Research On Image Reconstruction Algorithm Based On 'Soft-field' Characteristics

Electrical Tomography (ET) is a technique for reconstructing electrical properties (conductivity or permittivity) of the interior structures. In ET, an array of electrodes is attached around the object and alternating voltages/currents are injected via these electrodes and the resulting capacitances/voltages are measured. Using measurements on the boundary, an approximation for the spatial distribution of conductivity or permittivity within the object can be reconstructed.Due to the advantages of non-radiant, non-intrusive, rapid response and low cost, ET technique is of great potential in three principal areas: medical imaging, industrial process imaging and geophysical surveying.Electrical Capacitance Tomography (ECT) and Electrical Resistance Tomography (ERT) based on different principle are two important categories of ET. ECT is suitable to detect dielectric material, while ERT is capable to measure conducting medium. The dual-mode electrical tomography (ERT/ECT) technique is proposed to measure conducting and dielectric materials in multi-phase application.Mathematically, the physical model for ET meets the Laplace elliptic partial differential equation. Since there is no analytical solution for an arbitrary conductivity or permittivity distribution in the volume, Finite Element Method (FEM) is a nice choice to solve the forward problem in ET. The ET reconstruction problem is a nonlinear ill-posed inverse problem which requires the use of particular methods to obtain accurate solution.In this thesis, the forward problem in ET is solved using COMSOL Multiphysics? with Matlab? which can be modeled flexibly and solved accurately. The interactions of these two modes are analyzed and optimum design of the electrodes configuration and size for them are obtained respectively.Besides, basic theories of inverse problem are discussed, and several new approaches of ET image reconstruction are proposed.Firstly, a hybrid method is proposed for solving the inverse problem for ET, which combines the Krylov subspace and the Tikhonov regularisation for double levels of regularisation to the ill-posed problem. Numerical simulation results using the hybrid method are presented and compared to those by Truncated singular value decomposition (TSVD) regularisation and the Tikhonov regularisation. Experimental results with the hybrid method are also presented, indicating that the hybrid method can reduce the computation time, and improve the resolution of reconstructed images with the regularisation parameter automatically chosen by the L-curve method. Then, to solve the inverse problem of ET, a two-level pre-iteration reconstruction algorithm is introduced which splits the solution space into two subspaces.Experimental results indicate that the algorithm is much more stable and efficient comparing to direct methods and normal iterative methods. At the same time, the parameter choosing, filter factor and convergence property are discussed.Thirdly, Reconstruction algorithm for electrical tomography based on adaptive mesh refinement which combines with prior information is discussed. The adaptive finite element method is introduced and the posteriori error, mesh refinement, mesh quality are analyzed. More accurate potential distribution in the investigated field domain is derived. The regularized Newton-Raphson algorithm is adopted based on adaptive mesh refinement to reconstruct the interior conductivity distribution. Experimental results show that this algorithm can not only improve the resolution of the recovered image but also reduce the reconstruction time.Finally, the model of pulmo is built, and a novel reconstruction method which exploits available prior information is proposed. Results show that this method can improve the image quality greatly and exhibit the attractive developing potential of this kind of methods tremendously.