Electrical Capacitance Tomography: A compressive sensing approach

We present a new image reconstruction method for Electrical Capacitance Tomography (ECT). ECT image reconstruction is generally ill-posed because the number of measurements is small whereas the image dimensions are large. Here, Compressive Sensing is used to provide better reconstruction from the small number of measurements. Given the sparsity of the signal (image), the idea is to apply an efficient and stable algorithm through L1 regularization to recover the sparse signal with sufficient measurements that have cardinality comparable to the sparsity of the signal. In this paper, we present Total Variation (TV) regularization for ECT image reconstruction, and apply an efficient Split-Bregman Iteration (SBI) approach to solve the problem. We propose a joint metric of positive re-construction rate (PRR) and false reconstruction rate (FRR) to evaluate image reconstruction performance. The results on both synthetic and real data show that the proposed TV-SBI method can better preserve the edges of images and better resolve different objects within reconstructed images, as compared to a representative state-of-the-art ECT image re-construction algorithm, Projected Landweber Iteration with Linear Back Projection initialization (LBP-PLI).