乘法正则化的电阻抗层析成像

Ke Zhang, Maokun Li, Fan Yang, Shenheng Xu, A. Abubakar
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引用次数: 1

摘要

本文将一种乘法正则化方案应用于EIT数据反演。采用一种基于l2范数的加权正则化方法作为乘法约束。该方案避免了代价函数中正则化参数的设置,并且可以在反演过程中自适应调整数据失拟与正则化之间的相对权重。本文采用高斯-牛顿法迭代最小化代价泛函。在最小化过程中,需要计算正则化因子的梯度。这需要在三角形或四面体网格上离散地表示梯度和散度算子。为此,引入了一种基于离散外演算(DEC)理论的方法来严格描述网格上的这些算子。利用合成数据和实验数据对反演算法进行了验证。结果表明,在EIT反问题中,乘法正则化具有良好的保边性能和抗噪声性能。
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Electrical impedance tomography with multiplicative regularization
In this work, a multiplicative regularization scheme is applied to EIT data inversion. A weighted L2-norm-based regularization with edge-preserving characteristics is used as a multiplicative constraint. In this scheme, the setting of regularization parameter in the cost functional is avoided, and the relative weights between the data misfit and the regularization can be adjusted adaptively during the inversion. In this work, Gauss-Newton method is used to minimize the cost functional iteratively. In the minimization process, the gradient of the regularization factor needs to be computed. This requires discrete representation of gradient and divergence operators on triangular or tetrahedral meshes. To this end, a method based on the theory of discrete exterior calculus (DEC) is introduced to rigorously describe these operators on meshes. The inversion algorithm is tested using both synthetic and experimental data. The results show good edge-preserving and anti-noise performance of the multiplicative regularization in the EIT inverse problem.
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来源期刊
Advances in Engineering Education
Advances in Engineering Education Social Sciences-Education
CiteScore
2.90
自引率
0.00%
发文量
8
期刊介绍: The journal publishes articles on a wide variety of topics related to documented advances in engineering education practice. Topics may include but are not limited to innovations in course and curriculum design, teaching, and assessment both within and outside of the classroom that have led to improved student learning.
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