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中文摘要：
电容层析成像图像重建是一个典型的病态问题,其解是不稳定的。为获得良好的重建效果,需要采用既保证解的稳定性且又能提高重建图像质量的算法。本文提出了一种新的图像重建算法。在分析标准Tikhonov正则法的基础上,针对ECT逆问题的病态性进行改进,并推导出两步图像重建算法：第一步利用标准Tikhonov正则法的计算值获得权矩阵的估计;第二步采用本文所推导的改进Tikhonov正则法获得最终的重建图像。数值实验表明,该算法所获得的图像重建质量得到了明显的提高,且该算法无需迭代,保证了算法实时性。
英文摘要：
ECT image reconstruction is a typical ill-posed problem, and its solution is unstable. Methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain better reconstruction results. In this paper, a novel image reconstruction algorithm for ECT is presented. On the basis of analyzing standard Tikhonov regularization method, the method is improved to alleviate the ill-posed characteristics of the ECT inverse problem, and a two-step image reconstruction algorithm is deduced. The proposed algorithm is divided into two steps. In the first step, a weight matrix is estimated using the solution of the standard Tikhonov regularization method; in the second step, the image is reconstructed via the improved algorithm given in this paper. Numerical simulations indicate that the quality of the reconstructed images using the improved algorithm is markedly enhanced, and iterative procedure is unnecessary, thus the real-time performance can be ensured.
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