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Transform coding to sparsify signal representations remains crucial in animage compression pipeline. While the Karhunen-Lo\`{e}ve transform (KLT)computed from an empirical covariance matrix $\bar{C}$ is theoretically optimalfor a stationary process, in practice, collecting sufficient statistics from anon-stationary image to reliably estimate $\bar{C}$ can be difficult. In thispaper, to encode an intra-prediction residual block, we pursue a hybridmodel-based / data-driven approach: the first $K$ eigenvectors of a transformmatrix are derived from a statistical model, e.g., the asymmetric discrete sinetransform (ADST), for stability, while the remaining $N-K$ are computed from$\bar{C}$ for performance. The transform computation is posed as a graphlearning problem, where we seek a graph Laplacian matrix minimizing a graphicallasso objective inside a convex cone sharing the first $K$ eigenvectors in aHilbert space of real symmetric matrices. We efficiently solve the problem viaaugmented Lagrangian relaxation and proximal gradient (PG). Using WebP as abaseline image codec, experimental results show that our hybrid graph transformachieved better energy compaction than default discrete cosine transform (DCT)and better stability than KLT.

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