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

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.