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

arXiv: https://arxiv.org/abs/2203.01186 · HTML: https://mlsanity.com/paper/2203.01186/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 2 Mar 2022.

## Builds on (most cited first, 7 of 7)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Graph Spectral Image Processing](https://mlsanity.com/paper/1801.04749/) (2018)
- [Graph Fourier Transform with Negative Edges for Depth Image Coding](https://mlsanity.com/paper/1702.03105/) (2017)
- [Learning Sparse Graph Laplacian with K Eigenvector Prior via Iterative GLASSO and Projection](https://mlsanity.com/paper/2010.13179/) (2020)
- [Graph-based Transforms for Video Coding](https://mlsanity.com/paper/1909.00952/) (2019)
- [Pre-demosaic Graph-based Light Field Image Compression](https://mlsanity.com/paper/2102.07883/) (2021)

## Abstract (arXiv)

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.