Normalization of a spatially variant image reconstruction problem in electrical impedance tomography using system blurring properties

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.

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