Compressive principal component pursuit
Compressive principal component pursuit
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DOI：
10.1109/isit.2012.6283062
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
John Wright;Arvind Ganesh;Kerui Min;Yi Ma
中科院分区：
文献类型：
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作者：
John Wright;Arvind Ganesh;Kerui Min;Yi Ma
我们考虑从一小组线性测量中恢复低秩和稀疏分量叠加的目标矩阵的问题。这个问题出现在压缩感知的结构化高维信号，如视频和高光谱图像，以及在分析变换不变的低秩恢复。我们分析了自然凸启发式算法解决这个问题的性能，假设测量值是随机均匀选择的。我们证明，这种启发式准确地恢复低秩和稀疏的条款，提供的观测数量超过了一个多对数因子的分量信号的固有自由度的数量。我们的分析介绍了几个想法，可能是独立的兴趣，更一般的问题，结构化信号的叠加压缩感知。
We consider the problem of recovering a target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises in compressed sensing of structured high-dimensional signals such as videos and hyperspectral images, as well as in the analysis of transformation invariant low-rank recovery. We analyze the performance of the natural convex heuristic for solving this problem, under the assumption that measurements are chosen uniformly at random. We prove that this heuristic exactly recovers low-rank and sparse terms, provided the number of observations exceeds the number of intrinsic degrees of freedom of the component signals by a polylogarithmic factor. Our analysis introduces several ideas that may be of independent interest for the more general problem of compressive sensing of superpositions of structured signals.