Image Coding With Data-Driven Fast Transforms Based on Approximate Givens Factorizations
Bibliographic record
Abstract
In image compression, adaptive transform coding with optimal linear transforms computed from data being coded has been shown to outperform the widely used two-dimensional discrete cosine transform (2D-DCT). However, unlike the 2D-DCT for which fast computation algorithms exist, data-driven transforms are random matrices with no particular structure that can be exploited for fast computations. We present an approach to low-complexity data-driven image coding using structured orthonormal transform matrices constructed from approximate Givens factorizations optimized for transform coding. These Givens factorization-based fast transforms (GFFTs) are optimized by a tree-search algorithm on the orthonormal matrix manifold to minimize the mean square error of high-rate transform coding. Experimental results obtained with an adaptation of the baseline JPEG algorithm are presented which show that, for many images, the GFFTs outperform the 2D-DCT at comparable or lower computational complexity, with peak signal-to-noise ratio (PSNR) improvements as high as 6 dB in some cases.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".