Study Of Difference Image Reconstruction Algorithms For Electrical Impedance Tomography

Electrical Impedance Tomography(EIT)is an imaging technique,aiming to reconstruct the conductivity distribution based on boundary data.EIT is potential for the applications of medicine science,industry and geology,but its relatively low spatial resolution restricts the development severely.The ill-posedness and ill-condition of the math problem of EIT is the main cause of the relatively low spatial resolution.The absolute reconstruction algorithm,whose target is to reconstruct the absolute conductivity value of the object,cannot address the above two problems and obtain the satisfactory spatial resolution,so the difference reconstruction method is employed.The difference EIT imaging,which reconstructs the change of the conductivity distribution,is able to remove the systematic errors and additive noise,improving the spatial resolution.The difference EIT imaging can be divided into the time difference EIT imaging and frequency difference EIT imaging.The time difference EIT imaging technique is to reconstruct the conductivity difference between two moments;the frequency EIT imaging technique is to reconstruct the conductivity difference between two frequencies.The difference EIT imaging cannot match the practical requirements even its spatial resolution is superior to the absolute EIT imaging.Thus,the studies of improving the spatial resolution of the time difference EIT imaging and frequency difference EIT imaging,and by using reconstruction correction have been conducted in this thesis.The main contributions of the thesis are shown as following:The thesis proposes a time difference EIT reconstruction method based on Region Of Interest(ROI).This method applies the improved graph cut method to obtain ROI,and weights the regularisation matrix using ROI.The proposed method significantly improves the spatial resolution of the EIT reconstruction with the trivial extra time cost.ROI,as prior knowledge,has been employed to enhance the spatial resolution of EIT reconstruction.However,the current approaches to obtain EIT require a lot of EIT images,and the methods of using ROI disobey its role as prior knowledge.The proposed algorithm utilises a discrete optimisation method-graph cut method based on the binary property of ROI,and improves this method to overcome the nonsubmodularity in order to generate the ROI fast;the proposed algorithm weights the regularisation matrix by using ROI according to the property that ROI should be treated as prior knowledge.The proposed method demonstrates the better performance than the traditional one across all noise levels,and shows the higher spatial resolution in the experiments of the in vivo lung and breast data,simulations of epilepsy and the experiments of epilepsy of a human head model with skull.Tests verify that this method can reduce 20% to 40% total error compared to the traditional method.A multi-frequency difference EIT reconstruction algorithm based on the Total Variation(TV)regularisation is designed.This algorithm improves the traditional multi-frequency EIT method based on the fraction model through employing the TV regularisation technique.The contrast of the edges between the targets and background is significantly increased due to the TV regularisation,and the spatial resolution is improved as well.The traditional multi-frequency EIT algorithm based on the fraction model cannot reconstruct the edges clearly because of the application of the L2 norm regularisation technique.Therefore,the proposed algorithm combines the primal-dual interior point method and gradient projection method,to address the inverse problem based on the fraction model,improving the spatial resolution through increasing the edge contrast.Tests verify that the proposed method has better peformance across all noise levels,although it converge slower than the traditional method.Furthermore,this method demonstrates higher spatial resolution in the tank experiments and the stroke simulations.It is testified that the proposed method can reduce approximately 20% image noise and 30% shape error.The thesis proposes a correction method to compensate the inhomogeneous sensivity.This correction methd improves the spatial resolution by compensating the inhomogeneous sensivity caused by the Jacobian inverse matrix and the inequivilent noise distribution.The elements have various sensivities due to the different positions,and the information contained in the elements with low sensivity is easy to be covered by the elements with high sensivity,which reduces the spatial resolution of the EIT reconstruction.The proposed method calculates the sensivities caused by the Jacobian inverse matrix and inequivilent noise distribution,and applies the sensivities to weighting reconstruction results in order to compensate the inhomogeneous sensivity.A fast correction approach is also designed to reduce the computational and time cost.The performance of this method for different noise levels and regularisation techniques is evaluated through the simulations and experiments of epilepsy.The method is investigated in the in vivo rat experiment as well.Tests verify that the proposed method is important for the EIT applications on the high noise and complicated environments.