Addressing the computational cost of large EIT solutions

Abstract

Abstract. Electrical Impedance Tomography (EIT) is a soft field tomography modality based on the application of electric current to a body and measurement of voltages through electrodes at the boundary. The interior conductivity is reconstructed on a discrete representation of the domain using a FEM mesh and a parametrization of that domain. The reconstruction requires a sequence of numerically intensive calculations. There is strong interest in reducing the cost of these calculations.An improvement in the compute time for current problems would encourage further exploration of computationally challenging problems such as the incorporation of time series data, wide-spread adoption of three-dimensional simulations, and correlation of other modalities such as CT and ultrasound. Multicore processors offer an opportunity to reduce EIT computation times but may require some restructuring of the underlying algorithms to maximize the use of available resources.This work profiles two EIT software packages (EIDORS and NDRM) to experimentally determine where the computational costs arise in EIT as problems scale. Sparse matrix solvers, a key component for the FEM forward problem and sensitivity estimates in the inverse problem, are shown to take a considerable portion of the total compute time in these packages. A sparse matrix solver performance measurement tool, Meagre-Crowd, is developed to interface with a variety of solvers and compare their performance over a range of two-and threedimensional problems of increasing node density. Results show that distributed sparse matrix solvers that operate on multiple cores are advantageous up to a limit that increases as the node density increases. We recommend a selection procedure to find a solver and hardware arrangement matched to the problem and provide guidance and tools to perform that selection.

Adaptive techniques in electrical impedance tomography reconstruction

“…One significant contribution to the computational cost is solving the forward problem using the finite element model (FEM) (Boyle et al 2012). The FEM is widely used to obtain the numerical solution of the forward problem in EIT by incorporating domain geometry, boundary conditions and prior information about the conductivity distribution.…”

Neural learning of the topographic tactile sensory information of an artificial skin through a self-organizing map

“…Moreover, the Kohonen map showed advantages over the classical reconstruction methods in terms of performance (good resolution accuracy) with the possibility to sense tactile inputs in real-time (in average 20 ms versus 262 ms for EIDORS using the difference imaging of EIT). Although it has been reported that the difference EIT image reconstruction technique can be very fast and can achieve 40 − 50Hz [65], the computational cost or complexity of EIT reconstruction techniques has been shown to be a drawback when the matrix size augments [66]. The computational complexity of EIT methods requires to inverse one matrix of dimension n, which costs computationally at least O(n 2 × m), where m is the number of finite elements of the FEM, which means that as the matrix augments -, the size of the tactile sheet and the number of electrodes,-the computational time for image reconstruction will increase asymptotically.…”

Jointly reconstructing ground motion and resistivity for ERT-based slope stability monitoring

“…The 2-D rank-one update was 7.1 times faster than the 2.5-D method across most mesh sizes, which is accounted for by the numerical integration implied by (13). There are likely to be further gains from optimizing this implementation for multiple processing cores because key portions of the Jacobian calculation ( 14), ( 15), ( 26), ( 29) can be performed in parallel and the Jacobian typically consumes a significant portion of the total calculation time in each Gauss-Newton iteration (Boyle et al 2012b). Mesh density was measured as the inverse of the maximum element height h (elements per metre) for both 2-D and 3-D meshes.…”