| Electromagnetic inversion technology is an important means to obtain the distribution of the detection targets’ electrical parameters in the unknown region,which reconstructs target’s shape,dielectric constant and other parameters by inversion algorithm.Electromagnetic inversion technology is nondestructive and contactless,which has been widely used in the fields of ground penetrating radar,medical imaging,weather prediction and other fields.Based on the inverse scattering model,this paper aims at the ill-conditioned and nonlinear problem of inverse scattering problem and raises a series of electromagnetic inversion algorithms,which has high inversion performance and excellent robustness.The specific research contents are as follows:1.Firstly,the integral equation of electromagnetic field is derived based on Maxwell’s equations from the point of view of mathematics and physics;then the born approximation method is used to transform the nonlinear electromagnetic field integral equation into linear equation;in order to alleviate its ill-condition,a sparse regularization method based on Compressed Sensing(CS)is introduced,which specifically includes Orthogonal Matching Pursuit(OMP)algorithm,Bayesian Compressed Sensing(BCS)algorithm and Total Variational Comprehensive Sensing(TVCS);finally,a series of numerical simulation experiments is designed to verify the advantage and weakness of these algorithms mentioned above.2.Electromagnetic inversion algorithm based on born iterative and sparse theory is proposed.We apply the born iterative algorithm to the nonlinear model and combine the compressed sensing method with it to propose two new electromagnetic inversion methods: Hybrid Born IterativeBayesian Theory(HBI-BT)and Hybrid Born Iterative-Total Variation Theory(HBI-TVT).Firstly,the algorithms address the nonlinear problem as a series of linear ones by born iterative,then the illcondition of linear problem is solved by compressed sensing algorithm.Experimental results verify the proposed algorithm’s effectiveness and excellent performance.3.Electromagnetic inversion algorithm based on approxiamtion born iterative and sparse theory is proposed.Electromagnetic inversion algorithm based on born iterative and sparse theory needs to repeatedly compute forward problems to update the total field during iteration,it has low efficiency and high computational complexity,therefore,Hybrid Approxiamtion Born IterativeBayesian Theory(HABI-BT)and Hybrid Approxiamtion Born Iterative-Total Variation Theory(HABI-TVT)is proposed.The algorithms use a form of matrix operation to update the total field,so the proposed algorithms not only improve the reconstruction accuracy and robustness,but also shorten the running time and improve the reconstruction efficiency. |
