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
Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the...Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the step function to formulate a doublesparsity constrained optimization problem,wherein a linear equality constraint is also taken into consideration.By defining aτ-Lagrangian stationary point and a KKT point,we establish the first-order and second-order necessary and sufficient optimality conditions for the problem.Furthermore,we thoroughly elucidate their relationships to local and global optimal solutions.Finally,special cases and examples are presented to illustrate the obtained theorems.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.
基金Supported by the National Key R&D Program of China(No.2023YFA1011100)NSFC(No.12131004)。
文摘Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the step function to formulate a doublesparsity constrained optimization problem,wherein a linear equality constraint is also taken into consideration.By defining aτ-Lagrangian stationary point and a KKT point,we establish the first-order and second-order necessary and sufficient optimality conditions for the problem.Furthermore,we thoroughly elucidate their relationships to local and global optimal solutions.Finally,special cases and examples are presented to illustrate the obtained theorems.
