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基于鲁棒自适应Kalman滤波的PET放射性浓度重建
引用本文:沈云霞,刘华锋.基于鲁棒自适应Kalman滤波的PET放射性浓度重建[J].中国图象图形学报,2011,16(2):185-190.
作者姓名:沈云霞  刘华锋
作者单位:浙江大学现代光学仪器国家重点实验室,浙江大学现代光学仪器国家重点实验室
基金项目:国家自然科学基金项目(60872068, 60772125);浙江省科技计划项目(2008C23060)
摘    要:针对正电子发射断层成像重建过程中存在的系统模型误差和投影数据不确定性,提出了基于状态空间体系的鲁棒自适应Kalman滤波法。该方法根据药物动力学先验信息建立状态方程,结合PET测量方程组成状态空间模型。引入虚拟噪声来表示模型的系统矩阵误差之后,通过应用鲁棒自适应Kalman滤波法对未知的系统噪声以及观测噪声进行估计的同时完成PET放射性浓度的重建。实验结果表明,此算法比传统的最大似然法和滤波反投影法更具鲁棒性,适合应用于实际PET系统中。

关 键 词:模型误差    状态空间体系    自适应Kalman滤波    虚拟噪声    鲁棒性
收稿时间:2009/3/25 0:00:00
修稿时间:2009/10/13 0:00:00

Robust adaptive Kalman filter for PET image reconstruction
shen Yunxia and Liu Huafeng.Robust adaptive Kalman filter for PET image reconstruction[J].Journal of Image and Graphics,2011,16(2):185-190.
Authors:shen Yunxia and Liu Huafeng
Affiliation:state key laboratory of modern optical instrumentation, zhejiang university
Abstract:A modified adaptive Kalman filtering algorithm considering the system matrix uncertainty and data instability of the state space theory for Positron emission tomography(PET) reconstruction was proposed. Based on tracer kinetic theory, an evolution equation of the tracer is introduced as a prior to constrain the reconstruction. Along with the observation equation of the detectors, the two equations constitute a state spatial model. After introducing virtual noise to represent the error of the system matrix, the modified adaptive Kalman filter is applied to estimate the process and the observation noise and meantime completes the PET reconstruction. The performance of the algorithm was verified by computer simulations, which show that modified adaptive Kalman filter is more robust than the traditional maximum likelihood expectation maximization method and filtered back projection methods. The results are meaningful and particularly suitable for the real positron emission tomography system.
Keywords:system matrix uncertainty  state space  adaptive Kalman filtering  virtual noise  robust
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