Boundary estimation with gravitational search algorithm based optimization in electrical impedance tomography

Abstract

Electrical impedance tomography (EIT) is a noninvasive image reconstruction method. It reconstructs the cross-sectional conductivity distribution of the domain. EIT is applied in various areas of applications such as medical, industrial, and geophysical. However, it suffers from poor spatial resolution due to the ill-posed and non-linear nature of the problem. Boundary or shape estimation is the alternative approach to solve this poor resolution problem. In this approach, the number of unknowns to be estimated is reduced which improves the spatial resolution. The conductivity of the closed disjoint region of the domain is assumed to be known as prior for the boundary estimation. In this thesis, for the closed boundary, the complex shape is defined by the Fourier series coefficients and the shape estimation is done with a heuristic algorithm. In this work, we have presented three scenarios for the boundary estimation in EIT.

The first study is the estimation of the bladder boundary in the pelvic domain. In this, the boundary is estimated by a heuristic algorithm gravitational search algorithm (GSA). The estimation of the bladder using the noninvasive method is necessary for paraplegia patients. These patients are unable to discharge urine at the right time due to a weaker sensation for bladder volume. If the urine is not discharged in time, then the bladder size will increase and affect the neighboring organs and tissues. Size estimation of the bladder with EIT can clarify the bladder status. The bladder is a nonuniform structure with a complex shape; therefore, higher-order Fourier series is needed to represent the true shape. Estimating higher-order Fourier coefficients by a conventional modified Newton-Raphson (mNR) algorithm does not give the desired performance. GSA is proposed in this work to estimate the Fourier series coefficients as it is known for solving optimization problems in high-dimensional search space. Also, GSA has fast convergence and does not require the computation of Jacobian. Numerical experiments and phantom studies are performed to estimate the bladder size and it is compared with the estimated result by mNR.

The second case is the estimation of the defect on the single-layer graphene sheet by PSOGSA. A PSOGSA is a hybrid algorithm that is the combination of particle swarm optimization (PSO) and GSA. Recently, graphene has gained a lot of attention in the electronic industry due to its unique properties and can overcome the limits of miniaturization making way for novel devices in the field of electronics. For the development of new device applications, it is necessary to grow large wafer-sized monolayer graphene. Among the methods to synthesize large graphene films, chemical vapour deposition (CVD) is one of the promising and common techniques but defects such as cracks, holes, or wrinkles are hard to avoid. Electrical impedance tomography (EIT) can be used to detect those defects on a graphene sheet. The conductivity is assumed to be known as prior and the geometry of the defect is estimated. These defect geometries are defined by truncated Fourier series coefficient which can represent the complex shapes. Numerical and experimental studies are done for graphene characterization and the results showed that the proposed PSOGSA has good performance in locating the defects present on a graphene surface.

The third is the open boundary case where the interlayer boundary of the subsurface is estimated. Subsurface topology estimation is important for the geophysical survey. The subsurface region can be approximated as piece-wise separate regions with constant conductivity in each region; therefore, the conductivity estimation problem is transformed to estimate the shape and location of the layer boundary interface. Each layer interface boundary is treated as an open boundary that is described using front points. A DNN model is used to estimate the front points describing the multi-layer interface boundaries. This DNN model is tuned for hidden layer nodes using PSOGSA. The PSOGSA tuned DNN model is trained for interlayer boundary reconstruction using training data that consists of pairs of voltage measurements of the subsurface domain. The tuned DNN model estimation result is compared with the 7-layer DNN model. The study on all three cases shows the proposed method has a better estimation result than the compared method.