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

Area of Science:

• Medical Imaging
• Biomedical Engineering
• Computational Science

Background:

• Electrical Impedance Tomography (EIT) image reconstruction is an ill-posed problem, susceptible to noise and spatial variance.
• Image artifacts in EIT arise from its ill-posed nature, necessitating regularization techniques.
• Spatial variance in EIT reconstruction can lead to inaccuracies, particularly affecting quantitative analysis.

Purpose of the Study:

• To address the spatial variance in EIT image reconstruction.
• To present methods for normalizing the EIT reconstruction problem by equalizing the point spread function (PSF).
• To evaluate different normalization schemes for improving EIT image accuracy.

Main Methods:

• Investigated reconstruction blurring properties from the sensitivity matrix to equalize the PSF.
• Compared three normalization schemes: pixel-wise scaling (PWS), weighted pseudo-inversion (WPI), and weighted minimum norm method (WMNM).
• Utilized the quantity index (QI) to assess spatial variance and evaluated methods with truncated singular value decomposition (TSVD) and WMNM regularization.

Main Results:

• Normalization methods based on PSF equalization successfully achieved a spatially invariant QI.
• WMNM normalization combined with WMNM regularized reconstruction demonstrated superior performance.
• The proposed normalization techniques improved reconstruction accuracy for both full array and hemiarray electrode configurations.

Conclusions:

• Equalizing the PSF is an effective strategy to normalize the spatially variant EIT reconstruction problem.
• The WMNM normalization method applied to WMNM regularized reconstruction offers the best overall performance for EIT imaging.
• These findings enhance the accuracy and reliability of quantitative EIT analysis.