Construction of Fast Data-driven Transforms for Image Compression via Multipath Coordinate Descent on Orthogonal Matrix Manifold

Recent research indicates that data-driven transforms can outperform the widely used separable two-dimensional discrete cosine transform (2D-DCT) in applications such as video coding. However, unlike the 2D-DCT, data-driven transforms are random matrices with no structure and do not lend themselves to fast computations. In this paper, we investigate a new approach to construct low-complexity data-driven transforms by exploiting a connection between the Givens rotation matrices and coordinate descent on the orthonormal matrix manifold. We propose a multi-path coordinate descent algorithm which is observed to produce better transform matrices than the simple coordinate descent. Our experiments with many images showed that the proposed algorithm can be used to design fast data-driven transforms which achieve a higher coding gain than the 2D-DCT in some image blocks.