A Sparse Reconstruction Method for Electrical Tomography Based on Firm Threshold Iteration

Abstract

The invention relates to an electrical tomography sparse reconstruction method based on Firm threshold iteration, wherein the method is used for electrical tomography of non-continuous medium. According to the method, an electrical tomography problem is seen for settling a linear ill-posed problem, and an objective function is determined. The reconstruction method comprises the steps of according to a tested field domain, acquiring a relative boundary measured value vector and a sensitivity matrix required for reconstruction; setting an initial parameter; performing acceleration pretreatment; according to a regularization parameter which is calculated in a previous cycle, namely a threshold value which is selected in threshold iterative calculation in this time, and performing threshold iterative calculation on a previous iteration result after acceleration processing; calculating the number of non-zero elements in a solution which is obtained in iteration in this time, and updating sparseness; determining whether iteration is finished; and performing imaging according to a gray value which is obtained through final solving. The electrical tomography sparse reconstruction method improves applicability and usability of an algorithm and furthermore expands application range of a sparse reconstruction method.

Description

technical field [0001] The invention belongs to the technical field of electrical tomography, and relates to a sparse regularization method to realize image reconstruction and a threshold iterative solution method. Background technique [0002] Electrical tomography (Electrical Tomography, ET) appeared in the late 1980s. It is a process tomography technology based on the sensitive mechanism of electrical properties. It is based on the measurement of the electrical properties (conductivity / Permittivity / complex admittance / permeability) distribution information is imaged, and then the distribution information of the medium is obtained. Electrical tomography mainly includes electrical resistance tomography (Electrical Resistance Tomography, ERT), electrical capacitance tomography (Electrical Capacitance Tomography, ECT), electrical impedance tomography (Electrical Impedance Tomography, EIT) and electromagnetic tomography (Electrical Magnetic Tomography). Tomography, EMT). Ele...

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Problems solved by technology

[0009] The purpose of the present invention is to propose a new sparse regularization objective function based on a new threshold iteration method, and update the regularization parameters adaptively to solve the sparse reconstruction problem of electrical tomography

Based on the Firm iterative threshold method, the present invention solves the new sparse regularization objective function, and adaptively updates the regularization parameter value in each step of the iterative calculation according to the field distribution, so as to solve the problem of difficult selection and calculation of the sparse regularization parameters The problem of slower speed, without changing the regularization parameters, can still get high-quality images in image reconstruction with different field distributions; it also solves the problem of L 1 Regularize the problem that the image reconstruction result is too sparse and the reconstructed image is smaller than the real distribution, and improve the solution accuracy and image quality of the inverse problem of electrical tomography

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