迭代块张量奇异值保持法提取图像低秩分量
Iterative Block Tensor Singular Value Thresholding for Extraction of Low Rank Component of Image Data
摘要：
张量主成分分析（TPCA）是主成分分析的多线性扩展，它将一组相关的测量值转换为多个主成分。本文提出了一种基于张量奇异值分解的鲁棒TPCA方法来提取多路数据的主成分。张量被分成许多相同大小的块。采用迭代张量奇异值阈值法提取每个块张量的低秩分量。多路数据的PRIN-UNR分量是所有块张量的所有低秩分量的级联。给出了保证分解成功的块张量不相干条件。这种分解具有与由奇异值分解得到的低秩矩阵相似的最优性。实验上，我们证明了它的有效性，在两个应用程序中，包括运动分离的监控视频和光照归一化的人脸图像。
英文摘要：
Tensor principal component analysis (TPCA) is a multi-linear extension of principal component analysis which converts a set of correlated measurements into several principal components. In this paper, we propose a new robust TPCA method to extract the princi- pal components of the multi-way data based on tensor singular value decomposition. The tensor is split into a number of blocks of the same size. The low rank component of each block tensor is extracted using iterative tensor singular value thresholding method. The prin- cipal components of the multi-way data are the concatenation of all the low rank components of all the block tensors. We give the block tensor incoherence conditions to guarantee the successful decom- position. This factorization has similar optimality properties to that of low rank matrix derived from singular value decomposition. Ex- perimentally, we demonstrate its effectiveness in two applications, including motion separation for surveillance videos and illumination normalization for face images.
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