A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations|Ax|^(2)=y.The algorithms are developed by exploiting the inherent low rank structure of the problem...A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations|Ax|^(2)=y.The algorithms are developed by exploiting the inherent low rank structure of the problem based on the embedded manifold of rank-1 positive semidefinite matrices.Theoretical recovery guarantee has been established for the truncated variant,showing that the algorithm is able to achieve successful recovery when the number of equations is proportional to the number of unknowns.Two key ingredients in the analysis are the restricted well conditioned property and the restricted weak correlation property of the associated truncated linear operator.Empirical evaluations show that our algorithms are competitive with other state-of-the-art first order nonconvex approaches with provable guarantees.展开更多
In this paper,we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed frequency.I...In this paper,we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed frequency.It is well-known that the modulus of the far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field,so it is impossible to reconstruct the location of the underlying scatterers.Based on some new research results on the impenetrable obstacle and inhomogeneous isotropic medium,we consider different types of superpositions of incident waves to break the translation invariance property.展开更多
In this paper a new approach for microwave imaging of unknown objects embedded in the freespace from phaseless data is presented. Firstly a cost functional is constructed by using the measured amplitude of the total f...In this paper a new approach for microwave imaging of unknown objects embedded in the freespace from phaseless data is presented. Firstly a cost functional is constructed by using the measured amplitude of the total field, which is the norm of the discrepancy between the measured amplitude and the calculated one. Then both the amplitude and phase of the scattered field are retrieved by minimizing the above cost functional. Finally, the geometrical and electrical parameters are reconstructed by using the retrieved scattered field. The phase retrieval process can be achieved in a very short time without adding any burden to the whole inverse scattering problem. The equivalent current density is introduced to reduce the nonlinearity of the inverse problem. The reconstruction of the non-radiating component of the equivalent current density improves the imaging quality. Experimental results are presented for the first time to show the feasibility of inverse scattering from phaseless data. The experimental results also show the validity and stability of the proposed method.展开更多
We propose a reliable direct imaging method based on the reverse time migration for finding extended obstacles with phaseless total field data.We prove that the imaging resolution of the method is essentially the same...We propose a reliable direct imaging method based on the reverse time migration for finding extended obstacles with phaseless total field data.We prove that the imaging resolution of the method is essentially the same as the imaging results using the scattering data with full phase information when the measurement is far away from the obstacle.The imaginary part of the cross-correlation imaging functional always peaks on the boundary of the obstacle.Numerical experiments are included to illustrate the powerful imaging quality.展开更多
We consider the inverse fluid-solid interaction scattering of incident plane wave from the knowledge of the phased and phaseless far field patterns.For the phased data,one direct sampling method for location and shape...We consider the inverse fluid-solid interaction scattering of incident plane wave from the knowledge of the phased and phaseless far field patterns.For the phased data,one direct sampling method for location and shape reconstruction is proposed.Only inner product is involved in the computation,which makes it very simple and fast to be implemented.With the help of the factorization of the far field operator,we give a lower bound of the proposed indicator functional for the sampling points inside the elastic body.While for the sampling points outside,we show that the indicator functional decays like the Bessel function as the points go away from the boundaries of the elastic body.We also show that the proposed indicator functional continuously dependents on the far field patterns,which further implies that the novel sampling method is extremely stable with respect to data error.For the phaseless data,to overcome the translation invariance,we consider the scattering of point sources simultaneously.By adding a reference sound-soft obstacle into the scattering system,we show some uniqueness results with phaseless far field data.Numerically,we introduce a phase retrieval algorithm to retrieve the phased data without the additional obstacle.The novel phase retrieval algorithm can also be combined with the sampling method for phased data.We also design two novel direct sampling methods using the phaseless data directly.Finally,some numerical simulations in two dimensions are conducted with noisy data,and the results further verify the effectiveness and robustness of the proposed numerical methods.展开更多
针对现有无相位近场数据的偶极子建模很难精确对干扰源进行等效的问题,对现有无相位近场数据的干扰源等效建模中所采用的双面迭代方法进行了改进,改进方法主要是采用2个以上不同高度的磁场幅度数据;对双面迭代方法中平面的选择以及改进...针对现有无相位近场数据的偶极子建模很难精确对干扰源进行等效的问题,对现有无相位近场数据的干扰源等效建模中所采用的双面迭代方法进行了改进,改进方法主要是采用2个以上不同高度的磁场幅度数据;对双面迭代方法中平面的选择以及改进方法中平面数量和起始面的选择进行了讨论;以干扰源辐射磁场重构的均方根误差(Root Mean Square Error,RMSE)作为偶极子建模准确度评价依据,与现有双面迭代方法及其他优化方法等效建模出的偶极子模型进行了对比验证,对比结果显示该改进方法具有更高的准确度。展开更多
文摘A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations|Ax|^(2)=y.The algorithms are developed by exploiting the inherent low rank structure of the problem based on the embedded manifold of rank-1 positive semidefinite matrices.Theoretical recovery guarantee has been established for the truncated variant,showing that the algorithm is able to achieve successful recovery when the number of equations is proportional to the number of unknowns.Two key ingredients in the analysis are the restricted well conditioned property and the restricted weak correlation property of the associated truncated linear operator.Empirical evaluations show that our algorithms are competitive with other state-of-the-art first order nonconvex approaches with provable guarantees.
