Research On Electrical Impedance Tomography Based On Trust Region Method

In the biology, different biological tissues have different electric parameters, such asresistivity and conductivity. Making use of the electrical properties and its changes, EIT formssimulation images of electric resistivity or conductivity within the body through measuring thecurrent of the surface. As a kind of functional imaging technique, EIT is non-invasive, low-cost,portable, rapid responsive and continuous-monitoring. EIT has a wider application prospect ingeophysical prospecting, environment monitoring as well as clinical medicine.Image reconstruction for EIT is a highly ill-posed nonlinear inverse problem and itsreconstructed solution has serious ill-posed property, which requires the regularization method toreduce this ill-posed character of the solution. The purpose of this paper is to improve theprecision and the speed of image reconstruction. On the basis of using traditional trust region(TR) method to realize the image reconstruction, a nonmonotonic and self-adaptive trust region(NSTR) method, a modified nonmonotonic and self-adaptive trust region (MNSTR) method anda variable arameter nonmonotonic trust region (VANTR) method are provided respectively, as aresult the precision and the speed of image reconstruction are improved greatly.Main points of this paper are as follows:1. Using the boundary element method, the solving model of the forward problem for EIT isbuilded and is also solved. The differential control equation of EIT is transformed into boundaryintegral equations, then boundary discrete and function interpolation are applied to this integralequation, and the exact expression of discrete boundary element integral is obtained by usinganalytical methods. On this basis, the system of linear equations is formed to solve the EITforward problem, and this system of equations is solved by using the QR decompositionalgorithm.2. It is the first time that the boundary image construction for EIT is realized based on thetraditional TR method. The numerical simulation experiment is performed, and the reconstructedimages of single boundary and multiple boundaries in different shapes are obtained. For theconvex boundary or the smooth concave boundary, traditional TR method can realize precisereconstruction, and has advantages of fast reconstruction speed and stable reconstructionalgorithm, etc.3. Aiming at the drawback of traditional TR method that the objective function must bedescending in each step, the trust region subproblem is solved repeatedly and the trust regionradius is adjusted mechanical, the NSTR method is provided. As a result, the accuracy of the reconstructed image and the reconstruction speed are improved largely. Compared with thetraditional TR method, NSTR method can not only realize accurate reconstruction of convexboundary, and for single or multiple concave boundaries, it can also realize the accuratereconstruction, and can provide faster reconstruction speed and higher reconstruction quality.4. Considering the NSTR method depends on the parameter values and the trust regionradius is calculated long time consuming, so the MNSTR method is proposed to improve thestability of algorithm to parameter and the convergence speed. By means of correcting theparameter, the MNSTR method is stable for this parameter; by redefining the adjustment formulaof trust region radius, the speed of image reconstruction is also improved. Simulation experimentresults show that this method can reconstruct multiple concave boundaries, and has highreconstruction accuracy, fast reconstruction speed, etc.5. The VANTR method is proposed, in this algorithm the two parameters can be adjustedautomatically. This method has fast convergence speed, and can reconstruct accurately mostsingle boundary and multiple boundaries. Compared with NSTR method and MNSTR method,this method has an incomparable advantage in reconstructing some complex multipleboundaries.