Non-linear electrical tomography reconstruction of simple test objects and a simulated head slice

Fully non-linear reconstruction in Electrical Tomography produces images with well-defined characteristics when explicit guides are imposed on the accessible solutions. In this paper, we revisit the formulation of the problem and apply the algorithm to some simulated test objects, and to a simple 2-dimensional model of the human head. The results demonstrate the best fidelity of reconstruction which may be achieved with existing and potentially attainable levels of signal to noise. We use a finite element model with some adaptive capability so that the images generated by the chosen constraint are not perturbed by the coarseness of the mesh. The algorithm incorporates a number of optimisations to reduce the required computing power and storage space, these include:Sparse matrix storage scheme and optimised sparse numerical handlingProblem-adapted element shape and densityUsage of high quality finite element meshesPre-evaluation of used quantities and matrices and application of numerical techniques such as the Woodbury formul