Supershape Recovery From Electrical Impedance Tomography Data
Danping Gu, Dong Liu, Danny Smyl, Jiansong Deng, Jiangfeng Du
Abstract
The idea of accounting for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> shape information is gaining increasing levels of interest and traction in the electrical impedance tomography (EIT) reconstruction. A supershape-based reconstruction approach is proposed for EIT. We begin by assuming that the conductivity profile to be reconstructed in the measured domain is piecewise constant distributed. Using this formulation, the image reconstruction problem is transformed into a shape reconstruction problem. The inclusion boundary (e.g., interface between the inclusion and the background) to be estimated is treated as a supershape and expressed through a single equation—the so-called super formula. We illustrate the performance of the proposed approach using synthetic and experimental water tank data. In addition, robustness studies considering different regularization types ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> norms), varying noise levels and different initial settings are tested of the proposed approach. Four evaluation matrices relative size coverage ratio (RCR), structural similarity index (SSIM), relative contrast (RCo), and correlation coefficient (CC) are used to quantitatively evaluate the performance of the proposed method. Both the simulation and experimental results show that the supershape-based method leads to reliable and robust reconstructions and improves the ability to simultaneously reconstruct objects with smooth boundaries and/or sharp features. The proposed approach provides an excellent opportunity for the shape reconstruction framework to express a wide variety of shapes, including geometric primitives. Supershapes can simply represent regular polygons and natural shapes with various symmetries while maintaining a parametric representation.