Transform learning for computational imaging

Abstract

Electrical Impedance Tomography (EIT) is an imaging modality aimed at finding the electrical properties in a region of interest. It has shown promise in various applications across medical and industrial fields thanks to its favourable properties such as rapid reconstruction, non-invasive imaging, portability and low cost. The EIT inverse problem is ill-posed, thus, a regularization term is usually included in the optimization model to impose any a priori information or assumptions on the reconstructed image. Sparsity-promoting regularizers assume that the image is approximately sparse under a certain transform domain, such as Wavelets. They have been used in EIT and have generally performed well. To further exploit the sparsity property in EIT, we incorporate the recent method of Transform Learning (TL), which is a self-supervised learning method to adapt a sparsifying transform to the given data, into EIT image reconstruction. The new method, called TL-EIT, is formulated under the assumption of sparsity of the patches of the reconstructed image under the learned transform. We propose an efficient block coordinate descent algorithm which finds the optimum sparsifying transform, as well as the reconstruction. We also develop a "sliding window" scheme to incorporate time series data during multi-frame EIT image reconstruction. Using both synthetic and in-vivo data, we conduct experiments to test the TL-EIT method and compare it to EIT reconstruction methods that are currently popularly deployed. We concluded that the proposed TL-EIT method is more robust towards noise and provide reconstruction results that are more consistent to the true images with only a small latency.