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

TL;DR

AQMP is an innovative image compression method that adaptively refines quadtree blocks and employs hyperparameter optimization to achieve higher compression ratios with maintained quality.

Contribution

It introduces a novel adaptive quadtree refinement combined with matching pursuit and hyperparameter optimization, outperforming traditional fixed-block methods.

Findings

Achieves up to 4x higher compression than JPEG at similar SSIM.

Offers significant parallelization opportunities during compression.

Provides a publicly available implementation for reproducibility.

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.