Elastic-net regularization for nonlinear electrical impedance tomography with a splitting approach
Elastic-net regularization for nonlinear electrical impedance tomography with a splitting approach
复制标题
采用分裂方法的非线性电阻抗断层扫描的弹性网络正则化
DOI：
10.1080/00036811.2018.1451644
复制
发表时间：
2017-12
影响因子：
1.1
通讯作者：
Wei Wang
中科院分区：
文献类型：
--
作者：
Jing Wang;Bo Han;Wei Wang
EIT图像重建在数学上是一个典型的非线性严重病态反问题。需要适当的优先权或处罚来实现重建。常用范数可以增强稳定性以保持局部平滑，而当前范数可以增强稀疏性以保持边缘锋利。考虑到-范数惩罚总是使解过于光滑和-范数惩罚总是使解过于稀疏的问题，针对全非线性EIT反问题，提出了-范数和-范数凸组合项的弹性网正则化方法。我们的目标是结合这两个术语的强度：变换域的稀疏性和物理域的平滑性，试图提高重建分辨率和对噪声的鲁棒性。所生成的复合最小化问题具有非线性和非光滑性，很难找到有效的数值解。在此基础上，提出了一种基于分裂Bregman技术的联合惩罚正则化简单快速的数值优化方案。用典型电导率分布的模拟数据对该方法进行了验证。结果表明，通过选择合适的参数，所提出的反演模型得到了有效的正则化解，提高了重建图像的质量。
ABSTRACT Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used -norm can enforce the stability to preserve local smoothness, and the current -norm can enforce the sparsity to preserve sharp edges. Considering the fact that -norm penalty always makes the solution overly smooth and -norm penalty always makes the solution too sparse, elastic-net regularization approach with a convex combination term of -norm and -norm emerges for fully nonlinear EIT inverse problems. Our aim is to combine the strength of both terms: sparsity in the transform domain and smoothness in the physical domain, in an attempt to improve the reconstruction resolution and robustness to noise. Nonlinearity and non-smoothness of the generated composite minimization problem make it challenging to find an efficient numerical solution. Then we develop one simple and fast numerical optimization scheme based on the split Bregman technique for the joint penalties regularization. The method is validated using simulated data for some typical conductivity distributions. Results indicate that the proposed inversion model with an appropriate parameter choice achieves an efficient regularization solution and enhances the quality of the reconstructed image.
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DOI：
10.1017/cbo9780511794308
发表时间：
2012
期刊：
--
影响因子：
--
作者：
Gitta Kutyniok
通讯作者：
Gitta Kutyniok
影响因子：
3.2
作者：
E. J. Woo;P. Hua;John G. Webster;Willis J. Tompkins
通讯作者：
E. J. Woo;P. Hua;John G. Webster;Willis J. Tompkins
影响因子：
3
作者：
Daubechies, I;Defrise, M;De Mol, C
通讯作者：
De Mol, C
DOI：
--
发表时间：
2007-06
期刊：
--
影响因子：
--
作者：
A. Borsic;B. Graham;A. Adler;W. Lionheart
通讯作者：
A. Borsic;B. Graham;A. Adler;W. Lionheart
DOI：
10.1109/iembs.2008.4649764
发表时间：
2008-10
期刊：
2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society
影响因子：
--
作者：
Tao Dai;A. Adler
通讯作者：
Tao Dai;A. Adler