Least-squares reverse-time migration(LSRTM) formulates reverse-time migration(RTM) in the leastsquares inversion framework to obtain the optimal reflectivity image. It can generate images with more accurate amplitudes...Least-squares reverse-time migration(LSRTM) formulates reverse-time migration(RTM) in the leastsquares inversion framework to obtain the optimal reflectivity image. It can generate images with more accurate amplitudes, higher resolution, and fewer artifacts than RTM. However, three problems still exist:(1) inversion can be dominated by strong events in the residual;(2) low-wavenumber artifacts in the gradient affect convergence speed and imaging results;(3) high-wavenumber noise is also amplified as iteration increases. To solve these three problems, we have improved LSRTM: firstly, we use Hubernorm as the objective function to emphasize the weak reflectors during the inversion;secondly, we adapt the de-primary imaging condition to remove the low-wavenumber artifacts above strong reflectors as well as the false high-wavenumber reflectors in the gradient;thirdly, we apply the L1-norm sparse constraint in the curvelet-domain as the regularization term to suppress the high-wavenumber migration noise. As the new inversion objective function contains the non-smooth L1-norm, we use a modified iterative soft thresholding(IST) method to update along the Polak-Ribie re conjugate-gradient direction by using a preconditioned non-linear conjugate-gradient(PNCG) method. The numerical examples,especially the Sigsbee2 A model, demonstrate that the Huber inversion-based RTM can generate highquality images by mitigating migration artifacts and improving the contribution of weak reflection events.展开更多
In this paper,an inverse source problem for the time-fractional diffusion equation is investigated.The observational data is on the final time and the source term is assumed to be temporally independent and with a spa...In this paper,an inverse source problem for the time-fractional diffusion equation is investigated.The observational data is on the final time and the source term is assumed to be temporally independent and with a sparse structure.Here the sparsity is understood with respect to the pixel basis,i.e.,the source has a small support.By an elastic-net regularization method,this inverse source problem is formulated into an optimization problem and a semismooth Newton(SSN)algorithm is developed to solve it.A discretization strategy is applied in the numerical realization.Several one and two dimensional numerical examples illustrate the efficiency of the proposed method.展开更多
Aiming at the low recognition accuracy of non-negative matrix factorization(NMF)in practical application,an improved spare graph NMF(New-SGNMF)is proposed in this paper.New-SGNMF makes full use of the inherent geometr...Aiming at the low recognition accuracy of non-negative matrix factorization(NMF)in practical application,an improved spare graph NMF(New-SGNMF)is proposed in this paper.New-SGNMF makes full use of the inherent geometric structure of image data to optimize the basis matrix in two steps.A threshold value s was first set to judge the threshold value of the decomposed base matrix to filter the redundant information in the data.Using L2 norm,sparse constraints were then implemented on the basis matrix,and integrated into the objective function to obtain the objective function of New-SGNMF.In addition,the derivation process of the algorithm and the convergence analysis of the algorithm were given.The experimental results on COIL20,PIE-pose09 and YaleB database show that compared with K-means,PCA,NMF and other algorithms,the proposed algorithm has higher accuracy and normalized mutual information.展开更多
基金supported by National Key R&D Program of China (No. 2018YFA0702502)NSFC (Grant No. 41974142, 42074129, and 41674114)+1 种基金Science Foundation of China University of Petroleum (Beijing) (Grant No. 2462020YXZZ005)State Key Laboratory of Petroleum Resources and Prospecting (Grant No. PRP/indep-42012)。
文摘Least-squares reverse-time migration(LSRTM) formulates reverse-time migration(RTM) in the leastsquares inversion framework to obtain the optimal reflectivity image. It can generate images with more accurate amplitudes, higher resolution, and fewer artifacts than RTM. However, three problems still exist:(1) inversion can be dominated by strong events in the residual;(2) low-wavenumber artifacts in the gradient affect convergence speed and imaging results;(3) high-wavenumber noise is also amplified as iteration increases. To solve these three problems, we have improved LSRTM: firstly, we use Hubernorm as the objective function to emphasize the weak reflectors during the inversion;secondly, we adapt the de-primary imaging condition to remove the low-wavenumber artifacts above strong reflectors as well as the false high-wavenumber reflectors in the gradient;thirdly, we apply the L1-norm sparse constraint in the curvelet-domain as the regularization term to suppress the high-wavenumber migration noise. As the new inversion objective function contains the non-smooth L1-norm, we use a modified iterative soft thresholding(IST) method to update along the Polak-Ribie re conjugate-gradient direction by using a preconditioned non-linear conjugate-gradient(PNCG) method. The numerical examples,especially the Sigsbee2 A model, demonstrate that the Huber inversion-based RTM can generate highquality images by mitigating migration artifacts and improving the contribution of weak reflection events.
基金supported by National Science Foundation of China No.11171305 and No.91230203 and the work of X.Lu is partially supported by National Science Foundation of China No.11471253,the Fundamental Research Funds for the Central Universities(13lgzd07)and the PSTNS of Zhu Jiang in Guangzhou city(2011J2200099).
文摘In this paper,an inverse source problem for the time-fractional diffusion equation is investigated.The observational data is on the final time and the source term is assumed to be temporally independent and with a sparse structure.Here the sparsity is understood with respect to the pixel basis,i.e.,the source has a small support.By an elastic-net regularization method,this inverse source problem is formulated into an optimization problem and a semismooth Newton(SSN)algorithm is developed to solve it.A discretization strategy is applied in the numerical realization.Several one and two dimensional numerical examples illustrate the efficiency of the proposed method.
基金This work was supported by the National Natural Science Foundation of China(Grant No.61501005)the Anhui Natural Science Foundation(Grant No.1608085 MF 147)+2 种基金the Natural Science Foundation of Anhui Universities(Grant No.KJ2016A057)the Industry Collaborative Innovation Fund of Anhui Polytechnic University and Jiujiang District(Grant No.2021cyxtb4)the Science Research Project of Anhui Polytechnic University(Grant No.Xjky2020120).
文摘Aiming at the low recognition accuracy of non-negative matrix factorization(NMF)in practical application,an improved spare graph NMF(New-SGNMF)is proposed in this paper.New-SGNMF makes full use of the inherent geometric structure of image data to optimize the basis matrix in two steps.A threshold value s was first set to judge the threshold value of the decomposed base matrix to filter the redundant information in the data.Using L2 norm,sparse constraints were then implemented on the basis matrix,and integrated into the objective function to obtain the objective function of New-SGNMF.In addition,the derivation process of the algorithm and the convergence analysis of the algorithm were given.The experimental results on COIL20,PIE-pose09 and YaleB database show that compared with K-means,PCA,NMF and other algorithms,the proposed algorithm has higher accuracy and normalized mutual information.