Research On The Uncertainty Quantification Of Eit Forward Problem

In electrical impedance tomography(EIT),the uncertainty of dielectric conductivity distribution will affect the calculation results of the forward problem,and then affect the accuracy of image reconstruction.Therefore,it is of great significance to study the influence of conductivity change on the uncertainty of EIT.In this thesis,the four-layer concentric circular head model is selected as the research object.Considering that the conductivity variables of the four layers are not fixed,Monte Carlo Simulation(MCS)and Non-Intrusive Polynomial Chaos Expansion(NIPCE)are used to uncertainty analyze the forward problem of EIT to obtain the probability distribution of the boundary voltage,and the accuracy and efficiency of the two methods are compared.When MCS method is used,it is assumed that the conductivity distribution obeys uniform or normal distribution.When the sample number reaches 10,000 times,the convergence is achieved and enough accuracy is obtained,and the probability distribution curve of the boundary voltage tends to normal distribution.When the Quasi-Monte Carlo(QMC)method is adopted,the mean change of boundary voltage tends to be stable when the sample size reaches only 1000 times,and the probability distribution is approximately normal.When NIPCE method is used,it is assumed that the conductivity distribution obeys uniform distribution,the curve of probability distribution function is gradually close to that obtained by MCS method with the increase of polynomial expansion order,the mean and standard deviation of boundary voltage are also gradually close to that obtained by MCS method,and the accuracy is obviously improved.When the expansion order is 4,the results are very close to the MCS method.It can be seen from the research results that both MCS method and NIPCE method can obtain the boundary voltage probability distribution with high accuracy.MCS method has higher accuracy,but the calculation amount is much larger.And NIPCE method has high calculation accuracy and high calculation efficiency as well.In addition,the sensitivity analysis method based on variance is combined in this thesis,using the results obtained by Monte Carlo method and non-interference chaos polynomial expansion method,the sensitivity indexes of EIT four-layer concentric circle model are calculated.The results show that in the input parameters of four-layer concentric circle model,the sensitivity index of the head cortex is the highest,followed by the skull layer,the brain layer and the cerebrospinal fluid layer from higher to lower.