A Non-Linear Reweighted Total Variation Image Reconstruction Algorithm for Electrical Capacitance Tomography

Abstract

A new iterative image reconstruction algorithm for electrical capacitance tomography (ECT) is proposed which is based on iterative soft thresholding of a total variation penalty and adaptive reweighted compressive sensing. This algorithm encourages sharp changes in the ECT image and overcomes the disadvantage of the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> minimization by equipping the total variation with an adaptive weighting depending on the reconstructed image. Moreover, the non-linear effect is also partially reduced due to the adoption of an updated sensitivity matrix. Simulation results show that the proposed algorithm recovers ECT images more precisely than existing state-of-the-art algorithms and therefore is suitable for the imaging of multiphase systems in industrial or medical applications. Specifically, quantitative permittivity measurements can be recovered.