Sparse two-dimensional singular value decomposition

In this paper, we propose a new data-driven transform, called sparse two-dimensional singular value decomposition (S2DSVD). By leveraging the advantages of discrete cosine transform and the conventional 2D SVD, we decompose a set of matrices into transform coefficient matrices with sparse and orthogonal basis functions. Such sparsity characteristic can significantly reduce their overhead, hence being beneficial to data compression. We formulate S2DSVD as a constrained optimization problem and solve it via alternative iteration. We demonstrate the efficacy of S2DSVD on image and video datasets, and observe that it can produce results with error comparable to 2D SVD whereas its space complexity is significantly smaller than 2D SVD.