Electrical capacitance tomography using an accelerated proximal gradient algorithm

Image reconstruction in electrical capacitance tomography requires a solution of an ill-posed inverse problem. This paper applies an accelerated proximal gradient (APG) singular value thresholding algorithm, which is originally proposed for the matrix completion problem, to image two-phase flow. Aiming to improve the image quality, a nuclear norm-based regularization technique is adopted to treat the ill-posedness of the inverse problem, and a simple updating technique is used to update the sensitivity matrix. Both typical and complicated distributions (e.g., "sun-rise" and cross-shape), have been examined based on a 16-electrode configuration. The results showed that the APG algorithm with updated sensitivity matrix could produce higher quality images when compared to the algorithm based on the typical sensitivity matrix. Both simulation and experiment results indicate that the algorithm developed has been able to achieve good quality reconstructed images with relativity fast computation speed for the cases tested in this paper.