锥束CT直接三维成像算法研究
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摘要
CT(Computed Tomography X射线计算机断层摄影术)自1972年问世以来得到了越来越广泛的应用。CT的广泛应用反过来又推动了对它的研究,使它得到进一步的发展,在30年的发展过程中,它基本上经历了6次大的变革。CT的这些发展变化主要体现在两个方面,一是提高扫描速度,二是改善图像的质量。
CT的断层图像是由计算机对物体的投影数据进行计算而获得的,因此CT的成像过程可以分为两大步,一是用X光系统进行投影数据的测量,获得充分的投影数据;二是用计算机对投影数据进行计算来获得断层图像。X光的投影测量结构可以分为三种,分别为平行束投影、扇束投影和锥束投影。平行束投影在工程上是不能直接实现的。和扇束投影相比,锥束投影一次性获得的信息量更大,因此锥束投影结构有利于提高扫描速度和图像质量。但是锥束投影数据和断层图像之间的关系很复杂,这会使计算的复杂度大大增加。近十年来,出现了很多针对锥束CT的研究,但基本上都不是很成熟,到目前为止还没有出现真正意义上的商业化锥束CT。针对锥束CT目前存在的主要问题,本文的主要研究內容有四点:
(一)结合锥束扫描的特点提出了一种中间函数重建算法。中间函数重建算法是一种基于傅立叶空间的精确解析算法,同时它也是一种反投影算法。它的基本算法思想是先对探测器采集到的数据进行傅立叶变换,得到一个中间函数;接下来是对中间函数的形式进行变换,找到它和图像函数傅立叶变换之间的关系,因此可以通过对这个变形的中间函数进行反投影而重建出图像。本文也利用实验对算法进行了验证。
(二)研究了锥束扫描时的直接三维重建技术。三维图像在医学领域得到越来越重要的应用,它可以帮助医生准确地进行病灶定位和确定手术方案。传统的CT三维图像是通过对二维断层图像进行后处理而获得的,主要是通过插值计算的方法来获得三维空间点。由于传统CT在z轴方向采集的间隔比较大,因而Z轴的分辨率比较低,再加上慢速扫描带来的z轴运动伪影,这样就使重建出的三维图像质量也比较差。直接三维重建是利用锥束投影时获得的大量数据,直接进行三维空间点的计算,然后再使用三维绘制技术来获得三维图像。由于
Since the birth of the first CT (computed tomography) scanner in 1972, CT has been widely used in the world. The wide uses of CT also generate great impetus for CT research. Several big changes have taken placed during the past 30 years. These changes mainly involve in two aspects- speed and image quality.The CT image is calculated from projection data by computer. So there are two steps to get image—using X-ray to measure projection data and calculating projection data to get image. There are three kinds of X-ray measure structures, parallel-beam, fan-beam and cone-beam. But the parallel-beam can not be realized directly in engineering. Compared with fan-beam, cone-beam projection system can gain more information in one projection, so it is of advantage to increasing scanning speed and image quality. But the relationship between cone-beam projection data and the cross section image is very complex. Accordingly the reconstruction algorithm and scan frame becomes more complex. In recent years, many scholars have researched the cone-beam scan technology, but the algorithms they developed are not very perfect, so the real commercial cone-beam CT is not appeared today. In order to solve the problem in cone-beam CT, Four main questions of cone-beam CT have been researched in this thesis.1. An intermediate function algorithm, which can be used in cone-beam CT, have been researched. It is a kind of exact resolution algorithm which is based on Fourier space, and at same time it is a kind of back-projection algorithm. The algorithm can be decomposed into three steps. Firstly, a partial Fourier transform is applied to the projection data and an intermediate function is got. Secondly, the same changes to the intermediate function are made and a form of inverse Fourier transform of object function is got. Finally, the image can be reconstructed by making back-projection to the new form of intermediate function. To verify the algorithm, some experiments have been done and the results are satisfied.2. Direct 3-D reconstruction technology has been researched. The using of 3-D image becomes more and more important in medical field. It can help doctor to find
an exact place of focus and to make plan for operation. Three-dimension image of traditional CT is made from 2-D image by late processing. The main method of processing is an interpolating calculation. Because of no enough sampling in z axes, the image space resolution of traditional CT is low. Traditional CT also has motive artifact which is resulted from low scan speed. These restrictions make the quality of 3-D image of traditional CT not satisfied. Direct 3-D reconstruction is done by using a lot of cone-beam projection data. A 3-D image can be got by directly calculating the value of 3-D space points. The 3-D points which are gained by direct reconstruction have same resolution in three directions, so the 3-D image which is based on these points has a same nature in all direction.3. By Researching data sufficient condition of VOI reconstruction, a new scan framework is designed to adapt the algorithm. The new framework is named double cone-beam three axes scan. The idea of three axes scan is an extending of spiral scan. The sample density in z direction will decrease when the pitch increases in fast scan. Double cone-beam framework, which can increase the sample density in z direction, uses two different focuses to produce two cone-beams in different place. Two focuses turn on alternation to avoid overlap of projection data. To fulfill this work mode, a kind of double anode tube is put forward in this paper.4. A new scan method which can be used in heart scan is designed. The scan structure is a double cone-beam three axes scan. General CT can not get heart's stationary image, because the heart is a fast moving organ. Three-dimension image of heart can be got directly by combining double cone-beam three axes scan technology and direct 3-D reconstruction algorithm.In this thesis, some other cone-beam scan reconstruction algorithms are also analyzed. These algorithms can be sorted by exactness, the length of object and scan mode. Every algorithm has its' virtue and limitation. Algorithms which are discussed in this paper are FDK, Grangeat, PI and PHI etc.
