Nonstationary shape estimation in electrical impedance tomography using a parametric level set-based extended Kalman filter approach

This paper presents a parametric level set based reconstruction method for non-stationary applications using electrical impedance tomography (EIT). Owing to relatively low signal to noise ratios in EIT measurement systems and the diffusive nature of EIT, reconstructed images often suffer from low spatial resolution. In addressing these challenges, we propose a computationally efficient shape-estimation approach where the conductivity distribution to be reconstructed is assumed to be piecewise constant, and the region boundaries are assumed to be non-stationary in the sense that the characteristics of region boundaries change during measurement time. The EIT inverse problem is formulated as a state estimation problem in which the system is modeled with a state equation and an observation equation. Given the temporal evolution model of the boundaries and observation model, the objective is to estimate a sequence of states for the nonstationary region boundaries. The implementation of the approach is based on the finite element method and a parametric representation of the region boundaries using level set functions. The performance of the proposed approach is evaluated with simulated examples of thorax imaging, using noisy synthetic data and experimental data from a laboratory setting. In addition, robustness studies of the approach w.r.t the modeling errors caused by inaccurately known boundary shape, non-homogeneous background and varying conductivity values of the targets are carried out and it is found that the proposed approach tolerates such kind of modeling errors, leading to good reconstructions in non-stationary situations

Parametric Level Set Methods for Inverse Problems

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypasses many difficulties with traditional level set methods, such as regularization, re-initialization and use of signed distance function. Moreover, we show that from a computational point of view, low order representation of the problem paves the path for easier use of Newton and quasi-Newton methods. Specifically for the purposes of this paper, we parameterize the level set function in terms of adaptive compactly supported radial basis functions, which used in the proposed manner provides flexibility in presenting a larger class of shapes with fewer terms. Also they provide a "narrow-banding" advantage which can further reduce the number of active unknowns at each step of the evolution. The performance of the proposed approach is examined in three examples of inverse problems, i.e., electrical resistance tomography, X-ray computed tomography and diffuse optical tomography

B-spline level set method for shape reconstruction in electrical impedance tomography

A B-spline level set (BLS) based method is proposed for shape reconstruction in electrical impedance tomography (EIT). We assume that the conductivity distribution to be reconstructed is piecewise constant, transforming the image reconstruction problem into a shape reconstruction problem. The shape/interface of inclusions is implicitly represented by a level set function (LSF), which is modeled as a continuous parametric function expressed using B-spline functions. Starting from modeling the conductivity distribution with the B-spline based LSF, we show that the shape modeling allows us to compute the solution by restricting the minimization problem to the space spanned by the B-splines. As a consequence, the solution to the minimization problem is obtained in terms of the B-spline coefficients. We illustrate the behavior of this method using simulated as well as water tank data. In addition, robustness studies considering varying initial guesses, differing numbers of control points, and modeling errors caused by inhomogeneity are performed. Both simulation and experimental results show that the BLS-based approach offers clear improvements in preserving the sharp features of the inclusions in comparison to the recently published parametric level set method

Shape reconstruction using Boolean operations in electrical impedance tomography

In this work, we propose a new shape reconstruction framework rooted in the concept of Boolean operations for electrical impedance tomography (EIT). Within the framework, the evolution of inclusion shapes and topologies are simultaneously estimated through an explicit boundary description. For this, we use B-spline curves as basic shape primitives for shape reconstruction and topology optimization. The effectiveness of the proposed approach is demonstrated using simulated and experimentally-obtained data (testing EIT lung imaging). In the study, improved preservation of sharp features is observed when employing the proposed approach relative to the recently developed moving morphable components-based approach. In addition, robustness studies of the proposed approach considering background inhomogeneity and differing numbers of B-spline curve control points are performed. It is found that the proposed approach is tolerant to modeling errors caused by background inhomogeneity and is also quite robust to the selection of control points

Selected Papers from the 9th World Congress on Industrial Process Tomography

Industrial process tomography (IPT) is becoming an important tool for Industry 4.0. It consists of multidimensional sensor technologies and methods that aim to provide unparalleled internal information on industrial processes used in many sectors. This book showcases a selection of papers at the forefront of the latest developments in such technologies

Damage tomography as a state estimation problem : crack detection using conductive area sensors

Typically, structural damage tomography (SDT) approaches aim to reconstruct a parameter field containing damage information from distributed data by solving an iterative inverse problem. Often, there are two shortcomings in adopting such an approach: (a) the high computational expense and (b) temporal information is inadequately used. In principle, both issues may be alleviated by approaching SDT as a state-estimation problem – i.e. treating the reconstruction problem as a temporally-evolving stochastic process. In this letter, we study the feasibility of state estimates in SDT. For this, we use an extended Kalman filter (EKF) for electrical resistance tomography (ERT) imaging of progressive cracking on an experimentally-tested reinforced concrete beam with an applied surface area sensing skin. In the investigation, we quantitatively analyze the effect of including multiple temporal data sets and corroborate EKF-ERT reconstructions with standard and advanced ERT approaches. It is shown that increasing the amount of temporal data significantly improves the quality of EKF-ERT reconstructions, which compare favorably with the standard and advanced ERT approaches. In addition, for the data sets used herein, the EKF-ERT regime computed seven reconstructions approximately 50-100 times faster than the standard and stacked approaches required to reconstruct one image, respectively