Inverse Radon method based on electrical field lines for dual modality electrical tomography

Usually, the sensitivity matrix-based algorithms are used for image reconstruction in electrical tomography. In these algorithms it is assumed that the inverse problem is like those in the well-established medical CT, which is of great success. In the medical CT, rather than using the matrix-based algorithms, the inverse Radon transform and its derivatives dominate. However, these inverse transforms have not been introduced to electrical tomography because the link between the parallel projections and electrical distributions is unclear. This paper presents a map between the electric field lines and the parallel lines in the inverse Radon transform and a novel image reconstruction algorithm for dual modality electrical tomography using the inverse Radon transform. The transform is realized by mapping the coordinates in the electric field to the assumed parallel projections, where the points of intersections between electric field lines from different exciting electrodes are mapped to those of parallel lines from related projections in typical inverse Radon transform. Unlike the medical CT. Different excitation schemes are related to different equivalent projections, and iterative scanning is used to apply all available projected data. Both simulated and experimental data are used to validate the feasibility and effectiveness of this proposed algorithm. Dynamic flames are monitored using the proposed method. Dual modality images of both conductivity and permittivity distributions are obtained to capture the ignition and blowout of the flame evolution in a Bunsen burner.