Optimising the time to solution in electrical impedance tomography

Electrical impedance tomography (EIT) is an inverse imaging technique used to reconstruct resistive distributions. Some EIT inverse methods, such as the Gauss-Newton method, use the finite element method in the forward problem to solve for the Jacobian matrix. The authors detail methods to improve the solution time in the forward problem and accurate Jacobian calculation. The first suggestion is to keep the same node grounded for all projection angles by floating the current source. Details of an optimised Jacobian formation are also presented including full exploitation by sparse vector methods. The application of EIT to interface pressure distribution measurements makes use of a pressure sensitive resistive mat that can be cut to any shape or size. This flexibility can be taken advantage of and a square or rectangular domain comprising square bilinear elements is chosen. The sparse matrix nested dissection node renumbering algorithm then gives further speed advantages and also enables best optimisation with sparse vector techniques