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arxiv: 2605.09190 · v1 · submitted 2026-05-09 · 💻 cs.CV

AQMP: Image compression through Adaptive Quadtree Refinement and Matching Pursuit with Hyperparameter Optimization

Franco Cerino , Emmanuel Tassone , Manuel Tiglio This is my paper

Pith reviewed 2026-05-12 02:24 UTC · model grok-4.3

classification 💻 cs.CV
keywords image compressionadaptive quadtreematching pursuithyperparameter optimizationJPEG comparisonSSIM quality metricPareto optimization
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The pith

AQMP uses adaptive quadtree refinement to vary block sizes by local image complexity, allowing matching pursuit to reach up to four times the compression of JPEG at matching structural similarity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents AQMP as a codec that pairs adaptive quadtree partitioning with matching pursuit. It refines blocks to smaller sizes in detailed regions and larger sizes in uniform areas, unlike fixed-block versions of matching pursuit. This structure-aware allocation, guided by user parameters for accuracy and sparsity plus multi-objective hyperparameter tuning, produces higher compression rates than JPEG while keeping comparable SSIM scores. The design also opens parallel processing paths at the level of tree leaves and individual nodes. Experiments on representative images demonstrate the gains across a range of operating points.

Core claim

AQMP achieves up to 4× higher compression rates than JPEG at comparable SSIM values by dynamically adapting block sizes to local image structure through quadtree refinement and applying matching pursuit on the resulting variable-sized blocks, with the small set of governing hyperparameters optimized via the Tree-Structured Parzen Estimator to trace Pareto fronts between compression efficiency and visual quality.

What carries the argument

Adaptive quadtree refinement, which allocates finer partitions where the image is complex and coarser partitions where it is smooth, before running matching pursuit on each resulting block.

If this is right

  • Superior compression ratios compared to fixed-size block matching pursuit at equivalent image quality.
  • Significant parallelization opportunities at both the tree-leaf level and during compression of individual nodes.
  • Comprehensive Pareto fronts from multi-objective hyperparameter optimization that trace the efficiency-quality trade-off.
  • Competitive quality maintained across a broad range of compression regimes on representative test images.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same adaptive partitioning idea could be tested on video sequences by adding temporal consistency constraints to the quadtree decisions.
  • Hybrid systems might combine AQMP blocks with standard codecs to handle only the locally complex regions with matching pursuit.
  • The released implementation makes it straightforward to measure wall-clock speedups from the described parallel opportunities on modern hardware.

Load-bearing premise

The adaptive quadtree partitioning combined with matching pursuit on variable-sized blocks will deliver consistent gains over fixed-block baselines on images outside the tested set, and the hyperparameter optimization will not overfit to the chosen test images or SSIM metric.

What would settle it

A controlled test on a fresh collection of images never seen during hyperparameter search, showing that AQMP no longer exceeds JPEG compression rates at the same SSIM values.

Figures

Figures reproduced from arXiv: 2605.09190 by Emmanuel Tassone, Franco Cerino, Manuel Tiglio.

