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A non-convex regularization method combined with Landweber method for image reconstruction in electrical resistance tomography
Flow Measurement and Instrumentation ( IF 2.2 ) Pub Date : 2021-03-18 , DOI: 10.1016/j.flowmeasinst.2021.101917
Yanyan Shi , Qifeng Li , Meng Wang , Weina Liu , Zhiwei Tian

Electrical resistance tomography (ERT) is a promising technique with which the conductivity distribution in the detected region can be visualized. Mathematically, the reconstruction of conductivity distribution is a seriously ill-posed inverse problem which poses a great challenge for the ERT sensing technique. The regularization method has been found to be an effective approach in coping with the inverse problem. In this work, a novel reconstruction strategy which combines the non-convex regularization method with Landweber method is proposed for the image reconstruction in ERT. At each iteration, the non-convex regularization is used to constrain the conductivity calculated with the Landweber method. A simple and efficient generalized iterated shrinkage algorithm is developed to solve the proposed method. To validate the performance of the proposed method, a series of numerical simulation is conducted and comparative analysis with other methods is performed. From the results, it can be observed that images with high quality are obtained when reconstructing with the proposed method. The impact of noise on the reconstruction is also investigated which shows that the images reconstructed by the proposed method are the least sensitive to the noise. The performance of the proposed method in the image reconstruction is also verified by experimental data. The results demonstrate that the inclusion is accurately reconstructed and the background is clear when the proposed method is adopted for the image reconstruction.



中文翻译:

一种非凸正则化方法与Landweber方法相结合的电阻层析成像图像重建

电阻层析成像(ERT)是一种很有前途的技术,利用该技术可以可视化检测到的区域中的电导率分布。在数学上,电导率分布的重建是一个严重的不适定反问题,这对ERT传感技术提出了巨大挑战。已经发现,正则化方法是解决逆问题的有效方法。在这项工作中,提出了一种新的重建策略,该方法将非凸正则化方法与Landweber方法相结合,用于ERT中的图像重建。在每次迭代中,非凸正则化用于约束用Landweber方法计算的电导率。为解决该方法,提出了一种简单有效的广义迭代收缩算法。为了验证所提方法的性能,进行了一系列数值模拟,并与其他方法进行了比较分析。从结果可以看出,用所提出的方法重建时可以获得高质量的图像。还研究了噪声对重建的影响,这表明通过所提出的方法重建的图像对噪声最不敏感。实验数据也验证了该方法在图像重建中的性能。结果表明,采用本文提出的方法进行图像重建时,可以准确地重建包含物,并且背景清晰。可以观察到,用所提出的方法重建时可以获得高质量的图像。还研究了噪声对重建的影响,这表明通过所提出的方法重建的图像对噪声最不敏感。实验数据也验证了该方法在图像重建中的性能。结果表明,采用本文提出的方法进行图像重建时,可以准确地重建包含物,并且背景清晰。可以观察到,用所提出的方法重建时可以获得高质量的图像。还研究了噪声对重建的影响,这表明通过所提出的方法重建的图像对噪声最不敏感。实验数据也验证了该方法在图像重建中的性能。结果表明,采用本文提出的方法进行图像重建时,可以准确地重建包含物,并且背景清晰。实验数据也验证了该方法在图像重建中的性能。结果表明,采用本文提出的方法进行图像重建时,可以准确地重建包含物,并且背景清晰。实验数据也验证了该方法在图像重建中的性能。结果表明,采用本文提出的方法进行图像重建时,可以准确地重建包含物,并且背景清晰。

更新日期:2021-03-30
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