In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inver...In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.展开更多
We study the inverse problem of recovering the scatterer shape from the far-field pattern(FFP)in the presence of noise.Furthermore,only a discrete partial aperture is usually known.This problem is ill-posed and is fre...We study the inverse problem of recovering the scatterer shape from the far-field pattern(FFP)in the presence of noise.Furthermore,only a discrete partial aperture is usually known.This problem is ill-posed and is frequently addressed using regularization.Instead,we propose to use a direct approach denoising the FFP using a filtering technique.The effectiveness of the technique is studied on a scatterer with the shape of the ellipse with a tower.The forward scattering problem is solved using the finite element method(FEM).The numerical FFP is additionally corrupted by Gaussian noise.The shape parameters are found based on a least-square error estimator.If eu¥is a perturbation of the FFP then we attempt to find G,the scatterer shape,which minimizes k u¥−eu¥k using the conjugate gradient method for the denoised FFP.展开更多
基金Shanghai Youth Science FoundationSupported in Part by Shanghai ScienceTechnology Development Foundation
文摘In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.
文摘We study the inverse problem of recovering the scatterer shape from the far-field pattern(FFP)in the presence of noise.Furthermore,only a discrete partial aperture is usually known.This problem is ill-posed and is frequently addressed using regularization.Instead,we propose to use a direct approach denoising the FFP using a filtering technique.The effectiveness of the technique is studied on a scatterer with the shape of the ellipse with a tower.The forward scattering problem is solved using the finite element method(FEM).The numerical FFP is additionally corrupted by Gaussian noise.The shape parameters are found based on a least-square error estimator.If eu¥is a perturbation of the FFP then we attempt to find G,the scatterer shape,which minimizes k u¥−eu¥k using the conjugate gradient method for the denoised FFP.
