A D-Bar Algorithm with A Priori Information for 2-Dimensional Electrical Impedance Tomography
A D-Bar Algorithm with A Priori Information for 2-Dimensional Electrical Impedance Tomography
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DOI：
10.1137/15m1020137
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发表时间：
2016-01-01
影响因子：
2.1
通讯作者：
Mueller, Jennifer L.
中科院分区：
文献类型：
--
作者：
Alsaker, Melody;Mueller, Jennifer L.
提出了一种在二维D-BAR算法中加入先验信息的方法。结果表明，该方法还构成了D-bar方法的一种非线性正则化策略，在有正确先验信息的情况下，当噪声水平趋于零时，该策略收敛于真实电导率。在适当的Banach空间中得到了显式的收敛速度。给出了两种将电导值分配给先验的方法，每种方法对应于应用中的不同场景。对几个有噪声和无噪声的数值算例进行了测试，结果表明该方法对提高D-bar方法的空间分辨率是非常有效的。
A method for including a priori information in the 2-dimensional D-bar algorithm is presented. It is shown that this method also constitutes a nonlinear regularization strategy for the D-bar method that converges to the true conductivity as the noise level tends to zero in the case of a correct prior. An explicit rate of convergence in the appropriate Banach space is derived. Two methods of assigning conductivity values to the prior are presented, each corresponding to a different scenario in applications. The method is tested on several numerical examples with and without noise and is demonstrated to be highly effective in improving the spatial resolution of the D-bar method.