Forward Solving in Electrical Impedance Tomography with Algebraic Multigrid Wavelet Based Preconditioners

1. Abstract Electrical Impedance Tomography is a soft–field tomography modality, where image reconstruction is formulated as a non-linear least-squares model fitting problem. The NewtonRahson scheme is used for actually reconstructing the image, and this involves three main steps: forward solving, computation of the Jacobian, and the computation of the conductivity update. Forward solving relies typically on the finite element method, resulting in the solution of a sparse linear system. In typical three dimensional biomedical applications of EIT, like breast, prostate, or brain imaging, it is desirable to work with sufficiently fine meshes in order to properly capture the shape of the domain, of the electrodes, and to describe the resulting electric filed with accuracy. These requirements result in meshes with 100,000 nodes or more. The solution the resulting forward problems is computationally intensive. We address this aspect by speeding up the solution of the FEM linear system by the use of efficient numeric methods and of new hardware architectures. In particular, in terms of numeric methods, we solve the forward problem using the Conjugate Gradient method, with a wavelet–based algebraic multigrid (AMG) preconditioner. This preconditioner is faster to set up than other AMG preconditoiners which are not based on wavelets, it does use less memory, and provides for a faster convergence. We report results for a MATLAB based prototype algorithm an we discuss details of a work in progress for a GPU implementation.