A dynamic oppositional biogeography-based optimization approach for time-varying electrical impedance tomography

Abstract

Dynamic electrical impedance tomography-based image reconstruction using conventional algorithms such as the extended Kalman filter often exhibits inferior performance due to the presence of measurement noise, the inherent ill-posed nature of the problem and its critical dependence on the selection of the initial guess as well as the state evolution model. Moreover, many of these conventional algorithms require the calculation of a Jacobian matrix. This paper proposes a dynamic oppositional biogeography-based optimization (OBBO) technique to estimate the shape, size and location of the non-stationary region boundaries, expressed as coefficients of truncated Fourier series, inside an object domain using electrical impedance tomography. The conductivity of the object domain is assumed to be known a priori. Dynamic OBBO is a novel addition to the family of dynamic evolutionary algorithms. Moreover, it is the first such study on the application of dynamic evolutionary algorithms for dynamic electrical impedance tomography-based image reconstruction. The performance of the algorithm is tested through numerical simulations and experimental study and is compared with state-of-the-art gradient-based extended Kalman filter. The dynamic OBBO is shown to be far superior compared to the extended Kalman filter. It is found to be robust to measurement noise as well as the initial guess, and does not rely on a priori knowledge of the state evolution model.

B-Spline-Based Sharp Feature Preserving Shape Reconstruction Approach for Electrical Impedance Tomography

“…Such processes usually involve reformulating the problem of conductivity reconstruction as an inverse problem for a special geometrical representation of embedded objects. Among the approaches that have been applied are level sets [11]- [14], truncated Fourier series [15]- [18], shape perturbation method [19] and geometric constraint method [20], etc.…”

Shape Reconstruction Using Boolean Operations in Electrical Impedance Tomography

“…Factorization method [20]- [24] Upper and lower range bound of conductivity can be treated separately; has a chance to place fewer demands on the data since it only locates an embedded inhomogeneity Need to know the background conductivity in a priori; size estimation of the inclusion is biased; does not give the conductivity value inside the inclusion Linear sampling method [25], [26] Able to handle any number of discrete conductivity values provided the anomalies are separated from each other by the background Unable to give an indication of the conductivity level but rather locates the jump discontinuities in conductivity; Application to experiment data is still at an early stage Monotonicitybased method [27]- [30] Good performance for detecting convex shapes, and it is often possible to separate inclusions quite well in the presence of noise For non-convex shapes, one usually gets something that resembles a convex approximation to the shape, either because measurement noise and modeling errors or because of the restricted amount of current patterns; Need to know the background conductivity as a priori; Enclosure based method [31], [32] Good performance for detecting convex shapes Need to know the background conductivity as a priori; The performance for non-convex shape estimation is biased; Application to experiment data is still at an early stage Direct parameterization methods Shape perturbation method [33] Direct parameterization for interfacial (close) boundary; Dimension reduction Need to know the number of inclusions as a priori, and hard to handle topological changes; With possibility to be non-convergent; Sensitive to initial guesses Fourier series based methods [34], [35]…”

“…To do this in practice, we formulate the reconstruction problem as an inverse problem using a geometrical representation of embedded objects. Among the shape-based approaches that have been applied are, e.g., factorization methods [20]- [24], linear sampling methods [25], [26], monotonicity-based methods [27]- [30], enclosure based methods [31], [32], shape perturbation method [33], truncated Fourier series [34], [35], direct parameterization methods [36]- [38], geometric constraint methods [39], level set methods [40]- [45], and moving morphable components (MMCs) based method [46].…”

Nonstationary Shape Estimation in Electrical Impedance Tomography Using a Parametric Level Set-Based Extended Kalman Filter Approach

“…The parameterization significantly decreases the dimension of the problem, and thus, the problem becomes less computationally intense and less ill-posed. For example, truncated Fourier series was extensively applied for nonstationary close boundary estimation problems in [30], [35], [39]. Another regime for nonstationary boundary estimation, based on the particle filter approach, was studied in [40], where B-spline curves were used to represent the boundaries.…”