Figure 1
Figure 1. Figure 1: DCT matrix transforms. The image shows matrix transforms of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Encoder high level design. 2.3.1 Encoder At a high level, the encoder consists of three steps: (i) image pre-processing, (ii) Adaptive Quadtree Refinement with MP compression, and (iii) lossless coding. See [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Decoder high level design. Steps (i) and (iii) are lossless; Step (ii) is lossy. Although a full codec is presented here, the core contribution of this work is Step (ii), which is described in detail following the high-level description below. (i) The input image is pre-processed to serve as input to Step (ii). The color channels are converted to one of the supported formats, such as RGB or YCBCR, and each… view at source ↗
Figure 4
Figure 4. Figure 4: AQMP-compression path flow. 2.4 Hyperparameter Optimization (HPO) To perform AQMP, different parameters must first be defined before, which determine how the process is carried out, affecting both the final image qual￾ity and compression. The set of hyperparameters to take into account in our AQMP approach are the following: • max error: maximum squared norm of the residual (tol in the utilized OrthogonalM… view at source ↗
Figure 5
Figure 5. Figure 5: Illustrative probability distribution built from a set of hyperpa [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Illustrative cost function and associated distributions of best and [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Image compression results for the Clock.png image with resolution [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Hyperparameter Optimization for Clock image (256x256). The [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Hyperparameter Optimization for Splash image (512x512). The [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Hyperparameter Optimization for Airplane (U-2) iamge [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of AQMP with TPE, AQMP with Random Sampler, [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of AQMP with TPE, AQMP with Random Sampler, [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of AQMP with TPE, AQMP with Random Sampler, [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of AQMP with TPE, AQMP with Random Sampler, [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of AQMP with TPE, AQMP with Random Sampler, [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Compression-rate vs SSIM curves for AQMP (left) and JPEG [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Compression-rate vs SSIM curves for AQMP (left) and JPEG [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Compression-rate vs SSIM curves for AQMP (left) and JPEG [PITH_FULL_IMAGE:figures/full_fig_p027_18.png] view at source ↗
read the original abstract

We present AQMP, a novel image codec combining Adaptive Quadtree Refinement with Matching Pursuit. Unlike conventional Matching Pursuit methods that operate on fixed-size sub-images, AQMP dynamically adapts block sizes to local image structure, allocating finer partitions where the image is complex and coarser ones where it is smooth. This adaptivity yields superior compression ratios compared to fixed-size block Matching Pursuit at equivalent image quality, while offering significant parallelization opportunities at both the tree-leaf level and during compression of individual nodes. The algorithm is governed by user-specified accuracy and sparsity parameters alongside a small set of additional hyperparameters. To navigate the trade-off between compression efficiency and visual quality, we perform multi-objective hyperparameter optimization using the Tree-Structured Parzen Estimator, producing comprehensive Pareto fronts. Experimental results show that AQMP achieves up to $4\times$ higher compression rates than JPEG at comparable SSIM values, while maintaining competitive quality across a broad range of compression regimes. Performance evaluation is provided using a representative set of test images. To ensure reproducibility and promote adoption, we have made our implementation publicly available on GitHub under the MIT license.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper introduces AQMP, an image compression codec that combines adaptive quadtree refinement (dynamically varying block sizes based on local image complexity) with matching pursuit for sparse representation on variable-sized blocks. Hyperparameters including accuracy and sparsity parameters are tuned via multi-objective Tree-Structured Parzen Estimator optimization to generate Pareto fronts trading off compression rate and visual quality (measured by SSIM). The central empirical claim is that AQMP achieves up to 4× higher compression rates than JPEG at comparable SSIM values across a range of regimes, with a public MIT-licensed implementation provided for reproducibility on a representative set of test images.

Significance. If the results hold under proper controls, the work offers a practical contribution to adaptive image compression by exploiting image structure for variable partitioning and providing open code, which supports reproducibility. The multi-objective optimization producing Pareto fronts is a methodological strength for navigating quality-compression trade-offs. However, the purely empirical nature of the claims, without parameter-free derivations or machine-checked elements, means significance depends entirely on the robustness of the experimental protocol.

major comments (2)
  1. [Experimental results and hyperparameter optimization sections] Experimental results and hyperparameter optimization sections: The manuscript does not specify whether TPE optimization was performed on a held-out validation split or directly on the same 'representative set of test images' used to report the final 4× compression gain over JPEG. If the latter, the selected operating points can overfit to both image content and the SSIM metric, rendering the headline performance comparison non-generalizable and undermining the central empirical claim.
  2. [Methods and experimental protocol] Methods and experimental protocol: No details are provided on the exact baselines (e.g., fixed-block matching pursuit variants, other quadtree codecs), the precise definition of 'compression rate' (bits per pixel or ratio), the number of test images, or any statistical measures (standard deviation, multiple random seeds) supporting the 'up to 4×' and 'competitive quality' statements.
minor comments (3)
  1. [Abstract and Methods] The abstract and methods mention 'a small set of additional hyperparameters' without enumerating them or their ranges, making it difficult to assess the optimization space.
  2. [Experimental results] No discussion of known limitations of SSIM (e.g., its insensitivity to certain artifacts or poor correlation with human perception at low bitrates) is included, despite its central role in the quality metric.
  3. [Conclusion/Reproducibility] The public GitHub implementation is mentioned but without instructions on how to reproduce the exact Pareto fronts or the reported JPEG comparisons.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address each major comment below, acknowledging where the original manuscript was insufficiently clear or rigorous, and describe the specific revisions that will be made.

