Date of Award
Master of Science (MS)
School of Mathematical and Statistical Sciences
Electrical impedance tomography, also known as EIT, is a type of diffusive imaging modality that is non-invasive, radiation-free, and cost-effective for recovering electrical properties within a closed domain from surface measurements. The process involves injecting electrical current into a set of electrodes to measure the voltage on the smooth surface of the domain. The recovered EIT images show how well different materials or tissues within the domain conduct or impede electrical flow, which is helpful in detecting and locating anomalies. For the EIT inverse problem, it is challenging to recover reliable and resolvable electrical conductivity images since it is highly nonlinear and severely ill-posed, especially when the data is corrupted with noise.
To address this issue, we propose (1) a wavelet-based modified Gauss-Newton (WGN) method that uses wavelets as a form of regularization and parameter reduction. In (1), we enforce regularization through the use of wavelet coefficients by projecting the original formulation to the wavelet domain and then only retaining the wavelet coefficients of highest power. The projected wavelet formulation is of a smaller dimension and, therefore, shows promise in improving the ill-posedness of the EIT inverse problem. Different wavelet families are implemented to capture localized features, smoothness, and irregularities within the domain.
In addition, we also propose (2) a novel deep learning algorithm to solve the EIT inverse problem. In (2), we develop a deep neural network (DNN) with multiple transposed convolutional layers and activation functions to recover the EIT images. The DNN is first trained on a large set of EIT images and data, and then we recover EIT images in real-time from the trained DNN. We compare the image reconstructions from the DNN with a benchmark algorithm. For model validation, we employed a set of synthetic examples with various anomalies to test the performance and efficacy of both the DNN and WGN method. The results from both methods show promise in improving EIT image reconstructions.
Kupis, Shyla Rae, "Methods for the Electrical Impedance Tomography Inverse Problem: Deep Learning and Regularization with Wavelets" (2021). All Theses. 3543.