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

• URL: http://arxiv.org/abs/2203.01186v1
• Date: Wed, 2 Mar 2022 15:36:44 GMT
• Title: Hybrid Model-based / Data-driven Graph Transform for Image Coding
• Authors: Saghar Bagheri, Tam Thuc Do, Gene Cheung, Antonio Ortega
• Abstract summary: We present a hybrid model-based / data-driven approach to encode an intra-prediction residual block. The first $K$ eigenvectors of a transform matrix are derived from a statistical model, e.g., the asymmetric discrete sine transform (ADST) for stability. Using WebP as a baseline image, experimental results show that our hybrid graph transform achieved better energy compaction than default discrete cosine transform (DCT) and better stability than KLT.
• Score: 54.31406300524195
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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