Optimization of 3D Impedance Tomography reconstruction on multi–core computing platforms

This manuscript presents results relative to the optimization of 3D impedance tomography reconstruction algorithms for execution on multi–core computing platforms. Speed–ups obtainable by the use of modern computing architectures and by an optimized implementation allow the use of much finer FEM meshes in the forward model, leading ultimately to a better image quality. We formulate the reconstruction as widely common in the EIT community: as a non–linear, least squares, Tikhonov regularized, discrete inverse problem. The forward model is based on a FEM solver that implements the Complete Electrode Model. By profiling a plain but careful MATLAB implementation of such an algorithm, we find that, in problems with mesh sizes in the order of 100.000 nodes, typically 95% of the computing time is spent in solving the forward problem and in computing the Jacobian matrix from the forward solutions. We have focused on optimizing the execution of these two functions, and we report relative results. On an octal Xeon 5355 based PC, on problems with forward meshes with a number of nodes in the range of 59,000 nodes to 146,000 nodes, the optimized algorithm has a speed-up of up to 7 times compared to an equivalent MATLAB implementation that makes use of the multithreading capabilities of the platform.