Abstract
Electrical capacitance tomography (ECT) has great application potential in multiphase process monitoring, and its visualization results are of great significance for studying the changes in two-phase flow in closed environments. In this paper, compressed sensing (CS) theory based on dictionary learning is introduced to the inverse problem of ECT, and the K-SVD algorithm is used to learn the overcomplete dictionary to establish a nonlinear mapping between observed capacitance and sparse space. Because the trained overcomplete dictionary has the property to match few features of interest in the reconstructed image of ECT, it is not necessary to rely on the sparsity of coefficient vector to solve the nonlinear mapping as most algorithms based on CS theory. Two-phase flow distribution in a cylindrical pipe was modeled and simulated, and three variations without sparse constraint based on Landweber, Tikhonov, and Newton-Raphson algorithms were used to rapidly reconstruct a 2-D image.
Highlights
In industrial processes, it is often necessary to analyze information about two-phase flow in a pipeline or closed container
The classical orthonormal basis is better for some features of the image but is negative for two-phase distributions, because two-phase flow is always varied in a complex industrial process
To solve the above problems, this paper introduces the idea of compressed sensing (CS) and dictionary learning to electrical capacitance tomography [4] (ECT) theory [28,29], which is called DCS-ECT
Summary
It is often necessary to analyze information about two-phase flow in a pipeline or closed container. The objective of ECT is to obtain projection data through a sensor array fixed on the outer wall of a pipe or container, and use an algorithm to obtain the internal permittivity distribution, which is presented with 2-D or 3-D images. The classical orthonormal basis is better for some features of the image but is negative for two-phase distributions, because two-phase flow is always varied in a complex industrial process. Different flow patterns are used to train the transform basis so that it matches the different features of the permittivity distribution as much as possible to improve the accuracy of the reconstructed image [30]. The overcomplete dictionary is flexible and adaptive It captures different features of the signal through multiple atoms and improves the redundancy of the transform system to approximate the original signal.
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