锥束扇束CT优质重建算法研究
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摘要
计算机体层成像(Computerized tomography,CT)使得层面成像第一次得到了广泛的应用,而且取得了突破性的发展。自上世纪七十年代第一台商用CT扫描机面世以来,CT成像技术已经经历了三十多年的长足发展,现在CT已经成为放射诊断领域内不可缺少的一部分,是一种成熟的、在临床上普遍认可的检查方法。目前CT正处于快速的技术发展阶段,并再次扩展了它的应用领域,如心脏、肺的动态检查及CT血管造影。螺旋CT的发展以及从单层扫描向快速扫描的转变使得CT再次富有吸引力,并使得CT在技术和临床前景方面有决定性的发展。
八十年代FDK算法的提出,实现了三维意义上的CT重建。鉴于FDK算法可以基本解决小、中锥角效应对图像重建的影响,一直是实际应用的主流算法。但随着面积探测器技术的发展以及现代医疗对成像速度和精度要求的进一步提升,将会使基于该技术和要求的快速精确三维锥束CT重建算法代表了当前许多研发部门正在研究和开发的关键性课题。
现代医疗技术为了减少X射线对正常器官的辐射,希望以最少的X射线剂量获取最好的图像重建质量,一方面可以通过感兴趣区域重建,即尽量能对病灶区域集中成像;另一方面可以通过研究低剂量条件下重建图像中存在的噪声和诊断结果之间的关系,设计优良的CT成像算法。前者的实现要求射束的视场应该尽量小,能罩住感兴趣区同时要求扫描的轨道应该尽可能短;后者要求根据图像噪声与诊断结果之间的统计关系建立合适的数学模型。上述两方面均是日前临床上CT应用中急需解决的问题。
在影像诊断中高密度的物体,如金属植入物、外科固定器以及口腔填充物等,往往会在CT成像时造成严重的金属伪影,以致严重影响临床诊断效果。因此,高效准确的CT图像金属伪影消除算法的研究始终是CT应用研究的热点问题,在临床上将直接有助于指导放射治疗计划的制定。
因此,为了解决上述的系列问题,我们需要真正意义上的三维重建算法,能够快速精确地获取优质的重建图像;需要针对感兴趣区精确成像的重建算法和低剂量条件下的重建算法,以期在最小的剂量下获取最好的图像重建质量;我们还需要高效准确的CT图像金属伪影消除算法,辅助临床诊断。
本论文的主要创新点集中表现如下:
●提出一种新的基于混合滤波的螺旋锥束CT优质精确重建算法。新算法采用Katsevich算法框架,巧妙地将现有FDK类型算法和Katsevich算法的不同优点有机地融合,完全回避投影数据中关于探测器坐标变量的直接微分运算,提高了成像质量,减少了重建伪影。同时新算法的滤波过程仍是平移不变滤波且与FDK类型重建算法相比数据冗余加权是在滤波过程之后进行,增强了数值计算的灵活性且没额外增加计算复杂度。
●提出一种新的螺旋锥束CT精确重建公式。新重建公式利用数学上严格的推导,将Katseivch重建公式中关于旋转角度的微分运算完全回避,使得成像质量得到较大改善,减少了重建伪影。同时新算法仍然基于平移不变滤波且数据冗余加权在滤波过程之后进行,保持了数值计算的灵活性。
●提出一种新的基于PI线的扇形束CT超短扫描优质重建算法,新算法仍采用经典的FBP重建算法框架,当且仅当满足通过感兴趣区域的任一直线均与扫描轨道相交时,就可以有效地进行该区域的精确重建。新重建公式中回避了投影数据的求导运算,将加权Hilbert滤波转化为Hilbert滤波与Ramp滤波的组合形式。由于实际重建过程中要对离散数据进行处理,新算法中导数的回避将增加数值计算稳定性,提高重建图像质量。
●提出一种新的基于广义Gibbs先验的低剂量CT重建算法。新算法首先对投影数据进行统计建模,其后采用Bayesian最大后验估计方法,将投影数据中非局部的先验信息加诸于该数据的恢复中,达到抑制噪声的效果,最后仍采用经典的滤波反投影方法对恢复后的投影数据进行解析CT重建。其中非局部先验我们称之为广义Gibbs先验,其原因在于该先验具有传统Gibbs先验形式的同时,可以通过选择较大邻域和自适应的加权方式充分利用投影数据的全局信息进行数据恢复。
●建立一种新的针对由金属伪影造成的CT图像质量退化的恢复算法。利用自适应各向异性高斯滤波器对原始CT图像进行全局滤波,从而有效地滤除原始图像中的噪声并对射线状金属伪影进行了平滑,其后配合最大互信息量分割算法从图像中分割出伪影成份,并利用其周围非伪影部分的像素对伪影类像素进行插值处理得到一个称之为“伪组织”类的图像,通过融合“伪组织”图像的sinogram和原始CT图像的sinogram得到校正的sinogram;最后采用滤波反投影重建算法获得金属伪影的CT校正图像。新方法可以对含有金属伪影的CT图像进行有效伪影消除,其中射线状伪影消除效果显著。另外,新方法还可以锐化器官轮廓,避免了临床上由于金属伪影导致的放射治疗效果下降。
X-ray computed tomography (CT) has experienced tremendous growth in recently 30 years and has achieved substantial enhancement both in efficiency and precise. Since the introduction of helical and multi-slice CT, many new clinical applications have been developed. CT is again becoming one of the most exciting modalities in the medical imaging field.