CT的断层图像是由计算机对物体的投影数据进行计算而获得的,因此CT的成像过程可以分为两大步,一是用X光系统进行投影数据的测量,获得充分的投影数据;二是用计算机对投影数据进行计算来获得断层图像。X光的投影测量结构可以分为三种,分别为平行束投影、扇束投影和锥束投影。平行束投影在工程上是不能直接实现的。和扇束投影相比,锥束投影一次性获得的信息量更大,因此锥束投影结构有利于提高扫描速度和图像质量。但是锥束投影数据和断层图像之间的关系很复杂,这会使计算的复杂度大大增加。近十年来,出现了很多针对锥束CT的研究,但基本上都不是很成熟,到目前为止还没有出现真正意义上的商业化锥束CT。针对锥束CT目前存在的主要问题,本文的主要研究內容有四点:
(一)结合锥束扫描的特点提出了一种中间函数重建算法。中间函数重建算法是一种基于傅立叶空间的精确解析算法,同时它也是一种反投影算法。它的基本算法思想是先对探测器采集到的数据进行傅立叶变换,得到一个中间函数;接下来是对中间函数的形式进行变换,找到它和图像函数傅立叶变换之间的关系,因此可以通过对这个变形的中间函数进行反投影而重建出图像。本文也利用实验对算法进行了验证。
(二)研究了锥束扫描时的直接三维重建技术。三维图像在医学领域得到越来越重要的应用,它可以帮助医生准确地进行病灶定位和确定手术方案。传统的CT三维图像是通过对二维断层图像进行后处理而获得的,主要是通过插值计算的方法来获得三维空间点。由于传统CT在z轴方向采集的间隔比较大,因而Z轴的分辨率比较低,再加上慢速扫描带来的z轴运动伪影,这样就使重建出的三维图像质量也比较差。直接三维重建是利用锥束投影时获得的大量数据,直接进行三维空间点的计算,然后再使用三维绘制技术来获得三维图像。由于
Since the birth of the first CT (computed tomography) scanner in 1972, CT has been widely used in the world. The wide uses of CT also generate great impetus for CT research. Several big changes have taken placed during the past 30 years. These changes mainly involve in two aspects- speed and image quality.The CT image is calculated from projection data by computer. So there are two steps to get image—using X-ray to measure projection data and calculating projection data to get image. There are three kinds of X-ray measure structures, parallel-beam, fan-beam and cone-beam. But the parallel-beam can not be realized directly in engineering. Compared with fan-beam, cone-beam projection system can gain more information in one projection, so it is of advantage to increasing scanning speed and image quality. But the relationship between cone-beam projection data and the cross section image is very complex. Accordingly the reconstruction algorithm and scan frame becomes more complex. In recent years, many scholars have researched the cone-beam scan technology, but the algorithms they developed are not very perfect, so the real commercial cone-beam CT is not appeared today. In order to solve the problem in cone-beam CT, Four main questions of cone-beam CT have been researched in this thesis.1. An intermediate function algorithm, which can be used in cone-beam CT, have been researched. It is a kind of exact resolution algorithm which is based on Fourier space, and at same time it is a kind of back-projection algorithm. The algorithm can be decomposed into three steps. Firstly, a partial Fourier transform is applied to the projection data and an intermediate function is got. Secondly, the same changes to the intermediate function are made and a form of inverse Fourier transform of object function is got. Finally, the image can be reconstructed by making back-projection to the new form of intermediate function. To verify the algorithm, some experiments have been done and the results are satisfied.2. Direct 3-D reconstruction technology has been researched. The using of 3-D image becomes more and more important in medical field. It can help doctor to find
an exact place of focus and to make plan for operation. Three-dimension image of traditional CT is made from 2-D image by late processing. The main method of processing is an interpolating calculation. Because of no enough sampling in z axes, the image space resolution of traditional CT is low. Traditional CT also has motive artifact which is resulted from low scan speed. These restrictions make the quality of 3-D image of traditional CT not satisfied. Direct 3-D reconstruction is done by using a lot of cone-beam projection data. A 3-D image can be got by directly calculating the value of 3-D space points. The 3-D points which are gained by direct reconstruction have same resolution in three directions, so the 3-D image which is based on these points has a same nature in all direction.3. By Researching data sufficient condition of VOI reconstruction, a new scan framework is designed to adapt the algorithm. The new framework is named double cone-beam three axes scan. The idea of three axes scan is an extending of spiral scan. The sample density in z direction will decrease when the pitch increases in fast scan. Double cone-beam framework, which can increase the sample density in z direction, uses two different focuses to produce two cone-beams in different place. Two focuses turn on alternation to avoid overlap of projection data. To fulfill this work mode, a kind of double anode tube is put forward in this paper.4. A new scan method which can be used in heart scan is designed. The scan structure is a double cone-beam three axes scan. General CT can not get heart's stationary image, because the heart is a fast moving organ. Three-dimension image of heart can be got directly by combining double cone-beam three axes scan technology and direct 3-D reconstruction algorithm.In this thesis, some other cone-beam scan reconstruction algorithms are also analyzed. These algorithms can be sorted by exactness, the length of object and scan mode. Every algorithm has its' virtue and limitation. Algorithms which are discussed in this paper are FDK, Grangeat, PI and PHI etc.
引文
[1] http://www.medical.siemens.corn/webapp
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