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。

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.