Journal
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
Volume 60, Issue 3, Pages 900-907Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIM.2010.2045255
Keywords
Calderon's method; conformal transformation; direct algorithm; electrical capacitance tomography (ECT); square cross section
Funding
- National Basic Research Program of China [2009CB724001]
- National Natural Science Foundation of China [61001135, 60910001]
- New Century Excellent Researchers Funding Scheme [NCET-07-0046]
- China Postdoctoral Science Foundation [20080430296, 200902045]
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Calderon's method was generalized to electrical capacitance tomography (ECT) for sensors of square cross sections in this paper. It is a direct algorithm of image reconstruction, as neither matrix inversion nor an iterative process is required for image reconstruction. Since the major calculations are implemented in terms of a circular region, complicated calculations required by Calderon's method for a noncircular cross section are avoided. A unique conformal transformation was used to establish a map from a circular region to a square. Results were obtained for a sensor of square cross section by using the conformal transformation. Two approximations of the scattering transform used in Calderon's method were compared with simulated data. The Gauss-Legendre quadrature was applied to provide a fast-speed and high-quality image reconstruction. The reconstructed results validated the feasibility and effectiveness of the proposed treatment of Calderon's method in ECT with a sensor of noncircular cross section.
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