关键词: Landweber迭代方法, 收敛速度, 预处理, 电容层析成像, 图像重建

Abstract: 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.