Oh Sungho, Tang Te, Tucker A S, Sadleir R J
J Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL, USA.
Physiol Meas. 2009 Mar;30(3):275-89. doi: 10.1088/0967-3334/30/3/004. Epub 2009 Feb 6.
The electrical impedance tomography (EIT) image reconstruction problem is ill posed and spatially variant. Because of the problem's ill-posed nature, small amounts of measurement noise can corrupt reconstructed images. The problem must be regularized to reduce image artifacts. In this paper, we focus on the spatially variant characteristics of the problem. Correcting errors due to spatial variance should improve reconstruction accuracy. In this paper, we present methods to normalize the spatially variant image reconstruction problem by equalizing the point spread function (PSF). In order to equalize the PSF, we used the reconstruction blurring properties obtained from the sensitivity matrix. We compared three mathematical normalization schemes: pixel-wise scaling (PWS), weighted pseudo-inversion (WPI) and weighted minimum norm method (WMNM) to equalize images. The quantity index (QI), defined as the integral of pixel values of an EIT conductivity image, was considered in investigating spatial variance. The QI values along with reconstructed images are presented for cases of two-dimensional full array and hemiarray electrode topologies. We found that a spatially invariant QI could be obtained by applying normalization methods based on equalization of the PSF using conventional regularized reconstruction methods such as truncated singular value decomposition (TSVD) and WMNM. We found that WMNM normalization applied to WMNM regularized reconstruction was the best of the methods tested overall, for both hemiarray and full array electrode topologies.
电阻抗断层成像（EIT）图像重建问题是不适定且空间变化的。由于该问题的不适定性质，少量的测量噪声就可能使重建图像失真。必须对该问题进行正则化处理以减少图像伪影。在本文中，我们关注该问题的空间变化特性。校正由空间变化引起的误差应能提高重建精度。在本文中，我们提出了通过均衡点扩散函数（PSF）来对空间变化的图像重建问题进行归一化的方法。为了均衡PSF，我们利用了从灵敏度矩阵获得的重建模糊特性。我们比较了三种数学归一化方案：逐像素缩放（PWS）、加权伪逆（WPI）和加权最小范数方法（WMNM）以均衡图像。在研究空间变化时考虑了数量指标（QI），其定义为EIT电导率图像像素值的积分。给出了二维全阵列和半阵列电极拓扑情况下的QI值以及重建图像。我们发现，通过使用诸如截断奇异值分解（TSVD）和WMNM等传统正则化重建方法，基于PSF均衡应用归一化方法可以获得空间不变的QI。我们发现，对于半阵列和全阵列电极拓扑，应用于WMNM正则化重建的WMNM归一化在所有测试方法中总体上是最好的。
