Adaptive Selection of Truncation Radius in Calderon’s Method for Direct Image Reconstruction in Electrical Capacitance Tomography

Abstract

Calderon’s method has been successfully used for the direct image reconstruction in electrical capacitance tomography. In the method, the truncation radius adopted in numerical integral greatly influences the reconstruction results. In the past, the truncation radius is selected as a constant empirically according to the permittivity distribution pattern and noise level. In this paper, the influence of the truncation radius in Calderon’s method on the reconstruction results was first analyzed by numerical simulation. Then, a strategy for adaptive selection of the truncation radius was proposed. The amplitude information of the elements in the scattering transform matrix computed from the Dirichlet-to-Neumann (DN) map was used to determine the range for the truncation radius selection, and the phase information was further used to select a proper truncation radius value within this selection range. Finally, experiments were carried out to verify the strategy. Experimental results showed that small relative image error and good visual effect could be obtained by using the truncation radius selected by the proposed strategy.

Measurement of Three-Phase Holdup Distribution in Gas–Liquid–Solid Fluidized Bed Based on ERT/TMR-EMT

“…In addition to the algorithms based on the sensitivity matrix, the absolute image reconstruction algorithms, including the D-bar algorithm and the Calderon algorithm, can directly reconstruct the true distribution of electrical parameters. The Calderon algorithm is often used to solve low-contrast problems, and its overall imaging quality is not as good as the D-bar algorithm. , There has been much research on the D-bar algorithm in the field of ET. It has been proved that the D-bar algorithm can reconstruct the true value of the electrical parameters (conductivity/permittivity/permeability) of the distribution with high quality. − , Therefore, to obtain a more accurate holdup distribution image, the D-bar algorithm is used to reconstruct the true values of conductivity and permeability in this paper.…”

“…The Calderon algorithm is often used to solve low-contrast problems, and its overall imaging quality is not as good as the D-bar algorithm. 30,31 There has been much research on the D-bar algorithm in the field of ET. It has been proved that the D-bar algorithm can reconstruct the true value of the electrical parameters (conductivity/permittivity/perme- The DN map can be constructed as…”

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“…There is also another type of EIT system, EITS, also known as Multi-frequency EIT. This EITS system is composed electrical impedance spectroscopy (EIS) and EIT systems and uses frequency dependent properties of materials in the frequency domains [5,6].…”

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“…Calderon’s method has been successfully used for direct image reconstruction in ECT. In the method proposed in [11], the truncation radius adopted in the numerical integral greatly influences the reconstruction results. As our understanding of the complex value of ECT makes ECT a more versatile technology, the direct method proposed by the authors in [11], which directly reconstructs the admittivity, will become more important in near future.…”

“…In the method proposed in [11], the truncation radius adopted in the numerical integral greatly influences the reconstruction results. As our understanding of the complex value of ECT makes ECT a more versatile technology, the direct method proposed by the authors in [11], which directly reconstructs the admittivity, will become more important in near future. In [12], the authors introduce a new method to combine EIT and ultrasound tomography (UT).…”