Shape-based solutions have recently received attention for certain ill-posed inverse problems when the relevant constituent parameters can be modeled as isotropic and piecewise continuous or homogeneous. Their advantages include implicit imposition of relevant constraints and reduction in the number of unknowns, especially important for non-linear ill-posed problems. We introduce a method, based on modified B-splines and the boundary element method (BEM), for shape-based inverse problems and apply it to current-injection electrical impedance tomography (EIT) in the torso. We assume the general shape of piecewise constant inhomogeneities is known but their conductivities and their exact location and shape are not. We model the boundaries of the unknown inhomogeneities using bivariate spline basis shape functions and solve for the conductivities, locations, and boundaries. The performance of our method is illustrated via simulation in a realistic torso model.
['Saeed Babaeizadeh', 'Dana H. Brooks', 'David Isaacson']
A deformable-radius B-spline method for shape-based inverse problems, as applied to electrical impedance tomography