Di Pillo和Grippo提出的含参数C＞O的增广Lagrangian函数中,使用了最大函数,该函数可能在无穷多个点处不可微．为了克服这个问题,濮定国在2004年提出了一类带新的NCP函数的乘子法．该方法在增广Lagrangian函数和原问题之间存在很好的等...Di Pillo和Grippo提出的含参数C＞O的增广Lagrangian函数中,使用了最大函数,该函数可能在无穷多个点处不可微．为了克服这个问题,濮定国在2004年提出了一类带新的NCP函数的乘子法．该方法在增广Lagrangian函数和原问题之间存在很好的等价性；同时该方法具有全局收敛性,且在适当假设下,具有超线性收敛率．但是在该方法中,要求参数C充分大．为了实现算法及提高算法效率,本文给出了一个有效选择参数C的方法．展开更多
Seismic data typically contain random missing traces because of obstacles and economic restrictions,influencing subsequent processing and interpretation.Seismic data recovery can be expressed as a low-rank matrix appr...Seismic data typically contain random missing traces because of obstacles and economic restrictions,influencing subsequent processing and interpretation.Seismic data recovery can be expressed as a low-rank matrix approximation problem by assuming a low-rank structure for the complete seismic data in the frequency–space(f–x)domain.The nuclear norm minimization(NNM)(sum of singular values)approach treats singular values equally,yielding a solution deviating from the optimal.Further,the log-sum majorization–minimization(LSMM)approach uses the nonconvex log-sum function as a rank substitution for seismic data interpolation,which is highly accurate but time-consuming.Therefore,this study proposes an efficient nonconvex reconstruction model based on the nonconvex Geman function(the nonconvex Geman low-rank(NCGL)model),involving a tighter approximation of the original rank function.Without introducing additional parameters,the nonconvex problem is solved using the Karush–Kuhn–Tucker condition theory.Experiments using synthetic and field data demonstrate that the proposed NCGL approach achieves a higher signal-to-noise ratio than the singular value thresholding method based on NNM and the projection onto convex sets method based on the data-driven threshold model.The proposed approach achieves higher reconstruction efficiency than the singular value thresholding and LSMM methods.展开更多
基金financially supported by the National Key R&D Program of China(No.2018YFC1503705)the Science and Technology Research Project of Hubei Provincial Department of Education(No.B2017597)+1 种基金the Hubei Subsurface Multiscale Imaging Key Laboratory(China University of Geosciences)(No.SMIL-2018-06)the Fundamental Research Funds for the Central Universities(No.CCNU19TS020).
文摘Seismic data typically contain random missing traces because of obstacles and economic restrictions,influencing subsequent processing and interpretation.Seismic data recovery can be expressed as a low-rank matrix approximation problem by assuming a low-rank structure for the complete seismic data in the frequency–space(f–x)domain.The nuclear norm minimization(NNM)(sum of singular values)approach treats singular values equally,yielding a solution deviating from the optimal.Further,the log-sum majorization–minimization(LSMM)approach uses the nonconvex log-sum function as a rank substitution for seismic data interpolation,which is highly accurate but time-consuming.Therefore,this study proposes an efficient nonconvex reconstruction model based on the nonconvex Geman function(the nonconvex Geman low-rank(NCGL)model),involving a tighter approximation of the original rank function.Without introducing additional parameters,the nonconvex problem is solved using the Karush–Kuhn–Tucker condition theory.Experiments using synthetic and field data demonstrate that the proposed NCGL approach achieves a higher signal-to-noise ratio than the singular value thresholding method based on NNM and the projection onto convex sets method based on the data-driven threshold model.The proposed approach achieves higher reconstruction efficiency than the singular value thresholding and LSMM methods.
