基于列约束的低秩矩阵恢复方法
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引用本文:裘国永,张 力.基于列约束的低秩矩阵恢复方法[J].计算技术与自动化,2017,(4):110-114
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裘国永,张 力 (陕西师范大学 计算机科学学院陕西 西安 710119) 
中文摘要:由于在成像过程中出现遮挡现象,图像矩阵的元素有缺失。在正投影相机模型下,提出一种基于列约束的低秩矩阵恢复方法。该方法利用图像矩阵是一个低秩矩阵从而图像序列具有冗余性的特性,利用奇异值分解由图像矩阵的列空间构造出一个投影矩阵,得到图像矩阵的列所满足的约束条件,将缺失元素的恢复转化为迭代求解二次型的极值问题,利用它恢复出图像矩阵的缺失元素。该方法从理论上能够保证收敛到全局最小值。仿真实验表明,此方法具有收敛速度快,恢复精度高等优点。
中文关键词:遮挡点  低秩矩阵  奇异值分解  列约束
 
Low-rank Matrix Recovery Method Based on Column Metric Constraints
Abstract:To recover the position of occlusion,the image matrix has some missing elements because of occluding in the imaging process.An low-rank matrix recovery method based on column metric constraints under orthographic projection is presented.Utilizing the property that the image matrix is of low rank and the redundancy that exists in an image sequence,a projective matrix is constructed via singular value decomposition to get the image matrix’s column metric constraints.The method iteratively solves the minimum of a quadratic function to recover the missing elements of the image matrix.The method can guarantee to converge to the global optimal solution theoretically.The simulated experiments show that the proposed method has the advantages of fast convergence speed and small error.
keywords:occlusion  low-rank matrix  singular value decomposition  column metric constraints
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