In 1980, a novel 3-D reconstruction method was proposed, which plays a critically important role in the history of CT imaging although that was an approximate method. Because FDK is satisfied with small cone angular high quality imaging, it is the main stream algorithm for commercial applications. But with the development of multi-row detector and the improvement of imaging speed and precise in modern clinical application, fast and precise 3-D cone beam CT reconstruction method study presents the highlight project for many research departments.
Modern clinical techniques require as less as possible radiation towards normal tissues surrounding the diseased region, which would reduce unnecessary harm to the healthy organs. At the same time, we expect to get better reconstructed images with low dose radiation. Therefore, one side we can use a special region of interest, such as only diseased region imaging, which required to accommodate incomplete projection data with serious truncation. Other side we can conduct to understand the relationship between the noise present in the image and the outcome of diagnosis, which supervise the novel low dose CT reconstruction.
More considerably, high-density objects, such as metallic implants, surgical clips and dental fillings, often cause severe artifacts on computed tomography scans, and many render images non-diagnostic. This problem is due to the fact that satisfactory images cannot be calculated from projections if data are missing or distorted. So, metal artifacts reduction is also the highlight for the CT application research, which is helpful for the radiotherapy process.
The main contributions in this PhD dissertation are as following,
We present an alternative approach to reconstructing exactly an image from helical cone-beam projections, which is the combination of Hilbert filter and Ramp filter. Based on the Katsevich reconstructed algorithm framework, the proposed algorithm takes the different advantages of the FDK-type algorithms and Katsevich algorithm, which completely avoids the direct derivatives with respect to the coordinates on the detector plane. This alternative expression has a significant practical implication, thus leading to the images with quality improvement and reduced artefacts. At the same time, although the filtering process of the proposed algorithm is composed of Hilbert and Ramp filters, in contrast the FDK-type reconstructed algorithm, however, the new still performs a 1D shift-invariant filtering of the modified data on the detector plane and the redundancy weight is applied after filtering, allowing a more efficient numerical implementation. The complexity of the new algorithm compared with Katsevich algorithm does not extra increase.
We present a new FBP image reconstruction algorithm based on the Katsevich's original algorithm paradigm. This proposed algorithm successfully avoids the direct derivatives with respect to rotation angle, which achieves good image quality improvement and fewer artifacts. The new algorithm still performs a 1D shift-invariant filtering of the modified data on the detector plane and the redundancy weight is applied after filtering, allowing a more efficient numerical implementation. Results in these studies confirm the observation that the proposed algorithm can improve the image resolution over Katsevich's original algorithm with noiseless and noise projection data.
An improved super-short-scan reconstruction algorithm was proposed for fan-beam computed tomography based on Pi-line. The new algorithm was also based on a FBP algorithm, which could achieve exact region of interest (ROI) recon- struction if and only if all lines passing through the region of interest (ROI) intersect the source trajectory. The new reconstruction formula successfully avoided the direct derivatives with respect to projection data and was expressed as the combination of Hilbert filter and Ramp filter instead of only Hilbert filter, which increased the numerical stability and achieved good image quality improvement in the real discrete data reconstruction.
In order to obtain the high quality reconstruction images for low-dose CT, we proposed a new generalized Gibbs prior based low-dose CT reconstruction method. First, CT projection data was modeled as a statistics process. Then based on Bayesian maximum a posteriori estimation method, we designed a novel Gibbs prior named as generalized Gibbs prior, which exploits nonlocal information of the data to suppress noise. Last, we used the filtered back-projection method to finish the final CT reconstruction. The reason for the name of generalized Gibbs prior is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations through the selection of larger neighborhood and adaptively weight form with global information of an image.
We develop a corrective method in which the distorted segments in sinogram were identified and interpolated using non distorted neighbor projections, to reduce distorted tomography metal artifacts caused by high-density objects. First, the Anisotropic Gaussian (ASG) Pre-filter reduces the noise content and smoothes streak artifacts in CT image. Next, the filtered image is segmented into several regions by mutual information maximized segmentation (MMS). Then the artifacts class is converted to the CT number with the surrounding material, called "artifact-tissue" class, and after that an "artifact-tissue sinogram" was produced using forward projection method. A final image is reconstructed by the filtered back-projection from appropriately combination of original sinogram and artifacts-tissue sinogram.
