We consider a convex relaxation of sparse principal component analysisproposed by d' Aspremont et al. (SIAM Rev. 49:434 448, 2007). This convex relax-ation is a nonsmooth semidefinite programming problem in which ...We consider a convex relaxation of sparse principal component analysisproposed by d' Aspremont et al. (SIAM Rev. 49:434 448, 2007). This convex relax-ation is a nonsmooth semidefinite programming problem in which the ξ1 norm of thedesired matrix is imposed in either the objective function or the constraint to improvethe sparsity of the resulting matrix. The sparse principal component is obtained by arank- one decomposition of the resulting sparse matrix. We propose an alternating di-rection method based on a variable-splitting technique and an augmented I agrangianframework for solving this nonsmooth semidefinite programming problem. In con-trast to the first-order method proposed in d' Aspremont et al. (SIAM Rev. 49:434448, 2007), which solves approximately the dual problem of the original semidefiniteprogramming problem, our method deals with the primal problem directly and solvesit exactly, which guarantees that the resulting matrix is a sparse matrix. A globalconvergence result is established for the proposed method. Numerical results on bothsynthetic problems and the real applications from classification of text data and senatevoting data are reported to demonstrate the efficacy of our method.展开更多
传统图像去噪法基于有用信息和噪声频率特性的差别实现去噪,实际中,有用信息和噪声在频带上往往存在重叠,因此,传统去噪法在抑制噪声的同时,往往损失了细节信息,使图像变模糊.本文引入稀疏与低秩矩阵分解模型描述图像去噪问题,基于该模...传统图像去噪法基于有用信息和噪声频率特性的差别实现去噪,实际中,有用信息和噪声在频带上往往存在重叠,因此,传统去噪法在抑制噪声的同时,往往损失了细节信息,使图像变模糊.本文引入稀疏与低秩矩阵分解模型描述图像去噪问题,基于该模型,采用交替方向法(Alternating direction method,ADM)得到复原图像.实验证明该方法比常用的中值滤波法更有效地抑制了椒盐噪声,同时更好地保持了原始图像的细节信息.展开更多
经典的鲁棒主成分分析(Robust Principal Component Analysis,RPCA)目标检测算法使用l1范数逐一判别每一像素点是否属于运动目标,未能考虑到运动目标在空间分布的连续性,不利于提升运动目标检测的鲁棒性.本文提出了一种基于l0群稀疏RPC...经典的鲁棒主成分分析(Robust Principal Component Analysis,RPCA)目标检测算法使用l1范数逐一判别每一像素点是否属于运动目标,未能考虑到运动目标在空间分布的连续性,不利于提升运动目标检测的鲁棒性.本文提出了一种基于l0群稀疏RPCA模型的运动目标检测方法.首先运用Ncuts算法进行区域过分割,生成多个同性区域,将其作为群稀疏约束的分组信息;第二步构造基于l0群稀疏RPCA模型,运用群稀疏准则判别过分割后的各同性区域是否为运动目标,采用交替方向乘子算法对模型进行快速求解,约束过分割形成的同性区域具有相同检测结果,进而将背景环境和运动前景分离,能够更加准确地度量运动目标的区域边界,且对复杂的背景扰动更加鲁棒,达到了运动目标鲁棒检测的目的.展开更多
为了在缓解阶梯效应的同时更好地保留去噪后图像的细节信息,提出一种基于增强高阶非凸全变分(higher order non-convex total variation,HONTV)模型的图像去噪算法。该算法将每一次去噪后的图像和原始图像取平均作为增强HONTV模型下一...为了在缓解阶梯效应的同时更好地保留去噪后图像的细节信息,提出一种基于增强高阶非凸全变分(higher order non-convex total variation,HONTV)模型的图像去噪算法。该算法将每一次去噪后的图像和原始图像取平均作为增强HONTV模型下一次循环的输入并更新参数,然后采用增广拉格朗日乘子法和交替方向乘子法进行循环求解,经过多次迭代,最终得到的去噪图像包含较多的细节信息。在基于全变分的图像去噪方法中,对添加不同标准差大小的高斯白噪声的测试图像和视频进行实验。实验结果表明,所提算法在视觉性能和客观评价指标方面均优于对比算法。展开更多
文摘We consider a convex relaxation of sparse principal component analysisproposed by d' Aspremont et al. (SIAM Rev. 49:434 448, 2007). This convex relax-ation is a nonsmooth semidefinite programming problem in which the ξ1 norm of thedesired matrix is imposed in either the objective function or the constraint to improvethe sparsity of the resulting matrix. The sparse principal component is obtained by arank- one decomposition of the resulting sparse matrix. We propose an alternating di-rection method based on a variable-splitting technique and an augmented I agrangianframework for solving this nonsmooth semidefinite programming problem. In con-trast to the first-order method proposed in d' Aspremont et al. (SIAM Rev. 49:434448, 2007), which solves approximately the dual problem of the original semidefiniteprogramming problem, our method deals with the primal problem directly and solvesit exactly, which guarantees that the resulting matrix is a sparse matrix. A globalconvergence result is established for the proposed method. Numerical results on bothsynthetic problems and the real applications from classification of text data and senatevoting data are reported to demonstrate the efficacy of our method.
文摘传统图像去噪法基于有用信息和噪声频率特性的差别实现去噪,实际中,有用信息和噪声在频带上往往存在重叠,因此,传统去噪法在抑制噪声的同时,往往损失了细节信息,使图像变模糊.本文引入稀疏与低秩矩阵分解模型描述图像去噪问题,基于该模型,采用交替方向法(Alternating direction method,ADM)得到复原图像.实验证明该方法比常用的中值滤波法更有效地抑制了椒盐噪声,同时更好地保持了原始图像的细节信息.
文摘经典的鲁棒主成分分析(Robust Principal Component Analysis,RPCA)目标检测算法使用l1范数逐一判别每一像素点是否属于运动目标,未能考虑到运动目标在空间分布的连续性,不利于提升运动目标检测的鲁棒性.本文提出了一种基于l0群稀疏RPCA模型的运动目标检测方法.首先运用Ncuts算法进行区域过分割,生成多个同性区域,将其作为群稀疏约束的分组信息;第二步构造基于l0群稀疏RPCA模型,运用群稀疏准则判别过分割后的各同性区域是否为运动目标,采用交替方向乘子算法对模型进行快速求解,约束过分割形成的同性区域具有相同检测结果,进而将背景环境和运动前景分离,能够更加准确地度量运动目标的区域边界,且对复杂的背景扰动更加鲁棒,达到了运动目标鲁棒检测的目的.
文摘为了在缓解阶梯效应的同时更好地保留去噪后图像的细节信息,提出一种基于增强高阶非凸全变分(higher order non-convex total variation,HONTV)模型的图像去噪算法。该算法将每一次去噪后的图像和原始图像取平均作为增强HONTV模型下一次循环的输入并更新参数,然后采用增广拉格朗日乘子法和交替方向乘子法进行循环求解,经过多次迭代,最终得到的去噪图像包含较多的细节信息。在基于全变分的图像去噪方法中,对添加不同标准差大小的高斯白噪声的测试图像和视频进行实验。实验结果表明,所提算法在视觉性能和客观评价指标方面均优于对比算法。