read point-by-point responses

  1. Referee: [Experimental results and hyperparameter optimization sections] Experimental results and hyperparameter optimization sections: The manuscript does not specify whether TPE optimization was performed on a held-out validation split or directly on the same 'representative set of test images' used to report the final 4× compression gain over JPEG. If the latter, the selected operating points can overfit to both image content and the SSIM metric, rendering the headline performance comparison non-generalizable and undermining the central empirical claim.

    Authors: We acknowledge the validity of this concern. The TPE optimization was performed directly on the representative test images to generate the Pareto fronts and the reported operating points. This choice was made because the optimization is an integral part of configuring the codec for the given image content. However, we agree that this procedure introduces a risk of overfitting to both the specific images and the SSIM metric, which limits the strength of the generalizability claim. In the revised manuscript we will (i) explicitly state that optimization occurred on the test set, (ii) discuss the implications for the 4× claim, and (iii) add results on a separate held-out collection of images to provide supporting evidence that the performance advantage is not limited to the original test set. revision: yes

  2. Referee: [Methods and experimental protocol] Methods and experimental protocol: No details are provided on the exact baselines (e.g., fixed-block matching pursuit variants, other quadtree codecs), the precise definition of 'compression rate' (bits per pixel or ratio), the number of test images, or any statistical measures (standard deviation, multiple random seeds) supporting the 'up to 4×' and 'competitive quality' statements.

    Authors: We agree that these omissions reduce the clarity and reproducibility of the experimental protocol. The revised manuscript will add: (1) explicit descriptions of all baselines, including fixed-block-size matching pursuit variants and other quadtree-based codecs; (2) a precise definition of compression rate as bits per pixel (bpp); (3) the exact number and provenance of the test images; and (4) statistical summaries (means and standard deviations) of the reported metrics across the test set. Because the core AQMP algorithm is deterministic once the image and hyperparameters are fixed, multiple random seeds are not applicable; we will state this explicitly. revision: yes

Circularity Check

0 steps flagged

No circularity in claimed results or derivation

full rationale

The paper describes an algorithmic construction (adaptive quadtree partitioning combined with matching pursuit) controlled by hyperparameters that are optimized via TPE to produce Pareto fronts, then reports empirical compression and SSIM outcomes on a representative set of test images. No mathematical derivation, first-principles prediction, or fitted quantity is presented as reducing to its own inputs by construction; the performance numbers are framed as experimental measurements rather than tautological outputs of the optimization procedure itself. No self-citation load-bearing steps or ansatz smuggling appear in the provided text.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The method rests on standard image-processing assumptions about local structure and sparsity; it introduces no new physical entities and only a modest number of user-tunable parameters.

free parameters (3)
  • accuracy parameter
    User-specified target accuracy that controls how closely each block must be approximated.
  • sparsity parameter
    Controls the number of matching-pursuit coefficients retained per block.
  • additional hyperparameters
    Small set of extra settings tuned via Tree-Structured Parzen Estimator.
axioms (2)
  • domain assumption Natural images exhibit spatially varying complexity that can be captured by recursive quadtree partitioning.
    Invoked to justify adaptive block sizing over fixed blocks.
  • domain assumption A dictionary of basis functions exists from which sparse linear combinations can approximate image blocks.
    Underlying assumption of the matching-pursuit stage.

pith-pipeline@v0.9.0 · 5498 in / 1285 out tokens · 59226 ms · 2026-05-12T02:24:01.180352+00:00 · methodology

discussion (0)

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