Research On A Constrained Image Reconstruction Algorithm For Electrical Impedance Tomography

Electrical Impedance Tomography(EIT) is an impedance imaging technique which calculates the internal conductivity distribution of a medium from electrical measurements made at a series of electrodes on the medium boundary. The reconstruction problem of Electrical Impedance Tomography is a severely nonlinear ill-posed inverse problem, the solution of which necessitates the use of regularization techniques as well as optimization methods to exploit available prior information. The defects of the unconstrained image reconstruction methods are as follows:(1) They are unable to make full use of the available prior information due to the fact that only one conductivity reference value is incorporated.(2) Because there are no limit placed on the solution, they suffer from low accuracy and poor disturbance performance. To solve this, a novel method called GKREIT is proposed in this thesis.Firstly, a brief introduction of the components of EIT reconstruction method is given, following with the discussion of intrinsic reasons for the ill-posed nature of the reconstruction problem. Accordingly, some methods are provided. By analyzing the frameworks of three typical unconstrained methods(i.e., Gauss-Newton method, Quasi-Newton method and Conjugate Gradient method) for EIT reconstruction problem, the thesis examines the fact that unconstrained methods become less robust against noise/disturbance because there are no constraint on the solution.Secondly, the design of GKREIT is elaborated mathematically. The method is realized through:(1) Transforming the image reconstruction problem to a constrained problem by incorporating the prior information of conductivity variation range.(2) Proposing a constrained optimization method which can adjust the iteration tolerances dynamically and terminate the whole calculation in time to avoid noise amplification.Lastly, simulations based on three dimensional numerical models are constructed to evaluate the quality of reconstructed images and convergence behaviors of four methods. Results show that in comparison to unconstrained image reconstruction methods, GKREIT improves image reconstruction quality and stays robust against noise and disturbance.