Image reconstruction for electrical capacitance tomography exploiting sparsity

We present a new image reconstruction method for Electrical Capacitance Tomography (ECT) by exploiting the sparsity of reconstructed images. ECT image reconstruction is generally ill-posed because the number of measurements is small whereas the image dimensions are large. Inspired by recent developments in Compressive Sensing (CS), given the sparsity of the signal (image), our 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 apply an efficient GPSR (Gradient Projection for Sparse Reconstruction) algorithm to reconstruct the sparse signal under DCT basis (GPSR-DCT). Our results on real data show that the proposed GPSR-DCT algorithm can better preserve object boundary and shape, as compared to a representative state-of-the-art ECT image reconstruction algorithm, Projected Landweber Iteration with Linear Back Projection initialization (LBP-PLI).