八十年代FDK算法的提出,实现了三维意义上的CT重建。鉴于FDK算法可以基本解决小、中锥角效应对图像重建的影响,一直是实际应用的主流算法。但随着面积探测器技术的发展以及现代医疗对成像速度和精度要求的进一步提升,将会使基于该技术和要求的快速精确三维锥束CT重建算法代表了当前许多研发部门正在研究和开发的关键性课题。
现代医疗技术为了减少X射线对正常器官的辐射,希望以最少的X射线剂量获取最好的图像重建质量,一方面可以通过感兴趣区域重建,即尽量能对病灶区域集中成像;另一方面可以通过研究低剂量条件下重建图像中存在的噪声和诊断结果之间的关系,设计优良的CT成像算法。前者的实现要求射束的视场应该尽量小,能罩住感兴趣区同时要求扫描的轨道应该尽可能短;后者要求根据图像噪声与诊断结果之间的统计关系建立合适的数学模型。上述两方面均是日前临床上CT应用中急需解决的问题。
在影像诊断中高密度的物体,如金属植入物、外科固定器以及口腔填充物等,往往会在CT成像时造成严重的金属伪影,以致严重影响临床诊断效果。因此,高效准确的CT图像金属伪影消除算法的研究始终是CT应用研究的热点问题,在临床上将直接有助于指导放射治疗计划的制定。
因此,为了解决上述的系列问题,我们需要真正意义上的三维重建算法,能够快速精确地获取优质的重建图像;需要针对感兴趣区精确成像的重建算法和低剂量条件下的重建算法,以期在最小的剂量下获取最好的图像重建质量;我们还需要高效准确的CT图像金属伪影消除算法,辅助临床诊断。
本论文的主要创新点集中表现如下:
●提出一种新的基于混合滤波的螺旋锥束CT优质精确重建算法。新算法采用Katsevich算法框架,巧妙地将现有FDK类型算法和Katsevich算法的不同优点有机地融合,完全回避投影数据中关于探测器坐标变量的直接微分运算,提高了成像质量,减少了重建伪影。同时新算法的滤波过程仍是平移不变滤波且与FDK类型重建算法相比数据冗余加权是在滤波过程之后进行,增强了数值计算的灵活性且没额外增加计算复杂度。
●提出一种新的螺旋锥束CT精确重建公式。新重建公式利用数学上严格的推导,将Katseivch重建公式中关于旋转角度的微分运算完全回避,使得成像质量得到较大改善,减少了重建伪影。同时新算法仍然基于平移不变滤波且数据冗余加权在滤波过程之后进行,保持了数值计算的灵活性。
●提出一种新的基于PI线的扇形束CT超短扫描优质重建算法,新算法仍采用经典的FBP重建算法框架,当且仅当满足通过感兴趣区域的任一直线均与扫描轨道相交时,就可以有效地进行该区域的精确重建。新重建公式中回避了投影数据的求导运算,将加权Hilbert滤波转化为Hilbert滤波与Ramp滤波的组合形式。由于实际重建过程中要对离散数据进行处理,新算法中导数的回避将增加数值计算稳定性,提高重建图像质量。
●提出一种新的基于广义Gibbs先验的低剂量CT重建算法。新算法首先对投影数据进行统计建模,其后采用Bayesian最大后验估计方法,将投影数据中非局部的先验信息加诸于该数据的恢复中,达到抑制噪声的效果,最后仍采用经典的滤波反投影方法对恢复后的投影数据进行解析CT重建。其中非局部先验我们称之为广义Gibbs先验,其原因在于该先验具有传统Gibbs先验形式的同时,可以通过选择较大邻域和自适应的加权方式充分利用投影数据的全局信息进行数据恢复。
●建立一种新的针对由金属伪影造成的CT图像质量退化的恢复算法。利用自适应各向异性高斯滤波器对原始CT图像进行全局滤波,从而有效地滤除原始图像中的噪声并对射线状金属伪影进行了平滑,其后配合最大互信息量分割算法从图像中分割出伪影成份,并利用其周围非伪影部分的像素对伪影类像素进行插值处理得到一个称之为“伪组织”类的图像,通过融合“伪组织”图像的sinogram和原始CT图像的sinogram得到校正的sinogram;最后采用滤波反投影重建算法获得金属伪影的CT校正图像。新方法可以对含有金属伪影的CT图像进行有效伪影消除,其中射线状伪影消除效果显著。另外,新方法还可以锐化器官轮廓,避免了临床上由于金属伪影导致的放射治疗效果下降。
X-ray computed tomography (CT) has experienced tremendous growth in recently 30 years and has achieved substantial enhancement both in efficiency and precise. Since the introduction of helical and multi-slice CT, many new clinical applications have been developed. CT is again becoming one of the most exciting modalities in the medical imaging field.
