Two-Dimensional Singular Value Decomposition ( 2 DSVD ) for 2 D Maps and Images

@inproceedings{Ding2005TwoDimensionalSV,
  title={Two-Dimensional Singular Value Decomposition ( 2 DSVD ) for 2 D Maps and Images},
  author={Chris Ding and Jieping Ye},
  year={2005}
}
For a set of 1D vectors, standard singular value decomposition (SVD) is frequently applied. For a set of 2D objects such as images or weather maps, we form 2DSVD, which computes principal eigenvectors of rowrow and column-column covariance matrices, exactly as in the standard SVD. We study optimality properties of 2DSVD as low-rank approximation and show that it provides a framework unifying two recent approaches. Experiments on images and weather maps illustrate the usefulness of 2DSVD. 
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