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Electrical Impedance Tomography (EIT) is a well-known imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many applications in medical imaging for the detection and location of bodily tumors since it is an affordable and non-invasive method, which aims to recover the internal conductivity of a body using voltage measurements resulting from applying low frequency current at electrodes placed at its surface. Mathematically, the reconstruction of the internal conductivity is a severely ill-posed inverse problem and yields a poor quality image reconstruction. To remedy this difficulty, at least in part, we regularize and solve the nonlinear minimization problem by the aid of a Krylov subspace-type method for the linear sub problem during each iteration. In EIT, a tumor or general anomaly can be modeled as a piecewise constant perturbation of a smooth background, hence, we solve the regularized problem on a subspace of relatively small dimension by the Flexible Golub-Kahan process that provides solutions that have sparse representation. For comparison, we use a well-known modified Gauss–Newton algorithm as a benchmark. Using simulations, we demonstrate the effectiveness of the proposed method. The obtained reconstructions indicate that the Krylov subspace method is better adapted to solve the ill-posed EIT problem and results in higher resolution images and faster convergence compared to reconstructions using the modified Gauss–Newton algorithm.
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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 increasecomputational efficiency, accelerating tomographic inversion by several orders of magnitude, while the enhanced sensitivitytolerates higher noiselevels up to several orders of magnitude larger than standard methods.
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- Award ID(s):
- 1912694
- PAR ID:
- 10500855
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Physiological Measurement
- Volume:
- 45
- Issue:
- 4
- ISSN:
- 0967-3334
- Format(s):
- Medium: X Size: Article No. 045004
- Size(s):
- Article No. 045004
- Sponsoring Org:
- National Science Foundation
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