Study Of Vector Field Tomography Based On Spectral Conjugate Gradient Method

There are magnetic fields everywhere in the human world.As early as two thousand years ago,people identified the direction by measuring the magnetic field.At present,the magnetic field measurement devices can only measure the magnitude or power of the magnetic field,and can't measure the vector distribution of the magnetic field,which limits the application range of the magnetic field measurement technology.Amorphous wires have giant magneto impedance characteristics,that is,the impedance values at both ends of the amorphous wires are nonlinear with the axial magnetic field components.So,it is possible to obtain the vector field distribution of magnetic field by using this characteristic and combining with tomography technique.However,the existing vector field tomography technology assumes that the projection data is a linear integral about the vector field under the integral path,and it can't be directly used for vector field reconstruction of nonlinear projection data for amorphous wire sensing.The research of vector field tomography based on nonlinear projection data can enlarge the application range of tomography and magnetic field measurement technology.In this paper,starting from the basic principle of tomography,the basic principle of CT tomography and the analytic reconstruction method and iterative reconstruction method of image reconstruction are described.The vector field tomography method based on linear projection data is introduced,and the experiment is simulated by MATLAB.According to the formation principle of nonlinear projection data and the idea of algebraic reconstruction method,the nonlinear equations of nonlinear projection data and vector fields are established.A simple and fast calculation method for the projection coefficient matrix that affects the quality of reconstruction is designed.We transform the nonlinear equations into unconstrained optimization problems,and use the PRP conjugate gradient method and the spectral PRP conjugate gradient method to solve the problem,and verify the effectiveness of the algorithm by MATLAB simulation.The results show that the proposed method can reconstruct the vector field based on nonlinear projection data.Under the same conditions,the error of vector field reconstructed by spectral PRP conjugate gradient method is smaller than that by PRP conjugate gradient method.