Electrical capacitance tomography using an accelerated proximal gradient algorithm

Abstract

Image reconstruction in electrical capacitance tomography requires a solution of an ill-posed inverse problem. This paper applies an accelerated proximal gradient (APG) singular value thresholding algorithm, which is originally proposed for the matrix completion problem, to image two-phase flow. Aiming to improve the image quality, a nuclear norm-based regularization technique is adopted to treat the ill-posedness of the inverse problem, and a simple updating technique is used to update the sensitivity matrix. Both typical and complicated distributions (e.g., "sun-rise" and cross-shape), have been examined based on a 16-electrode configuration. The results showed that the APG algorithm with updated sensitivity matrix could produce higher quality images when compared to the algorithm based on the typical sensitivity matrix. Both simulation and experiment results indicate that the algorithm developed has been able to achieve good quality reconstructed images with relativity fast computation speed for the cases tested in this paper.

Investigation of gas–solid bubbling fluidized beds using ECT with a modified Tikhonov regularization technique

“…Equation is commonly employed to calculate the sensitivity matrix: where defines the sensitivity between the i th and j th electrodes at the location of the pixel p(x,y) and φ i (x,y) and φ j (x,y) are the potential distributions inside the sensing domain when the i th and j th electrodes are excited by applying voltages of V i and V j , respectively.…”

“…The results of the Tikhonov regularization are basically satisfied in the central area, even with multiple objects like four rods and four bubbles. However, the biggest problem associated with the Tikhonov regularization is that some unphysical artifacts appear in the near‐wall region, especially in the case of low‐permittivity materials presenting in a high‐permittivity background, which is exactly the case in a gas–solid bubbling fluidized bed, where discrete bubbles are dispersed in a continuous emulsion phase with a shell of solid particles in which solid concentration increases continuously . When the Landweber iteration is used, the best images can be obtained in almost all cases; however, it can only be applied as an off‐line reconstruction method due to its slow reconstruction speed.…”

“…In general, a generic sensitivity matrix calculated based on a vacuum permittivity distribution is used for both single‐step and iterative algorithms, while it will change with different permittivity distributions because of the “soft‐field” nature of ECT . Using a sensitivity matrix updated by the actual permittivity distribution, Xue et al found that image quality reconstructed using the Tikhonov regularization could be improved and that the artifacts in the reconstructed images could be reduced. However, updating the sensitivity matrix is not practical for on‐line image reconstruction.…”

“…The reasons are twofold: (1) the true distribution is unknown in real applications and (2) updating the sensitivity matrix would take much more time . Therefore, the method of Xue et al is not feasible for on‐line ECT measurements.…”

Performance analysis of a digital capacitance measuring circuit

“…[1][2][3][4] Challenges in the design of a capacitance measuring circuit are (1) the capacitance to be measured is usually very small and varies in a wide range; (2) the stray capacitance is usually much larger than the change in capacitance; (3) high speed measurement is required for some applications, such as multiphase flow measurement and flame monitoring by electrical capacitance tomography (ECT). [5][6][7][8] A number of capacitance measuring circuits have been reported in the past. [9][10][11][12] Among them, the charge-discharge circuit and AC-based circuit are most widely used because they are stray-immune, i.e., the stray capacitance would not affect the measurement.…”