In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed t...In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed to determine the transmission eigenvalues within a certain wavenumber interval based on far-field measurements. Based on a prior information given by the linear sampling method, the neural network approach is proposed for the reconstruction of the unknown scatterer. We divide the wavenumber intervals into several subintervals, ensuring that each transmission eigenvalue is located in its corresponding subinterval. In each such subinterval, the wavenumber that yields the maximum value of the indicator functional will be included in the input set during the generation of the training data. This technique for data generation effectively ensures the consistent dimensions of model input. The refractive index and shape are taken as the output of the network. Due to the fact that transmission eigenvalues considered in our method are relatively small,certain super-resolution effects can also be generated. Numerical experiments are presented to verify the effectiveness and promising features of the proposed method in two and three dimensions.展开更多
在水声信号处理中,高可靠、高分辨的DOA(Direction of Arrival)估计技术是后续信号处理的基础。论文采用一种新的波束形成算法FB(Functional Beamforming)实现DOA估计,算法对数据协方差矩阵进行特征值分解指数重构,波束图具有旁瓣低、...在水声信号处理中,高可靠、高分辨的DOA(Direction of Arrival)估计技术是后续信号处理的基础。论文采用一种新的波束形成算法FB(Functional Beamforming)实现DOA估计,算法对数据协方差矩阵进行特征值分解指数重构,波束图具有旁瓣低、主瓣窄的优点,并且算法过程不涉及矩阵求逆运算,具有较高的稳健性,可实现对目标的高可靠分辨。展开更多
基金supported by the Jilin Natural Science Foundation,China(No.20220101040JC)the National Natural Science Foundation of China(No.12271207)+2 种基金supported by the Hong Kong RGC General Research Funds(projects 11311122,12301420 and 11300821)the NSFC/RGC Joint Research Fund(project N-CityU 101/21)the France-Hong Kong ANR/RGC Joint Research Grant,A_CityU203/19.
文摘In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed to determine the transmission eigenvalues within a certain wavenumber interval based on far-field measurements. Based on a prior information given by the linear sampling method, the neural network approach is proposed for the reconstruction of the unknown scatterer. We divide the wavenumber intervals into several subintervals, ensuring that each transmission eigenvalue is located in its corresponding subinterval. In each such subinterval, the wavenumber that yields the maximum value of the indicator functional will be included in the input set during the generation of the training data. This technique for data generation effectively ensures the consistent dimensions of model input. The refractive index and shape are taken as the output of the network. Due to the fact that transmission eigenvalues considered in our method are relatively small,certain super-resolution effects can also be generated. Numerical experiments are presented to verify the effectiveness and promising features of the proposed method in two and three dimensions.
文摘在水声信号处理中,高可靠、高分辨的DOA(Direction of Arrival)估计技术是后续信号处理的基础。论文采用一种新的波束形成算法FB(Functional Beamforming)实现DOA估计,算法对数据协方差矩阵进行特征值分解指数重构,波束图具有旁瓣低、主瓣窄的优点,并且算法过程不涉及矩阵求逆运算,具有较高的稳健性,可实现对目标的高可靠分辨。
