Research On Obstacle Inverse Scattering Problem Based On Phaseless Data

The inverse problem has a wide range of applications in many scientific fields such as radar,non-destructive testing,and medical imaging.In actual measurement,only the intensity information of far-field data or scattered-field data can be measured(that is,phaseless data).Due to the translation invariance of phaseless data,it is difficult to recover the position of obstacles with phaseless data measured in the full aperture.If the phaseless data of obstacles can only be obtained in a finite aperture,a large amount of obstacle information will be missing,which further increases the difficulty of recovering the position of obstacles.Therefore,the main concern of this paper is the use of full-aperture and finite-aperture phaseless far-field data to recover the position and shape of obstacles.Aiming at the problem of acoustic scattering in recovering the position and shape of obstacles with phaseless far-field data generated by full aperture and finite aperture,we build a two-layer sequence-to-sequence neural network model.First,the random forest method is used to preprocess the phaseless far-field data generated by the positive problem;secondly,the phaseless far-field data and the obstacle boundary curve equation parameters are used as input and output sequences,and the gate idea is controlled by the long and short-term memory neural network.With the long-term memory function,it selectively updates the network state and saves the data characteristics,and applies the gradient descent algorithm to update the model weights and offsets,which overcomes the difficulty of recovering the position and shape of obstacles from phaseless far-field data.In order to simplify the complexity of the model and increase the speed of model training,a gated recurrent unit neural network is used to replace the long and short-term memory neural network at the encoding and decoding ends of the sequence-to-sequence neural network,and a gated recurrent unit-to-gated recurrent unit neural network is proposed.The preprocessed phaseless far-field data and the Fourier truncation coefficient of the obstacle boundary curve equation are used as the input and output of the network,and the gradient descent algorithm is applied to train the network.We solve the problem of recovering the position and shape of obstacles with phaseless far-field data generated by full aperture and finite aperture.If the activation functions in the above two neural networks meet the uniformly bounded condition,it can be proved that they are convergent.In the process of numerical experiments,the sequence-to-sequence neural network has a fast convergence speed and a good recover effect.For a data set with noise,as long as the noise is controlled within a certain range,the recover effect of obstacles has a smaller deviation compared with the real obstacles.Compared with the sequence-to-sequence neural network,the gated recurrent unit-to-gated recurrent unit neural network has a simpler model,relatively reduced training time,and Speed up the convergence.The experimental results show that the two proposed neural networks can recover the position and shape of obstacles well.