Hybrid Model-based / Data-driven Graph Transform for Image Coding

Transform coding to sparsify signal representations remains crucial in an image compression pipeline. While the Karhunen-Lo`eve transform (KLT) computed from an empirical covariance matrix barC is theoretically optimal for a stationary process, in practice, collecting sufficient statistics from a non-stationary image to reliably estimate barC can be difficult. In this paper, to encode an intra-prediction residual block, we pursue a hybrid model-based / data-driven approach: the first K eigenvectors of a transform matrix are derived from a statistical model, e.g., the asymmetric discrete sine transform (ADST), for stability, while the remaining N-K are computed from barC for performance. The transform computation is posed as a graph learning problem, where we seek a graph Laplacian matrix minimizing a graphical lasso objective inside a convex cone sharing the first K eigenvectors in a Hilbert space of real symmetric matrices. We efficiently solve the problem via augmented Lagrangian relaxation and proximal gradient (PG). Using WebP as a baseline image codec, experimental results show that our hybrid graph transform achieved better energy compaction than default discrete cosine transform (DCT) and better stability than KLT.