The number of electrodes and basis functions in EIT image reconstruction

In electrical impedance tomography, many factors affect the image reconstruction results. Among them are the number of electrodes (NOE) and the number of conductivity basis functions (NOCBF) for image reconstruction. The NOCBF generally reflects the density of the mesh with which images are reconstructed. How and to what extent do these factors affect the image reconstruction and corresponding images? In this area detailed analysis is still lacking. This study aims to address the above question. In this study, image reconstruction and its ill-posed condition were analysed by singular value decomposition (SVD) and spectral expansion theory with different configurations of NOE and NOCBF. The results in this study indicate that for a circular 2D plane object with electrodes evenly located around the boundary: (1) Under certain conditions, increasing the NOE enables us to improve the ill-posed condition in image reconstruction and hence improve the image quality. Generally more improvement is expected near the image periphery than in the image centre. (2) Increasing the NOCBF generally worsens the ill-posed condition. But it enables the solution to be sought in a finer subspace and may be able to improve the image quality on the periphery, while generally the result in image centre depends more on the prior information incorporated in the regularization.