基于有限元仿真的ECT感兴趣区域高分辨率图像重建

doi:10.16182/j.issn1004731x.joss.23-0847

摘要/Abstract

摘要：

感兴趣区域的高分辨率图像重建是电容层析成像（electrical capacitance tomography，ECT）技术的研究热点之一。均匀电极分布的ECT模型仅在重建场域的边界位置具有较高的灵敏度系数，不适用于感兴趣区域成像。为改善感兴趣区域中的灵敏度分布，提高图像分辨率，提出了一种基于有限元仿真ECT感兴趣区域高分辨率图像重建方法，根据保角变换理论优化电极分布。进行了仿真实验，将均匀电极和优化电极分布的灵敏度矩阵代入Tikhonov算法、Landweber算法和ART算法，重建结果表明上述方法可有效提高感兴趣区域的图像重建精度。

关键词: 电容层析成像, 有限元仿真, 感兴趣区域, 灵敏度矩阵, 保角变换, 电极分布

Abstract:

High-resolution image reconstruction of interest region is one of the research hotspots of electrical capacitance tomography (ECT) technology. The ECT model with uniform electrode distribution only has a high sensitivity coefficient at the boundary position of the reconstructed field and is not suitable for imaging regions of interest. In order to improve the sensitivity distribution in the region of interest and improve image resolution, a high-resolution image reconstruction method of ECT region of interest based on finite element simulation is proposed, and the electrode distribution is optimized according to the conformal transformation theory. Simulation experiments are conducted, and the sensitivity matrices of uniform electrodes and optimized electrode distribution are substituted into the Tikhonov, Landweber, and ART algorithms. Reconstruction results show that the above method can effectively improve image reconstruction accuracy of interest region.

Key words: electrical capacitance tomography, finite element simulation, region of interest, sensitivity matrix, conformal transformation, electrode distribution

中图分类号:

TP391

张立峰,陈达 . 基于有限元仿真的ECT感兴趣区域高分辨率图像重建[J]. 系统仿真学报, 2024, 36(8): 1823-1831.

Zhang Lifeng,Chen Da . High-resolution Image Reconstruction of ECT Region of Interest Based on Finite Element Simulation[J]. Journal of System Simulation, 2024, 36(8): 1823-1831.

图/表 15

图1

图2

图3

图4

图5

图6

图7

图8

图9

表1

感兴趣区域的位置信息

感兴趣区域	\|OE\|	r_E	$θ$
Ⅰ	0.3	0.2	$π / 4$
Ⅱ	0.2	0.4	$7 π / 6$
Ⅲ	0.2	0.2	$5 π / 3$

表1

图10

图11

图12

图13

表2

均匀电极和优化电极在三种算法的比较

模型	评价指标	算法
		均匀电极			优化电极
		Tikhonov	Landweber	ART	Tikhonov	Landweber	ART
a	$E R$	1.240 3	1.221 6	1.070 2	0.829 1	0.798 0	0.579 1
a	C	0.385 1	0.401 3	0.423 5	0.723 7	0.744 5	0.823 1
b	$E R$	0.735 6	0.834 6	0.760 8	0.659 5	0.658 1	0.674 4
b	C	0.665 5	0.590 7	0.638 2	0.704 0	0.714 1	0.668 6
c	$E R$	1.088 0	1.518 6	1.194 1	1.438 0	1.241 3	1.037 7
c	C	0.318 9	0.291 7	0.194 1	0.385 3	0.443 2	0.553 8
d	$E R$	0.811 2	0.915 0	0.807 1	0.864 1	0.866 8	0.798 3
d	C	0.615 2	0.561 1	0.607 7	0.648 7	0.647 2	0.674 5
e	$E R$	1.232 9	1.191 5	1.107 8	1.466 6	1.216 7	1.059 6
e	C	0.319 4	0.331 6	0.359 1	0.375 1	0.427 5	0.442 8
f	$E R$	0.935 7	1.010 5	1.152 3	0.927 3	0.981 6	0.821 4
f	C	0.428 5	0.415 1	0.268 0	0.547 0	0.546 0	0.591 8
g	$E R$	1.221 2	1.344 6	1.106 1	0.983 1	1.013 1	0.975 7
g	C	0.125 3	0.166 1	0.259 8	0.363 6	0.369 8	0.346 1
h	$E R$	1.114 7	1.170 7	1.084 7	0.972 9	0.980 8	0.991 1
h	C	0.135 5	0.130 1	0.165 3	0.272 2	0.254 8	0.286 5

表2

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