少被讨论。本次审查旨在探讨造成这种差异的原因，并就如何解决这一问题提供建议。我们以压缩传感（CS）领域为例，从实践医学物理学家的角度总结这一新的研究领域，并解释理论研究与应用研究之间的脱节。利用工程师以非常具体的方式解决的一些 CT 特有问题，我们尝试提炼每个问题背后的数学问题，希望证明通过深入分析可以产生一些具有普遍重要性的有趣数学问题的具体问题。然后，我们勾勒出一些非常规 CT 成像设计，如果应用数学家和工程师/物理学家之间的联系更加牢固，这些设计可能会对 CT 应用产生影响。最后，我们以一些关于如何加强这种联系的意见作为结束。我们相信，通过解决这些问题，存在着快速提高 CT 和相关断层扫描成像技术性能的重要机会。