Pan Xiaochuan, Sidky Emil Y, Vannier Michael
Department of Radiology MC-2026, The University of Chicago, 5841 S. Maryland Avenue, Chicago, IL 60637, USA.
Inverse Probl. 2009 Jan 1;25(12):1230009. doi: 10.1088/0266-5611/25/12/123009.
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.
尽管在X射线源、探测器阵列、机架机械设计尤其是计算机性能方面取得了重大进展，但在过去25年里，计算机断层扫描（CT）扫描仪的一个组件几乎没有变化——重建算法。在逆问题的解决方面，特别是断层重建方面取得了根本性进展，但这些成果尚未转化为临床及相关实践。原因并不明显，也很少被讨论。本综述旨在探讨这种差异的原因，并就如何解决该问题提出建议。我们以压缩感知（CS）领域为例，从实际医学物理学家的角度总结这一新兴研究领域，并解释理论研究与应用导向研究之间的脱节。利用工程师以非常具体的方式解决的一些CT特定问题，我们试图提炼出每个问题背后的数学问题，希望证明对特定问题的深入分析可能会产生具有普遍重要性的有趣数学问题。然后，我们概述了一些非常规的CT成像设计，如果应用数学家与工程师/物理学家之间的联系更加紧密，这些设计有可能对CT应用产生影响。最后，我们就如何加强这种联系发表了一些看法。我们认为，通过解决这些问题，有一个迅速提高CT及相关断层成像技术性能的重要机会。
