Corrected L-curve electrical tomography reconstruction method based on second-order differential

Abstract

The invention provides a corrected L-curve electrical tomography reconstruction method based on the second-order differential. The method is suitable for bubble flow tomography and includes the steps that according to a measured field domain, a relative boundary measured value vector b and a sensitivity matrix A which are needed for reconstruction are acquired; through Tikhonov regularization, an L-curve is calculated and drawn; whether a local inflection point exists in the L-curve or not is judged; if the local inflection point does not exist, an optimally-selected regularization coefficient is determined through an L-curve method; if the local inflection point exists, an optimally-selected regularization coefficient is determined through the corrected L-curve method. The method includes the steps that the local inflection point of the curve is determined by calculating a second largest peak value of the L-curve second-order differential, and the regularization coefficient corresponding to the local inflection point serves as the optically-selected coefficient; the regularization coefficient is substituted into Tikhonov regularization, and an image reconstruction inverse problem is solved; imaging is conducted. By the adoption of the method, the electrical tomography inverse problem can be accurately solved, and image reconstruction quality is improved.

Description

technical field

[0001] The invention belongs to the technical field of electrical tomography, and relates to the realization of image reconstruction by using a Tikhonov regularization method, in particular to the optimization and selection of Tikhonov regularization coefficients based on an L-curve. Background technique

[0002] Multiphase flow plays a very important role in industrial production and scientific research. They often appear in industrial processes such as power, chemical industry, petroleum, nuclear energy, and metallurgical engineering. They involve safety and economic issues. people challenged. The flow patterns of multiphase flow in pipelines with different geometric and dynamic characteristics are called flow patterns, which can be qualitatively described by the shape of components or phases. The common flow patterns in two-phase flow include bubbly flow, elastic flow flow, annular flow, etc.

[0003] Electrical tomography (Electrical Tomography, ET) is ...

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