本文为美国普渡大学（作者：Pengchong Jin）的博士论文，共99页。

基于模型的图像处理是一系列技术的集合，为解决成像系统中的逆问题提供了一个系统框架。在本论文中，利用基于模型的方法解决了CT成像系统中存在的三个问题：具有二维平行光束和三维多层结构的单能量X射线CT的图像重建，单能量X射线CT的同时图像重建和光束硬化校正，同时对CT图像进行金属伪影消除和图像分割。

在第一个主题中，研究了基于模型的迭代重建（MBIR）方法来解决CT图像重建问题。最近的研究表明，与传统的滤波反投影（FBP）方法相比，MRIR具有改善图像质量和去除伪影的潜力。在统计框架下，利用该公式建立了二维平行束和三维多层螺旋CT的MBIR算法，并用优化技术求解了重建问题。最后给出了在实际CT数据集上的实验结果，说明了图像质量的提高以及噪声和伪影的减少。

第二个课题研究单能量X射线CT的光束硬化校正问题。束流硬化是指材料对低能X射线的衰减比高能强的效果好，并且由于X射线源光谱较宽，它可以导致一些重建图像伪影，例如条纹。基于不同物质可以按密度分离的假设，建立了一个更精确的解释X射线谱的正演模型，并提出了一种新模型的MBIR算法。整个算法通过交替估计图像和未知模型参数来工作，因此不需要额外的信息。仿真和实际CT扫描结果表明，该方法能有效地减少重建过程中的金属条纹伪影。

第三个问题是在没有获取CT数据的情况下，对含有金属伪影的CT图像进行分割。从CT图像中分割出感兴趣的物体在医学诊断和安全检查中有着广泛的应用。然而，由于金属物体的密集性，原始CT图像往往含有条纹等伪影，这些伪影会给精确分割带来困难。提出了一种新的基于模型的联合估计分割和恢复图像的方法，其统一代价函数由三项组成：1）数据保真度项，该项将原始图像和恢复图像联系起来，并结合条纹掩模；2）基于字典的图像先验，对恢复图像进行正则化处理；3）一个基于连续松弛Potts模型的术语，它将恢复的图像强度和分割标签耦合起来。仿真和真实CT数据的结果表明，在不使用原始CT数据的情况下，联合分割和MAR可以产生更好的结果。

Model-based image processing is acollection of techniques that provides a systematic framework for solvinginverse problems in imaging systems. In this dissertation 1 , three problemsthat arise in CT imaging systems are addressed using the model based approach:image reconstruction for the single energy X-ray CT with both 2D parallel-beamand 3D multi-slice geometries, simultaneous image reconstruction and beamhardening correction for the single energy X-ray CT, and simultaneous metalartifact reduction and image segmentation for CT images. In the first topic,the methodology of model-based iterative reconstruction (MBIR) for solving CTimage reconstruction problems is studied. Recent research indicates that theMRIR has potential to improve image quality and remove artifacts comparing totraditional filtered back-projection (FBP) methods. The MBIR algorithms forboth 2D parallel-beam and 3D multi-slice helical CT geometries are developedusing the formulation under the statistical framework and the reconstruction issolved using optimization techniques. The result on the real CT baggage datasetis presented, which illustrates the image quality improvement and noise andartifact reduction. The second topic studies the beam hardening correctionproblem in the single energy X-ray CT. Beam hardening is the effect thatmaterial preferably attenuates more low-energy X-ray than high-energy, and witha broad X-ray source spectrum, it can lead to several reconstructed imageartifacts, such as streaks. Based on the assumption that distinct materials canbe separated according to their densities, a more accurate forward model thataccounts for the X-ray spectrum is developed and a MBIR algorithm thatincorporates this new model is proposed. The overall algorithms works byalternating estimation of the image and the unknown model parameters, thereforeno additional information is required. Results on both the simulated and realCT scan data show that the proposed method significantly reduces metal streakartifacts in the reconstruction. The third problem is the segmentation of CTimages with metal artifacts and without the access to the CT data. Segmentinginteresting objects from CT images has a wide range of applications in medicaldiagnosis and security inspection. However, raw CT images often containartifacts such as streak due to the dense metal objects, and these artifactscan make accurate segmentation difficult. A novel model based approach thatjointly estimates both the segmentation and the restored image is proposed andthe unified cost function consists of three terms: 1) a data fidelity term thatrelates the raw and restored image and incorporates a streak mask; 2) adictionary-based image prior which regularizes the restored image; 3) a termbased on the continuous-relaxed Potts model which couples the restored imageintensities and segmentation labels. Results on both simulated and real CT dataare presented and support that the joint segmentation and MAR can producesuperior results without the use of the raw CT data.

1. 基于模型的X射线CT系统迭代重建（MBIR）

2. 基于模型的同步束硬化校正迭代重建技术（MBIR-BHC）

3. CT图像中联合金属伪影的减少与分割算法

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