Parameterized inversion of electrical impedance tomography with sparse and dense case sampling

Objective.When electrical impedance tomography is applied to a known system, such as the human body, a parameterized model is shown to produce a more accurate reconstruction than a conductivity map. Furthermore, if the number of free parameters is less than the total number of independent measurements, the sensitivity volume method can be employed to identify a significantly reduced number of data measurements with the highest value for distinguishing these parameters.Approach.To achieve direct parametric inversion from this reduced set of measurements, a simple algorithm establishes the correspondence between training data and parameterized model cases. Here two training algorithms will be demonstrated. For sparse sampling, the parameters associated with each trained case are interpolated to generate a high density of invertible data cases. For dense sampling, enough cases are directly measured that a simple nearest-neighbor search in data space can invert the data.Main result.Once the training is established, a simple nearest-neighbor query in data space has a one-to-one correspondence with the model parameters for reconstruction. Sparse sampling is demonstrated with an insulating cylinder in a saltwater tub whose diameter and angular position constitute a two-dimensional (2D) model space, and whose reduced high-value data space consists of 9 independent tetrapolar data measurements made with 15 available electrodes. Dense sampling is demonstrated with a mechanical goldfish in a saltwater tub whose coordinates and orientation define a 3D model space, and whose reduced high-value data space consists of 16 tetrapolar data measurements made from 128 available electrodes.Significance.The parametric method demonstrated here reduces the necessary number of data measurements by orders of magnitude compared to standard electrical impedance tomography to achieve higher accuracy within the parametric representation, and can, in principle, be expanded to complex 3D systems such as organs within the human body to achieve fast, high fidelity parametric reconstructions.