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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，它的解是不稳定的。为了获得有意义的重建结果，能够保证解的稳定性而又能提高重建图像质量的方法应该被采用。本文提出了一个新的电容层析成像图像重建算法。在分析标准Tikhonov正则法的基础上，针对ECT逆问题的病态特点利用Quantile估计和加权lp范数构建扩展的目标泛函，将图像重建问题转化为一个最优化问题；在此基础上用Newton法求解该泛函。数值实验表明该算法是可行的，能够有效克服ECT罔像重建的数值不稳定性。就本文所考察的重建对象而言，该法所重建图像的空间分辨率得到了提高。而且该算法计算直接、无需任何复杂的技巧，从而为ECT图像重建提供了一种有效的方法。
英文摘要：
Electrical capacitance tomography （ECT） image reconstruction is a typical ill-posed problem, and its solution is unstable. Methods that ensure the stability of the solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. In this paper, a novel image reconstruction algorithm for ECT is presented. Aiming at the ill-posed characteristics of ECT, on the basis of analyzing the standard Tikhonov regularization method, an extended objective functional is established using the Quantile estimation and weighted lp norm, and the image reconstruction problem is transformed into an optimization problem. In addition, the Newton algorithm is employed to solve the objective functional. Numerical simulations indicate that the proposed algorithm is feasible and overcomes effectively the numerical instability of ECT image reconstruction. For the cases of the reconstructed objects considered in this paper, the spatial resolution of the reconstructed images is enhanced. Furthermore, the computation of the algorithm is direct, and does not involve complex techniques, which provides an efficient method for ECT image reconstruction.
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