Abstract
The inverse electrical impedance tomography (EIT) problem involves collecting electrical measurements on the smooth boundary of a region to determine the spatially varying electrical conductivity distribution within the bounded region. Effective applications of EIT technology emerged in different areas of engineering, technology, and applied sciences. However, the mathematical formulation of EIT is well known to suffer from a high degree of nonlinearity and severe ill-posedness. Therefore, regularization is required to produce reasonable electrical impedance images. Using difference imaging, we propose a spatially-variant variational method which couples sparsity regularization and smoothness regularization for improved EIT linear reconstructions. The EIT variational model can benefit from structural prior information in the form of an edge detection map coming either from an auxiliary image of the same object being reconstructed or automatically detected. We propose an efficient algorithm for minimizing the (non-convex) function based on the alternating direction method of multipliers. Experiments are presented which strongly indicate that using non-convex versus convex variational EIT models holds the potential for more accurate reconstructions.
Highlights
Electrical impedance tomography is an imaging technique that aims to reconstruct the inner conductivity distribution of a medium starting from a set of measured voltages registered by a series of electrodes that are positioned on the surface of the medium
Property i) in Proposition 1 for D and J matrices is required when the EIT inverse problem is solved by generalized Tikhonov regularization approaches which have been commonly used in electrical impedance tomography in the past [15,36]
For the class of nonlinear EIT methods (EIT-NL), we considered the Gauss–Newtons algorithm with linear regularization terms (IGNL) and non-linear regularization terms (Iterative Reweighted Least Squares, IRLS, [14]); while for the methods belonging to the class of linearized approaches (EITL), we compared with the One-step Gauss–Newton with Tikhonov priors, the (OGNT), the Primal–Dual Interior Point algorithm for Total Variation regularization (TVPIM, [5]), and the Newton One-Step Algorithm (NOSER [6]), which performs only the first step of the Newtons method for the solution of the (EIT-NL) problem
Summary
Electrical impedance tomography is an imaging technique that aims to reconstruct the inner conductivity distribution of a medium starting from a set of measured voltages registered by a series of electrodes that are positioned on the surface of the medium. EIT is a nondestructive testing technique, meaning that it allows to analyse the property of a material or structure without causing damage. It can be considered a tomographic modality due to the fact that it generates images of the internal features of a body. If compared to other tomography techniques, EIT provides lower spatial resolution outputs, but data can be
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