Inversion Of Mixed Scatterers Based On Neural Networks

Mixed scatterer inversion problems are widely used in medical imaging,nondestructive detection,remote sensing,radar detection and other fields,so the research on this kind of problems has great mathematical significance and application value.In this paper,the mixed backscattering problem of obstacle and crack coupling is mainly considered.Single obstacle and single crack,multiple obstacle and single crack,and single obstacle and multiple crack are respectively considered.The main research contents of this paper are as follows:Firstly,for the positive scattering problem of mixed scatters,the boundary integral equation is used to solve the scattering far field information,and the numerical solution of the scattering far field information is obtained.Secondly,the approximate position and shape of the mixed scatterers are reconstructed by qualitative linear sampling method according to the obtained far-field information,so as to extract the prior information of the shape parameters of the mixed scatterers.In this way,the inversion problem of the mixed scatterers is transformed into the estimation problem of the shape parameters of the mixed scatterers.Finally,based on the gated idea of LSTM and the optimization module Resblock,the mixed scatterer inversion model LRnet is constructed.The LRnet model can extract the corresponding far-field information from the solved far-field data,and take the far-field information as the far-field characteristics of the mixed scatterer to invert the shape parameters of the mixed scatterer.In this paper,the mean square error of the shape parameter and the real parameter is used as the error function,and the weight of the LRnet network is iteratively updated based on the gradient training.The finally trained model is used to invert the shape parameters of the mixed scatterers,and then the shape and position of the mixed scatterers are reconstructed.In order to verify the effectiveness of the proposed method,a number of numerical experiments are given.Firstly,numerical experiments are carried out under different noise levels,which shows that the LRnet method is effective for the inversion of mixed scatterers.Secondly,numerical experiments are carried out on mixed scatterers with different shapes,and LRnet model can reconstruct the mixed scatterers more accurately under the condition of full aperture and finite aperture.