Preconditioned Landweber iteration algorithm for electrical capacitance tomography

Abstract Electrical capacitance tomography (ECT) has been used to obtain the cross-section images of processes with different dielectric materials inside. Image reconstruction with ECT is to retrieve the permittivity distribution of materials inside the sensor from the capacitance measurements. Algorithms for ECT image reconstruction should be both precise and fast in order to satisfy the requirements of real-time monitoring of the dynamic behavior of processes. Several algorithms have been developed for ECT image reconstruction. The Landweber iteration is the most precise one. However, the low convergence rate of the Landweber iteration limits its application for on-line imaging. This paper introduces an iterative algorithm based on the Landweber method with preconditioning for ECT image reconstruction. A preconditioner, which is equivalent to a filter, is applied to the Landweber iteration. The convergence of this algorithm is analyzed. Its performance is evaluated by using simulated and experimental data corresponding to certain typical permittivity distributions. Preliminary numerical and experimental results show that this algorithm converges more rapidly than the Landweber iteration without preconditioning. Therefore, image reconstruction iteration can be accelerated, which makes on-line quantitative image reconstruction possible.

[1]  Roland Martin,et al.  Reconstruction of permittivity images from capacitance tomography data by using very fast simulated annealing , 2004 .

[2]  Supachai Bangliang,et al.  The use of simultaneous iterative reconstruction technique for electrical capacitance tomography , 2000 .

[3]  R. A. Williams,et al.  Chapter 1 – Introduction to process tomography , 1995 .

[4]  O. Strand.  Theory and methods related to the singular-function expansion and Landweber's iteration for integral equations of the first kind , 1974 .

[5]  Wuqiang Yang,et al.  Optimization of an iterative image reconstruction algorithm for electrical capacitance tomography , 1999 .

[6]  Lihui Peng,et al.  Image reconstruction algorithms for electrical capacitance tomography , 2003 .

[7]  Tomasz Dyakowski,et al.  Application of capacitance tomography to gas-solid flows , 1997 .

[8]  Tomasz Dyakowski,et al.  Process tomography - the state of the art , 1998 .

[9]  Wuqiang Yang,et al.  Principles and Industrial Applications of Electrical Capacitance Tomography , 1997 .

[10]  Wuqiang Yang,et al.  Prior-online iteration for image reconstruction with electrical capacitance tomography , 2004 .

[11]  William R B Lionheart,et al.  Reconstruction Algorithms for Permittivity and Conductivity Imaging , 2001 .

[12]  Wuqiang Yang,et al.  Hardware design of electrical capacitance tomography systems , 1996 .

[13]  Ø. Isaksen,et al.  A review of reconstruction techniques for capacitance tomography , 1996 .

[14]  Brian S. Hoyle,et al.  Electrical capacitance tomography for flow imaging: system model for development of image reconstruction algorithms and design of primary sensors , 1992 .

[15]  Dieter Mewes,et al.  Recent developments and industrial/research applications of capacitance tomography , 1996 .

[16]  Wuqiang Yang,et al.  An image-reconstruction algorithm based on Landweber's iteration method for electrical-capacitance tomography , 1999 .

[17]  Richard A Williams,et al.  Process tomography: a European innovation and its applications , 1996 .

[18]  L. Landweber.  An iteration formula for Fredholm integral equations of the first kind , 1951 .

[19]  Lihui Peng,et al.  Using Regularization Methods for Image Reconstruction of Electrical Capacitance Tomography , 2000 .

[20]  G. E. Fasching,et al.  Capacitive system for three-dimensional imaging of fluidized-bed density , 1994 .

[21]  Maurice Beck,et al.  Tomographic imaging of two-component flow using capacitance sensors , 1989 .

[22]  L. Trefethen,et al.  Numerical linear algebra , 1997 .