Research On A Kind Of Inverse Scattering Problem Of Impenetrable Cavity

The cavity scattering problem is a classic internal scattering problem,which plays an important role in the field of mathematics and physics.It is widely used in the fields of medical imaging,geological prospecting and non-destructive testing.However,in real life,only the intensity information of the scattering data can be measured,and it is difficult to measure the phase information of the scattering data.Compared with the problems of inverse cavity scattering with phase,the inverse cavity scattering with phaseless is more challenging.Therefore,this paper mainly uses neural network methods to solve the two problems of inverse cavity scattering with phase and inverse cavity scattering with phaseless.Aiming at the problem of inverse scattering from phased cavities,this paper proposes a near-field shape neural network(NSNN).The input of NSNN is near-field data,and the output is the shape parameter of the cavity.NSNN is mainly composed of self-attention mechanism connection,which is used to obtain the characteristic information of near-field data and the correlation between them.The weights and biases of NSNN are updated by gradient descent algorithm.It is proved that the loss function sequence related to the weight is a monotonically bounded non-negative sequence,which proves the convergence of NSNN.Numerical experiments show that NSNN can effectively invert the shape of the cavity when the approach data contains noise and finite aperture,indicating that the network has a certain degree of robustness.Aiming at the problem of inverse scattering with phaseless cavities,since the phaseless near-field data lacks phase information,if the phaseless approach data is used to invert the shape of the cavity,more observation data will be required,which will lead to the complexity and computational complexity of the model rise.In order to solve this problem,this paper proposes Star-NSNN based on the near-field shape neural network.The indirect self-attention mechanism of Star-NSNN is used to obtain the feature information of phase-free data and establish the relationship between local and nonlocal data.Self-attention value,using adaptive momentum estimation algorithm to update the weight and bias of the network to minimize the inversion error.Numerical experiments show that Star-NSNN can effectively solve the inverse problem of the cavity without phase data in the case of finite aperture.