文摘In this paper,we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed frequency.It is well-known that the modulus of the far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field,so it is impossible to reconstruct the location of the underlying scatterers.Based on some new research results on the impenetrable obstacle and inhomogeneous isotropic medium,we consider different types of superpositions of incident waves to break the translation invariance property.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60701010, 40774093)the Knowledge Innovation Program of Chinese Academy of Sciences
文摘In this paper a new approach for microwave imaging of unknown objects embedded in the freespace from phaseless data is presented. Firstly a cost functional is constructed by using the measured amplitude of the total field, which is the norm of the discrepancy between the measured amplitude and the calculated one. Then both the amplitude and phase of the scattered field are retrieved by minimizing the above cost functional. Finally, the geometrical and electrical parameters are reconstructed by using the retrieved scattered field. The phase retrieval process can be achieved in a very short time without adding any burden to the whole inverse scattering problem. The equivalent current density is introduced to reduce the nonlinearity of the inverse problem. The reconstruction of the non-radiating component of the equivalent current density improves the imaging quality. Experimental results are presented for the first time to show the feasibility of inverse scattering from phaseless data. The experimental results also show the validity and stability of the proposed method.
基金supported by National Basic Research Project under the grant 2011CB309700China NSF under the grants 11021101 and 11321061.
文摘We propose a reliable direct imaging method based on the reverse time migration for finding extended obstacles with phaseless total field data.We prove that the imaging resolution of the method is essentially the same as the imaging results using the scattering data with full phase information when the measurement is far away from the obstacle.The imaginary part of the cross-correlation imaging functional always peaks on the boundary of the obstacle.Numerical experiments are included to illustrate the powerful imaging quality.
基金partially supported by the National Natural Science Foundation of China under grants91630313 and 11971468National Centre for Mathematics and Interdisciplinary Sciences,CAS+1 种基金supported by the National Natural Science Foundation of China under grants 11571355 and 11971701the Youth Innovation Promotion Association,CAS。
文摘We consider the inverse fluid-solid interaction scattering of incident plane wave from the knowledge of the phased and phaseless far field patterns.For the phased data,one direct sampling method for location and shape reconstruction is proposed.Only inner product is involved in the computation,which makes it very simple and fast to be implemented.With the help of the factorization of the far field operator,we give a lower bound of the proposed indicator functional for the sampling points inside the elastic body.While for the sampling points outside,we show that the indicator functional decays like the Bessel function as the points go away from the boundaries of the elastic body.We also show that the proposed indicator functional continuously dependents on the far field patterns,which further implies that the novel sampling method is extremely stable with respect to data error.For the phaseless data,to overcome the translation invariance,we consider the scattering of point sources simultaneously.By adding a reference sound-soft obstacle into the scattering system,we show some uniqueness results with phaseless far field data.Numerically,we introduce a phase retrieval algorithm to retrieve the phased data without the additional obstacle.The novel phase retrieval algorithm can also be combined with the sampling method for phased data.We also design two novel direct sampling methods using the phaseless data directly.Finally,some numerical simulations in two dimensions are conducted with noisy data,and the results further verify the effectiveness and robustness of the proposed numerical methods.
文摘针对现有无相位近场数据的偶极子建模很难精确对干扰源进行等效的问题,对现有无相位近场数据的干扰源等效建模中所采用的双面迭代方法进行了改进,改进方法主要是采用2个以上不同高度的磁场幅度数据;对双面迭代方法中平面的选择以及改进方法中平面数量和起始面的选择进行了讨论;以干扰源辐射磁场重构的均方根误差(Root Mean Square Error,RMSE)作为偶极子建模准确度评价依据,与现有双面迭代方法及其他优化方法等效建模出的偶极子模型进行了对比验证,对比结果显示该改进方法具有更高的准确度。
