Multispectral Electrical Impedance Tomography using Optimization over Manifolds

Abstract

Electrical impedance tomography under spectral constraints uses a material basis decomposition to combine the different information embedded in the tissue spectra. This approach offers an alternative to static imaging while benefiting from systemic error cancellation using difference data. It suits well cases where no prior solution is known and the contrast lies entirely between frequencies, e.g. to diagnose acute stroke or cancer. In this work, a computational framework is presented to deal with the extra frequency dimensions and the constraints during reconstruction. A fraction volume approach is demonstrated with explicit Euclidean gradient, usage of a finite volume element solver and minimization over the oblique manifold. It is applied to synthetic data. Parameter estimations are compared between a monofrequency inversion and the proposed multispectral implementation. Results suggest that the proposed workflow enables to reduce the computational workload of multispectral inversion while ensuring valid proportions of materials within each control volume.