Format of Original
Society for Industrial and Applied Mathematics
SIAM Journal on Imaging Sciences
Original Item ID
The regularized D-bar method for electrical impedance tomography (EIT) provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e., without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed, leading to a loss of edge distinction. In this paper, a novel method that combines a D-bar approach with the edge-preserving nature of total variation (TV) regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-enhanced D-bar method produces reconstructions with sharper edges and improved contrast. This is achieved by using the TV-induced edges to increase the truncation radius of the scattering data in the nonlinear frequency domain, thereby increasing the radius of the low-pass filter. The algorithm is tested on numerically simulated noisy EIT data and demonstrates significant improvements in edge preservation and contrast which can be highly valuable for absolute EIT imaging.
Hamilton, Sarah J.; Reyes, J. M.; Siltanen, Samuli; and Zhang, X., "A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography" (2016). Mathematics, Statistics and Computer Science Faculty Research and Publications. 462.
Published version. SIAM Journal on Imaging Sciences, Vol. 9, No. 2 (2016): 770-793. DOI. © 2016 Society for Industrial and Applied Mathematics. Used with permission.