Compton scattering imaging is a novel radiation imaging method using scattered photons.Its main characteristics are detectors that do not have to be on the opposite side of the source,so avoiding the rotation process....Compton scattering imaging is a novel radiation imaging method using scattered photons.Its main characteristics are detectors that do not have to be on the opposite side of the source,so avoiding the rotation process.The reconstruction problem of Compton scattering imaging is the inverse problem to solve electron densities from nonlinear equations,which is ill-posed.This means the solution exhibits instability and sensitivity to noise or erroneous measurements.Using the theory for reconstruction of sparse images,a reconstruction algorithm based on total variation minimization is proposed.The reconstruction problem is described as an optimization problem with nonlinear data-consistency constraint.The simulated results show that the proposed algorithm could reduce reconstruction error and improve image quality,especially when there are not enough measurements.展开更多
This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military...This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.展开更多
This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation fo...This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formula- tion is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the NystrSm method for the new integral equation. Nu- merical examples are also shown to illustrate the applicability of the new integral equation formulation.展开更多
We propose a numerical procedure to extend to full aperture the acoustic farfield pattern(FFP)when measured in only few observation angles.The reconstruction procedure is a multi-step technique that combines a total v...We propose a numerical procedure to extend to full aperture the acoustic farfield pattern(FFP)when measured in only few observation angles.The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion.The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms.We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.展开更多
基金Project supported by the National Basic Research Program of China (Grant No. 2011CB707701)the National High Technology Research and Development Program of China (Grant Nos. 2009AA012200 and 2012AA011603)
文摘Compton scattering imaging is a novel radiation imaging method using scattered photons.Its main characteristics are detectors that do not have to be on the opposite side of the source,so avoiding the rotation process.The reconstruction problem of Compton scattering imaging is the inverse problem to solve electron densities from nonlinear equations,which is ill-posed.This means the solution exhibits instability and sensitivity to noise or erroneous measurements.Using the theory for reconstruction of sparse images,a reconstruction algorithm based on total variation minimization is proposed.The reconstruction problem is described as an optimization problem with nonlinear data-consistency constraint.The simulated results show that the proposed algorithm could reduce reconstruction error and improve image quality,especially when there are not enough measurements.
文摘This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.
文摘This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formula- tion is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the NystrSm method for the new integral equation. Nu- merical examples are also shown to illustrate the applicability of the new integral equation formulation.
文摘We propose a numerical procedure to extend to full aperture the acoustic farfield pattern(FFP)when measured in only few observation angles.The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion.The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms.We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.