Rank-R Approximation of Tensors: Using Image-as-Matrix Representation

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Rank-R Approximation of Tensors: Using Image-as-Matrix Representation
We present a novel multilinear algebra based approach for reduced dimensionality representation of image ensembles. We treat an image as a matrix, instead of a vector as in traditional dimensionality reduction techniques like PCA, and higher-dimensional data as a tensor. This helps exploit spatio-temporal redundancies with less information loss than image-as-vector methods. The challenges lie in the computational and memory requirements for large ensembles. Currently, there exists a rank-R approximation algorithm which, although applicable to any number of dimensions, is efficient for only low-rank approximations. For larger dimensionality reductions, the memory and time costs of this algorithm become prohibitive. We propose a novel algorithm for rank-R approximations of thirdorder tensors, which is efficient for arbitrary R but for the important special case of 2D image ensembles, e.g. video. Both of these algorithms reduce redundancies present in all dimensions. Rank-R tensor approx...
Hongcheng Wang, Narendra Ahuja
Added 12 Oct 2009
Updated 12 Oct 2009
Type Conference
Year 2005
Where CVPR
Authors Hongcheng Wang, Narendra Ahuja
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