Recursive tomographic image reconstruction using a Kalman filter approach in the time domain
Recursive tomographic image reconstruction using a Kalman filter approach in the time domain
复制标题
在时域中使用卡尔曼滤波器方法进行递归断层扫描图像重建
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
G. Tillack
中科院分区：
文献类型：
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作者：
V. Artemiev;A. Naumov;G. Tillack
这项工作的任务是开发一种最佳线性递归层析图像重建技术，允许重建过程与投影数据采集相结合。图像是一个离散随机场，由一组以时间为自变量的线性随机差分方程给出。所提出的技术适用于那些层析成像模式、扫描几何形状和采集模式，这些模式允许引入具有加性噪声成分的线性观察。利用时域上的卡尔曼滤波方法，将重构过程表示为最优线性递推估计过程，在每个重构步骤上都有最优解。该算法的递归特性允许数据采集过程和重构任务并行化。卡尔曼滤波方法应用的主要限制是问题的巨大维度和对引入的先验知识量的强烈要求。为了克服这些限制，研究了一种伪卡尔曼滤波方法。该方法基于用经验协方差矩阵代替先验协方差矩阵。先验知识的减少降低了问题的维数，也降低了算法的收敛速度。在数据采集过程中引入一种优化方案，可以部分补偿收敛过程的退化。
The task of this work is to develop a technique for optimal linear recursive tomographic image reconstruction allowing the combination of the reconstruction process with projection data acquisition. The image supposes to be a discrete random field given by a set of linear stochastic difference equations with time as an independent variable. The proposed technique is applicable those tomographic modalities, scan geometries, and acquisition patterns that allow the introduction of a linear observation with an additive noise component. As a result the Kalman filter approach in the time domain is employed and the reconstruction process is represented as the optimal linear recursive estimation procedure with the optimal solution on each reconstruction step. The recursive properties of the proposed algorithm allow the parallelization of the data acquisition process and the reconstruction task. The main restrictions for the application of the Kalman filter approach are given by the huge dimension of the problem and the strong requirements to the amount of prior knowledge introduced. To overcome these restrictions a pseudo Kalman filter approach is investigated. This approach is based on replacing the prior covariance matrix with an empirical one. The reduction of the amount of prior knowledge decreases the dimensionality of the problem as well as the convergence velocity of the algorithm. Introducing an optimized scheme for the data acquisition procedure can partially compensate the degradation of the convergence process.