Research On The Obstacle Inverse Problem Based On Neural Network

The numerical solution method of inverse obstacle problem is widely used in the fields of Medical Imaging,Radar Detection,Remote sensing and Non-Destructive Testing.However,the usual inverse obstacle problem has strong ill-posedness,which makes its theoretical analysis and numerical solution relatively difficult.Existed numerical solution methods mainly include qualitative methods and quantitative methods.The qualitative method has low computational complexity,but the inversion accuracy is slightly imprecise;the quantitative method has high inversion accuracy,but has relatively high computational complexity.Developing a numerical method with low computational complexity and high precision for obstacle inversion has become one of the main research contents of scholars at internal and abroad.Considering the shape reconstruction problem in inverse obstacle project,and combining the advantages of qualitative and quantitative numerical methods,a two-step method for obstacle shape inversion is proposed in this paper.Firstly,by qualitative linear sampling method,the problem of shape reconstruction of the obstacles is converted into shape parameters with the far-field data of the sound field.And the prior information of the shape parameters of the obstacle is extracted at the same time.Then build a shape parameter inversion model with the function of "memory" in the layer based on the quantitative gating idea and neural network(SPIMNNG).To form a far-field feature containing obstacle shape information,extract selectively the corresponding information from each component of far-field data.After that,the far-field features are gradually inverted into the shape parameters of obstacles.In order to continuously optimize network,this paper uses the inverse shape parameters and the real value of the mean square error as the error function,and use the gradient-based method to update the weight of the network iteratively through the training process.Finally,the shape parameters,namely the parameters of the boundary curve equation of the obstacle,are calculated by using the trained model to reconstruct the shape of the obstacle.This paper estimates the computational complexity and confirms the convergence of the proposed model SPIMNNG.In the numerical experiment,the cases of incident and observing far-field data in a full aperture and a finite aperture are respectively considered.The proposed method can reconstruct the shape of the obstacle more accurately,and the shape of the obstacle can also be reconstructed when the boundary conditions are very different.And this method is appropriate for solving the obstacle inversion problem with noise in the far field data.