Sensitivity volume as figure-of-merit for maximizing data importance in electrical impedance tomography

Abstract

Objective. Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the periphery of a heterogeneous conductor are inverted to map its internal conductivity. The EIT method proposed here aims to improve computational speed and noise tolerance by introducing sensitivity volume as a figure-of-merit for comparing EIT measurement protocols. Approach. Each measurement is shown to correspond to a sensitivity vector in model space, such that the set of measurements, in turn, corresponds to a set of vectors that subtend a sensitivity volume in model space. A maximal sensitivity volume identifies the measurement protocol with the greatest sensitivity and greatest mutual orthogonality. A distinguishability criterion is generalized to quantify the increased noise tolerance of high sensitivity measurements. Main result. The sensitivity volume method allows the model space dimension to be minimized to match that of the data space, and the data importance to be increased within an expanded space of measurements defined by an increased number of contacts. Significance. The reduction in model space dimension is shown to increase computational efficiency, accelerating tomographic inversion by several orders of magnitude, while the enhanced sensitivity tolerates higher noise levels up to several orders of magnitude larger than standard methods.