超分辨率图像复原是病态反问题.采用Geman & McClure范数来构造数据拟合项,并且在经典的双边全变分(Bilateral total variation,BTV)正则化模型基础上,提出了一种能更有效利用方向信息的正则化模型,该模型根据迭代次数来自适应选择...超分辨率图像复原是病态反问题.采用Geman & McClure范数来构造数据拟合项,并且在经典的双边全变分(Bilateral total variation,BTV)正则化模型基础上,提出了一种能更有效利用方向信息的正则化模型,该模型根据迭代次数来自适应选择正则化参数.实验表明,该方法比采用L1范数和L2范数能更好地抑制噪声和保持边缘,在视觉效果和峰值信噪比(Peak signal noise ratio,PSNR)两个方面都有一定的提高.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
文摘超分辨率图像复原是病态反问题.采用Geman & McClure范数来构造数据拟合项,并且在经典的双边全变分(Bilateral total variation,BTV)正则化模型基础上,提出了一种能更有效利用方向信息的正则化模型,该模型根据迭代次数来自适应选择正则化参数.实验表明,该方法比采用L1范数和L2范数能更好地抑制噪声和保持边缘,在视觉效果和峰值信噪比(Peak signal noise ratio,PSNR)两个方面都有一定的提高.
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.
