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

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.

Hyperparameter optimization of hp-greedy reduced basis for gravitational wave surrogates

In a previous work we introduced, in the context of gravitational wave science, an initial study on an automated domain-decomposition approach for reduced basis through hp-greedy refinement. The approach constructs local reduced bases of lower dimensionality than global ones, with the same or higher accuracy. These ``light'' local bases should imply both faster evaluations when predicting new waveforms and faster data analysis, in particular faster statistical inference (the forward and inverse problems, respectively). In this approach, however, we have previously found important dependence on several hyperparameters, which do not appear in global reduced basis. This naturally leads to the problem of hyperparameter optimization (HPO), which is the subject of this paper. We tackle the problem through a Bayesian optimization, and show its superiority when compared to grid or random searches. We find that for gravitational waves from the collision of two spinning but non-precessing black holes, for the same accuracy, local hp-greedy reduced bases with HPO have a lower dimensionality of up to $4 \times$ for the cases here studied, depending on the desired accuracy. This factor should directly translate in a parameter estimation speedup, for instance. Such acceleration might help in the near real-time requirements for electromagnetic counterparts of gravitational waves from compact binary coalescences. In addition, we find that the Bayesian approach used in this paper for HPO is two orders of magnitude faster than, for example, a grid search, with about a $100 \times$ acceleration. The code developed for this project is available as open source from public repositories.