Iterative Algorithms for Deblurring of Images in Case of Electrical Capacitance Tomography

Abstract

Electrical capacitance tomography (ECT) has been used to measure flow by applying gas-solid flow in coal gasification, pharmaceutical, and other industries. ECT is also used for creating images of physically confined objects. The data collected by the acquisition system to produce images undergo blurring because of ambient conditions and the electronic circuitry used. This research includes the principle of ECT techniques for deblurring images that were created during measurement. The data recorded by the said acquisition system ascends a large number of linear equations. This system of equations is sparse and ill-conditioned and hence is ill-posed in nature. A variety of reconstruction algorithms with many pros and cons are available to deal with ill-posed problems. Large-scale systems of linear equations resulting during image deblurring problems are solved using iterative regularization algorithms. The conjugate gradient algorithm for least-squares problems (CGLS), least-squares QR factorization (LSQR), and the modified residual norm steepest descent (MRNSD) algorithm are the famous variations of iterative algorithms. These algorithms exhibit a semiconvergence behavior; that is, the computed solution quality first improves and then reduces as the error norm decreases and later increases with each iteration. In this work, soft thresholding has been used for image deblurring problems to tackle the semiconvergence issues. Numerical test problems were executed to indicate the efficacy of the suggested algorithms with criteria for optimal stopping iterations. Results show marginal improvement compared to the traditional iterative algorithms (CGLS, LSQR, and MRNSD) for resolving semiconvergence behavior and image restoration.

Analysis of Complex Solid-Gas Flow under the Influence of Gravity through Inclined Channel and Comparison with Real-Time Dual-Sensor System

“…h(ε r ) is proportional to particle concentration while using parallel capacitors. A higher flow concentration results in larger capacitance values amongst the electrodes, and vice versa [21]. However, certain anomalies may result in inaccuracies.…”

Split Bregman algorithm based on adaptive parameter for planar array sensor imaging

“…Currently, researchers have used image reconstruction algorithms for cylindrical ECT to solve the planar array capacitance imaging inverse problem. Non-iterative algorithms are LBP (Yang and Peng 2002), Tikhonov (Peng et al 2000), iterative algorithms are Landeweber (Yang et al 1999), conjugate gradient (CG) (Jaffri et al 2021), etc and intelligent algorithms are particle swarm (Zhang and Chen 2021), neural networks (Deabes andKhayyat 2021, Jing et al 2022), etc. However, the problem of ill-posed is more serious because the planar array has fewer electrodes, resulting in less available data.…”