Image Reconstruction Based on Fuzzy Adaptive Kalman Filter in Electrical Capacitance Tomography
Ying Wang, Shijie Sun, Yu Tian, Jiangtao Sun, Lijun Xu
Abstract
In this article, a fuzzy adaptive Kalman filter (FAKaF)-based method was proposed for image reconstruction in electrical capacitance tomography (ECT). When the Kalman filter (KF) is applied for image reconstruction in ECT, two key parameters need to be predetermined, i.e., the observation noise covariance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> ) and the initial estimation error covariance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${P}_{0}$ </tex-math></inline-formula> ). These two parameters play significant roles in image reconstruction. For instance, a larger <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> may lead to a blurrier image. A larger <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${P}_{0}$ </tex-math></inline-formula> can cause increasing artifacts or even heavier distortion of the reconstructed image. In this work, a FAKaF was established to adjust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${P}_{0}$ </tex-math></inline-formula> using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> calculated from the measured capacitances so as to improve the quality of the reconstructed image. The implementation of the FAKaF-based reconstruction method was divided into offline and online parts. In the offline part, the Kalman gain and the corresponding fuzzy control table were precalculated, aiming to save resource consumption and improve imaging speed. Simulations and experiments were carried out to evaluate the image quality and computational cost of the proposed method. Comparisons were made with three widely-used algorithms. Results show that the proposed FAKaF-based method yields good quality images and few artifacts, needs few iterations and consumes less computational cost.