用于ECT图像重建的预处理Landweber迭代算法

针对Landweber迭代方法收敛速度慢的问题,采用预处理方法来加快其收敛速度,即减少为计算有效解所需的迭代步数,由求解方程ATAf=ATg变为求解DATAf=DATg,其中D是预处理矩阵.讨论了构建预处理矩阵的一般方法.采用两级预处理策略构建预处理矩阵,将大的奇异值聚合并与小的奇异值分隔开来,而不是将所有的奇异值聚合在一点上,避免信号与噪声混合.使用仿真数据对预处理Landweber方法的收敛速度以及重建图像质量进行了评价.实验表明,预处理投影Landweber迭代方法同未经预处理的Landweber相比只需很少的迭代步数就可以获得比较满意的重建结果,为电容层析成像技术在线进行定量的图像重建...

Preconditioning Landweber Iterative Method for ECT Image Reconstruction

To speed up the slow convergence rate of Landweber iteration method,a preconditioning approach is proposed to the convergence rate,i.e.,the number of iteration steps needed for a best approximate solution is reduced,so as to transform solving A~TAf=A~Tg into solving DA~TAf=DA~Tg where D is the preconditioning matrix.Discusses the conventional ways to construct the preconditioning matrix,and the two-level preconditioning strategy is picked out to construct the preconditioning matrix,by which the large singular values are aggregated and separated from the small ones instead of aggregating all singular values onto a point,thus avoiding the signal mixed with noise.An evaluation conducted using simulated data for the convergence rate and image reconstruction quality of preconditioned Landweber method.Experimental results showed that the projected Landweber iteration method with preconditioning can provide more satisfactory results through few iteration steps in comparison with the same method without preconditioning.The on-line quantitative image reconstruction is available to electrical capacitance tomography.