Basic Research for the Development of Helical Cone-Beam CT

锥束螺旋CT（基于锥束x射线曝光和螺旋扫描的结合）作为未来的快速三维CT越来越受到关注。但是，现阶段对其扫描仪设计和图像重建的基础研究还不够。本研究项目的目的是探讨以下三点，这是发展螺旋锥束CT扫描仪的重要。首先，我们提出了一种基于高效排列探测器元件的高效扫描仪设计方法。这使我们能够以大（最大）螺旋螺距扫描患者，即使在检测器元素数量有限的情况下。接下来，我们开发了以下两种图像重建方法。第一种是用于商用螺旋锥束CT扫描仪。其中包括一种基于3-D氡反演的精确算法和一种基于将锥形波束数据重新划分为扇形波束数据的近似（但非常快）算法。第二类用于血管造影和微ct系统。该算法是一种基于非线性规划对偶性的代数算法。在。在这些算法的发展过程中，我们也获得了关于CT图像重建基础数学的两个重要见解。这包括一种超短扫描图像重建和一种新的精确锥形光束重建方法。最后，作为对实际数据的应用，我们将所开发的代数重构算法应用于Marquette大学的micro-CT系统。结果表明，利用所开发的算法，仅用8个投影就可以重建高质量的大鼠肺（局限在一个边长为2cm的立方体内）的三维图像。

Cone-beam helical CT (based on combining the cone-beam x-ray exposure and the helical scanning) is receiving increased attention as a future fast 3-D CT. However, enough basic researches are not performed in the current stage about its scanner design and image reconstruction. The aim of this research project is to investigate the following three points which are important to develop helical cone-beam CT scanners. First, we developed an efficient scanner design method which is based on arranging detector elements very efficiently. This allows us to scan the patient with a large (maximum) helical pitch even in the case where the number of detector elements are limited. Next, we developed the following two types of image reconstruction methods. The first type aims at using in commercial helical cone-beam CT scanners. These include an exact algorithm based on the 3-D Radon inversion and an approximate (but very fast) algorithm based on rebinning cone-beam data into fan-beam data. The second type aims at using in angiography and micro-CT systems. The algorithm is an algebraic one which is based on the duality of non-linear programming. During the. development of these algorithms, we also obtained two important insights about basic mathematics of CT image reconstruction. These include a super-short-scan image reconstruction and a new exact cone-beam reconstruction method for general source trajectory. Finally, as an application to real data, we applied the developed algebraic reconstruction algorithm to the micro-CT system at Marquette university. The result demonstrates that it is possible to reconstruct a high-quality 3-D image of a rat lung (confined within a cube of side 2cm) from only 8 projections with the developed algorithm.