Research On EIT Forward And Inverse Problems Based On Support Vector Machine

The purpose of Electrical Impedance Tomography(EIT) which is a non-invasive method is to obtain the internal impedance distribution of a bounded region by measuring the surface voltages when currents are injected into the target region. Traditional methods of EIT are iterative methods. These methods not only had lower accuracy but also cost so much time that they can not meet the need of real-time. Machine learning is an off-line learning model. After the training process is finished, i.e., learning function is obtained, machine learning can get results very fast after samples are fed into the learning function.As a kind of machine learning method, Neural Network (NN) has good performances in many applications. But it is not a good learning machine since it cannot control generalization ability well following the Empirical Risk Minimization (ERM) principle. Using Wavelet Neural Network (WNN) to estimate head tissue conductivity, lower learning accuracy and generalization ability are presented, therefore a more effective method is needed.SLT based on the solid theoretical foundation, provides a new framework for the general learning problem of small-sample size statistics. SVM based on SLT, can overcome the problems NN encounters. The main advantages can be described as follows: Firstly, it aims at getting the optimal solution under the circumstance of small-sample size, not infinite-sample size. Secondly, the algorithm can transform the problem into a Quadratic Programming (QP) problem. Theoretically, it will obtain a global optimal solution so that it can overcome the local minimums problem of NN. In addition, the algorithm transforms the real problem into the high dimensional feature space and realizes non-linear discrimination in the original space through constructing linear discriminating function in the high dimensional feature space. Finally, based on SRM, it can effectively overcome over-fitting and under-fitting problems and has greater generalization ability. Consequently using SVM to solve EIT inverse problem may get good results.SVM is considered as a two-layer learning machine. Multi-Layer SVM (MLSVM) is proposed in this paper and it is used to solve Ordinary Differential Equations (ODEs). The method of using SVM to solve primitive function of integrable function is proposed and a simulation for solving primitive function of Radial Basis Function (RBF) is given in this paper. The essence of EIT forward problem is to solve Partial Differential Equations (PDEs). After general methods for solving ODEs and PDEs have been investigated, a method of using SVM to solve EIT forward problem is proposed. The method has been successfully tested on EIT forward problem and has yielded satisfactory results.Estimating head tissue conductivity for each layer is a high dimensional, non-linear and ill-posed problem which is part of EIT inverse problem. It is also a multi-input and multi-output system. A method using SVM is proposed to solve the problem in the multi-input and multi-output system named Multi-SVM (MSVM). Tissue conductivity for each layer in 2-D and 3-D head model is estimated effectively by MSVM. Compared with wavelet neural network, MSVM not only obtains higher accuracy of learning but also has greater generalization ability and faster computing speed as our experiment demonstrates.It is very difficult to select parameters by manual for SVM which can be seen as an optimization problem. Genetic Algorithm (GA) is introduced to select parameters for SVM. Then Genetic Support Vector Regression (GSVR) is proposed in this paper. Tissue conductivity for each layer in 2-D head model is estimated effectively by GSVR. Our experiment shows that GSVR has higher learning accuracy and greater generalization ability compared with selecting parameters by manual for SVM.