化工学报 ›› 2024, Vol. 75 ›› Issue (3): 836-846.DOI: 10.11949/0438-1157.20240001
收稿日期:
2024-01-03
修回日期:
2024-02-21
出版日期:
2024-03-25
发布日期:
2024-05-11
通讯作者:
张立峰
作者简介:
李宁(1975—),男,博士,教授,tdlnjohn@ctbu.edu.cn
基金资助:
Ning LI1(), Pengfei ZHU1, Lifeng ZHANG2(
), Dongchen LU2
Received:
2024-01-03
Revised:
2024-02-21
Online:
2024-03-25
Published:
2024-05-11
Contact:
Lifeng ZHANG
摘要:
搅拌器内两相混合是化工生产中常见的现象,电容层析成像(ECT)技术主要对两相分布进行可视化重构,以达到监测的目的。受稀疏贝叶斯学习的启发,提出了一种非凸与不可分离正则化(NNR)算法重建ECT图像。在稀疏先验的基础上引入矩阵低秩特性,采用最大后验估计在潜在空间中提出一个新的优化问题,利用对偶变量将潜在空间的目标函数映射到原始空间进行迭代求解,用来恢复同时稀疏与低秩的矩阵。与凸近似L1范数相比,NNR算法可获得更准确的重建图像,同时比非凸可分离方法更容易收敛到全局最优解。为验证NNR算法的重建效果,通过数值仿真与静态实验的方法分别与其他5种算法进行重建对比。结果表明:NNR算法可以有效减少重建伪影,提升中心物体的重建质量,为搅拌器内两相分布提供了高质量的重建算法。
中图分类号:
李宁, 朱朋飞, 张立峰, 卢栋臣. 基于非凸与不可分离正则化算法的电容层析成像图像重建[J]. 化工学报, 2024, 75(3): 836-846.
Ning LI, Pengfei ZHU, Lifeng ZHANG, Dongchen LU. Image reconstruction of electrical capacitance tomography based on non-convex and nonseparable regularization algorithm[J]. CIESC Journal, 2024, 75(3): 836-846.
分布 | IHT | L0.5 | L1 | Landweber | MSBL | NNR |
---|---|---|---|---|---|---|
a | 0.4811 | 0.4599 | 0.4879 | 0.5412 | 0.9179 | 0.3766 |
b | 0.9070 | 0.8207 | 0.8165 | 0.9825 | 0.9260 | 0.7309 |
c | 0.7719 | 0.6908 | 0.6149 | 0.5595 | 0.9311 | 0.4285 |
d | 0.6692 | 0.5451 | 0.6059 | 0.6792 | 0.9341 | 0.3842 |
e | 0.8826 | 0.7275 | 0.7291 | 0.9043 | 0.8737 | 0.5670 |
f | 0.8027 | 0.4123 | 0.4189 | 0.5876 | 0.9400 | 0.3557 |
g | 0.7914 | 0.6982 | 0.6402 | 0.7667 | 0.9399 | 0.5067 |
h | 0.7919 | 0.4133 | 0.4834 | 0.7566 | 0.9039 | 0.3946 |
i | 0.8747 | 0.7166 | 0.7168 | 0.9593 | 0.8735 | 0.5682 |
j | 0.7403 | 0.3552 | 0.5806 | 0.7853 | 0.9623 | 0.1175 |
表1 重建相对误差
Table 1 Reconstruction relative error
分布 | IHT | L0.5 | L1 | Landweber | MSBL | NNR |
---|---|---|---|---|---|---|
a | 0.4811 | 0.4599 | 0.4879 | 0.5412 | 0.9179 | 0.3766 |
b | 0.9070 | 0.8207 | 0.8165 | 0.9825 | 0.9260 | 0.7309 |
c | 0.7719 | 0.6908 | 0.6149 | 0.5595 | 0.9311 | 0.4285 |
d | 0.6692 | 0.5451 | 0.6059 | 0.6792 | 0.9341 | 0.3842 |
e | 0.8826 | 0.7275 | 0.7291 | 0.9043 | 0.8737 | 0.5670 |
f | 0.8027 | 0.4123 | 0.4189 | 0.5876 | 0.9400 | 0.3557 |
g | 0.7914 | 0.6982 | 0.6402 | 0.7667 | 0.9399 | 0.5067 |
h | 0.7919 | 0.4133 | 0.4834 | 0.7566 | 0.9039 | 0.3946 |
i | 0.8747 | 0.7166 | 0.7168 | 0.9593 | 0.8735 | 0.5682 |
j | 0.7403 | 0.3552 | 0.5806 | 0.7853 | 0.9623 | 0.1175 |
分布 | IHT | L0.5 | L1 | Landweber | MSBL | NNR |
---|---|---|---|---|---|---|
a | 0.8936 | 0.8915 | 0.8857 | 0.8734 | 0.3872 | 0.9299 |
b | 0.4015 | 0.5610 | 0.5640 | 0.5757 | 0.3716 | 0.7525 |
c | 0.6256 | 0.7851 | 0.8250 | 0.8258 | 0.3625 | 0.8969 |
d | 0.7324 | 0.8503 | 0.8239 | 0.7248 | 0.3435 | 0.9150 |
e | 0.4582 | 0.6802 | 0.6741 | 0.5526 | 0.4796 | 0.8278 |
f | 0.5801 | 0.9060 | 0.9051 | 0.7898 | 0.3349 | 0.9424 |
g | 0.5756 | 0.6909 | 0.7402 | 0.6070 | 0.3257 | 0.8501 |
h | 0.5590 | 0.8966 | 0.8548 | 0.5921 | 0.4027 | 0.9066 |
i | 0.4583 | 0.6815 | 0.6807 | 0.3916 | 0.4709 | 0.8227 |
j | 0.6498 | 0.9152 | 0.7936 | 0.5882 | 0.2357 | 0.9899 |
表2 重建相关系数
Table 2 Reconstruction correlation coefficient
分布 | IHT | L0.5 | L1 | Landweber | MSBL | NNR |
---|---|---|---|---|---|---|
a | 0.8936 | 0.8915 | 0.8857 | 0.8734 | 0.3872 | 0.9299 |
b | 0.4015 | 0.5610 | 0.5640 | 0.5757 | 0.3716 | 0.7525 |
c | 0.6256 | 0.7851 | 0.8250 | 0.8258 | 0.3625 | 0.8969 |
d | 0.7324 | 0.8503 | 0.8239 | 0.7248 | 0.3435 | 0.9150 |
e | 0.4582 | 0.6802 | 0.6741 | 0.5526 | 0.4796 | 0.8278 |
f | 0.5801 | 0.9060 | 0.9051 | 0.7898 | 0.3349 | 0.9424 |
g | 0.5756 | 0.6909 | 0.7402 | 0.6070 | 0.3257 | 0.8501 |
h | 0.5590 | 0.8966 | 0.8548 | 0.5921 | 0.4027 | 0.9066 |
i | 0.4583 | 0.6815 | 0.6807 | 0.3916 | 0.4709 | 0.8227 |
j | 0.6498 | 0.9152 | 0.7936 | 0.5882 | 0.2357 | 0.9899 |
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