  Transform coding to sparsify signal representations remains crucial in an
image compression pipeline. While the Karhunen-Lo\`{e}ve transform (KLT)
computed from an empirical covariance matrix $\bar{C}$ is theoretically optimal
for a stationary process, in practice, collecting sufficient statistics from a
non-stationary image to reliably estimate $\bar{C}$ 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
$\bar{C}$ 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.
