The D-Bar Algorithm Fusing Electrical Impedance Tomography with A Priori Radar Data: A Hands-On Analysis

• Published in: Algorithms Vol. 16; no. 1; p. 43
• Main Authors: Rixen, Jöran, Leonhardt, Steffen, Moll, Jochen, Nguyen, Duy Hai, Ngo, Chuong
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2023
• Subjects: Algorithms; Breast cancer; Conductivity; D-Bar; Electrical impedance; electrical impedance tomography; Electrodes; fusion; Inverse problems; Noise sensitivity; Partial differential equations; radar; Radar data; Random variables; Reconstruction; Spatial resolution; Tomography
• ISSN: 1999-4893; 1999-4893
• DOI: 10.3390/a16010043

Electrical impedance tomography (EIT) is an imaging modality that can estimate a visualization of the conductivity distribution inside the human body. However, the spatial resolution of EIT is limited because measurements are sensitive to noise. We investigate a technique to incorporate a priori information into the EIT reconstructions of the D-Bar algorithm. Our paper aims to help engineers understand the behavior of the D-Bar algorithm and its implementation. The a priori information is provided by a radar setup and a one-dimensional reconstruction of the radar data. The EIT reconstruction is carried out with a D-Bar algorithm. An intermediate step in the D-Bar algorithm is the scattering transform. The a priori information is added in this exact step to increase the spatial resolution of the reconstruction. As the D-Bar algorithm is widely used in the mathematical community and thus far has limited usage in the engineering domain, we also aim to explain the implementation of the algorithm and give an intuitive understanding where possible. Different parameters of the reconstruction algorithm are analyzed systematically with the help of the GREIT figures of merit. Even a limited one-dimensional a priori information can increase the reconstruction quality considerably. Artifacts from noisy EIT measurements are reduced. However, the selection of the amount of a priori information and the estimation of its value can worsen the reconstruction results again.