In 1980, a novel 3-D reconstruction method was proposed, which plays a critically important role in the history of CT imaging although that was an approximate method. Because FDK is satisfied with small cone angular high quality imaging, it is the main stream algorithm for commercial applications. But with the development of multi-row detector and the improvement of imaging speed and precise in modern clinical application, fast and precise 3-D cone beam CT reconstruction method study presents the highlight project for many research departments.
Modern clinical techniques require as less as possible radiation towards normal tissues surrounding the diseased region, which would reduce unnecessary harm to the healthy organs. At the same time, we expect to get better reconstructed images with low dose radiation. Therefore, one side we can use a special region of interest, such as only diseased region imaging, which required to accommodate incomplete projection data with serious truncation. Other side we can conduct to understand the relationship between the noise present in the image and the outcome of diagnosis, which supervise the novel low dose CT reconstruction.
More considerably, high-density objects, such as metallic implants, surgical clips and dental fillings, often cause severe artifacts on computed tomography scans, and many render images non-diagnostic. This problem is due to the fact that satisfactory images cannot be calculated from projections if data are missing or distorted. So, metal artifacts reduction is also the highlight for the CT application research, which is helpful for the radiotherapy process.
The main contributions in this PhD dissertation are as following,
We present an alternative approach to reconstructing exactly an image from helical cone-beam projections, which is the combination of Hilbert filter and Ramp filter. Based on the Katsevich reconstructed algorithm framework, the proposed algorithm takes the different advantages of the FDK-type algorithms and Katsevich algorithm, which completely avoids the direct derivatives with respect to the coordinates on the detector plane. This alternative expression has a significant practical implication, thus leading to the images with quality improvement and reduced artefacts. At the same time, although the filtering process of the proposed algorithm is composed of Hilbert and Ramp filters, in contrast the FDK-type reconstructed algorithm, however, the new still performs a 1D shift-invariant filtering of the modified data on the detector plane and the redundancy weight is applied after filtering, allowing a more efficient numerical implementation. The complexity of the new algorithm compared with Katsevich algorithm does not extra increase.
We present a new FBP image reconstruction algorithm based on the Katsevich's original algorithm paradigm. This proposed algorithm successfully avoids the direct derivatives with respect to rotation angle, which achieves good image quality improvement and fewer artifacts. The new algorithm still performs a 1D shift-invariant filtering of the modified data on the detector plane and the redundancy weight is applied after filtering, allowing a more efficient numerical implementation. Results in these studies confirm the observation that the proposed algorithm can improve the image resolution over Katsevich's original algorithm with noiseless and noise projection data.
An improved super-short-scan reconstruction algorithm was proposed for fan-beam computed tomography based on Pi-line. The new algorithm was also based on a FBP algorithm, which could achieve exact region of interest (ROI) recon- struction if and only if all lines passing through the region of interest (ROI) intersect the source trajectory. The new reconstruction formula successfully avoided the direct derivatives with respect to projection data and was expressed as the combination of Hilbert filter and Ramp filter instead of only Hilbert filter, which increased the numerical stability and achieved good image quality improvement in the real discrete data reconstruction.
In order to obtain the high quality reconstruction images for low-dose CT, we proposed a new generalized Gibbs prior based low-dose CT reconstruction method. First, CT projection data was modeled as a statistics process. Then based on Bayesian maximum a posteriori estimation method, we designed a novel Gibbs prior named as generalized Gibbs prior, which exploits nonlocal information of the data to suppress noise. Last, we used the filtered back-projection method to finish the final CT reconstruction. The reason for the name of generalized Gibbs prior is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations through the selection of larger neighborhood and adaptively weight form with global information of an image.
We develop a corrective method in which the distorted segments in sinogram were identified and interpolated using non distorted neighbor projections, to reduce distorted tomography metal artifacts caused by high-density objects. First, the Anisotropic Gaussian (ASG) Pre-filter reduces the noise content and smoothes streak artifacts in CT image. Next, the filtered image is segmented into several regions by mutual information maximized segmentation (MMS). Then the artifacts class is converted to the CT number with the surrounding material, called "artifact-tissue" class, and after that an "artifact-tissue sinogram" was produced using forward projection method. A final image is reconstructed by the filtered back-projection from appropriately combination of original sinogram and artifacts-tissue sinogram.
引文
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[3]X.Pan homepage,http://www.radiology.uchicago.edu/pan.htm.
[4]F.Noo homepage,http://www.ucair.med.utah.edu/noo.
[5]G.Wang homepage,http://www.imaging.sbes.vt.edu/gwang.
[6]M.Jiang homepage,http://www.iria.pku.edu.cn/jiangm.
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