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中文摘要：
电容层析成像因具有快速、廉价、非侵入传感等优点而被认为是具有广阔发展前景的过程成像技术。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。本文提出了一个基于1范数稳定的电容层析成像图像重建算法。将图像重建问题转化为一个最优化问题，并对目标泛函采用光滑逼近。在此基础上用Newton法求解该目标泛函。数值实验表明该算法是有效的，能够有效克服ECT图像重建的数值不稳定性，就本文所考察的重建对象而言，该法所获得的重建图像的质量有了一定的提高，从而为ECT图像重建引入了一种有效的方法。
英文摘要：
Electrical Capacitance Tomography （ECT） is considered as a promising process tomography technology due to the advantages such as high speed, low cost and non-intrusivesensing. 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 a meaningful reconstruction result. In this paper, an im- age reconstruction algorithm based on the 1-norm stabilizing is presented. The image reconstruction problem is trans- formed into an optimization problem and a smoothing method is used to approximate the objective function. In addition, Newton algorithm is employed to solve the objective function. Numerical experiments indicate that the algorithm is efficient and overcomes the numerical instability of ECT image reconstruction. For the cases of the reconstruction objects considered in this paper, the quality of the reconstructed image obtained using the proposed algorithm is enhanced; as a result, an efficient method for ECT image reconstruction is introduced.
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