Bayesian Shape Reconstruction Using B-Spline Level Set in Electrical Impedance Tomography

A new shape reconstruction framework that incorporates sparse Bayesian learning (SBL) and the B-spline level set (BLS) is proposed for difference electrical impedance tomography (EIT). To begin with, the conductivity distribution to be reconstructed is assumed to be piecewise constant under the BLS framework. Second, the boundaries of the inclusions are represented by the B-spline curves in a parametric and explicit way. Next, the optimal shapes are found by solving the unknown variables using the SBL method. Then, the proposed method takes full advantage of B-spline flexible representation and Bayesian learning capability, resulting in improvements in reconstruction performance, noise robustness, and computational efficiency. Finally, a series of numerical and experimental tests are performed to verify the feasibility of the proposed method. Furthermore, the robustness studies are also investigated considering the inhomogeneous background, different numbers of control points, and different initial guesses. The results show that the proposed method leads to reliable and robust shape reconstructions, as evaluated by several quantitative metrics. Specifically, the forced vital capacity (FVC) tests of ten healthy volunteers show that the mean error in the 1-s rate of the shape reconstructions is less than 5% compared with simultaneous spirometry measurements. Hence, the proposed method is promising in providing an effective assessment for lung imaging.