A nonlinear image reconstruction algorithm for electrical capacitance tomography

We present a total-variation-based image reconstruction algorithm for electrical capacitance tomography. This is a nonlinear iterative algorithm designed to minimize both the data error and the total variation of the permittivity, with iterations updated by the projected Gauss?Newton steps. We present numerical examples to illustrate the effectiveness of the algorithm in reconstructing permittivity images from both noise-free and noisy capacitance data.

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

[2]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[3]  Weifu Fang,et al.  Matrix properties of data from electrical capacitance tomography , 2005 .

[4]  Willis J. Tompkins,et al.  Comparing Reconstruction Algorithms for Electrical Impedance Tomography , 1987, IEEE Transactions on Biomedical Engineering.

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

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

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

[8]  Trevor A. York.  Status of electrical tomography in industrial applications , 2001, J. Electronic Imaging.

[9]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[10]  David Isaacson,et al.  Electrical Impedance Tomography , 1999, SIAM Rev..

[11]  Tomasz Dyakowski,et al.  Applications of electrical tomography for gas-solids and liquid-solids flows : a review , 2000 .

[12]  W. Ziemer.  Weakly differentiable functions , 1989 .

[13]  David C. Dobson.  Recovery of Blocky Images in Electrical Impedance Tomography , 1997 .

[14]  W J Tompkins,et al.  A regularised electrical impedance tomography reconstruction algorithm. , 1988, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.