Image reconstruction of electrical capacitance tomography based on non-convex and nonseparable regularization algorithm

doi:10.11949/0438-1157.20240001

Abstract

Abstract:

Two-phase mixing in a stirrer is a common phenomenon in chemical production. Electrical capacitance tomography (ECT) technology mainly visually reconstructs the distribution of the two phases for monitoring purposes. Inspired by sparse Bayesian learning, a non-convex and nonseparable regularization (NNR) algorithm is proposed to reconstruct ECT images. The low-rank characteristics of the matrix are introduced on the basis of the sparse prior, and a new optimization problem is proposed in the latent space by using the maximum posterior estimation. Dual variables are used to map the objective function of the latent space to the original space for an iterative solution, which is used to restore the simultaneous sparse and low-rank matrices. Compared with the convex approximation L¹ norm, the NNR algorithm can obtain more accurate reconstruction images, and it is easier to converge to the global optimal solution than the non-convex separable method. To verify the reconstruction effect of the NNR algorithm, the reconstruction was compared with the other five algorithms through numerical simulation and static experiments. The results show that the NNR algorithm can effectively reduce reconstruction artifacts, improve the reconstruction quality of the central object, and provide a high-quality reconstruction algorithm for the two-phase distribution in the stirrer.

Key words: electrical capacitance tomography, image reconstruction, non-convex and nonseparable regularization, sparse-low-rank model, two-phase mixture

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。

关键词: 电容层析成像, 图像重建, 非凸不可分离正则化, 稀疏-低秩模型, 两相混合

CLC Number:

TB 937

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.

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.

Figures/Tables 10

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分布	IHT	L^0.5	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	L^0.5	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	L^0.5	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

分布	IHT	L^0.5	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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