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

Vector-quantization based image compression has achieved strong rate--distortion performance, yet most of them still produce a separate compressed representation for each target bitrate. Such variable-rate behavior allows one model to operate at multiple rates, but it does not necessarily provide a progressive bitstream whose prefixes are themselves decodable and can be refined by appending additional bits. We propose \textbf{Tree-VQ}, a progressive tree-structured vector quantization framework for learned image compression. Tree-VQ organizes discrete codewords as a hierarchical binary tree and represents each latent token by a routed root-to-leaf path. Crucially, every prefix of this path corresponds to a valid quantized representation, so shallow internal nodes serve as coarse reconstruction codes and deeper nodes provide successive refinements. This allows a compressed image to be decoded from an early prefix and progressively improved as more branch symbols are received, rather than being re-encoded for different target rates. To make this structure practical for compression, we introduce a prefix-compatible tree entropy model that codes progressive continuation decisions and routed branch refinements using only causally available decoded contexts. We further use rate-aware refinement scheduling to decide which spatial blocks should receive additional tree bits under a given prefix budget, and hierarchical prefix supervision to ensure that internal nodes are directly decodable at low rates. Experiments show that Tree-VQ achieves a superior performance--efficiency trade-off, delivering the best perceptual compression results with much fewer parameters and lower latency than competing methods.

Recent advances in conventional and learning-based image coding have increased the demand for benchmark datasets that support fine-grained assessment of compressed image quality, particularly for learning-based image compression methods. This paper introduces Assessment of Image Coding 2026 (AIC2026), a large-scale dataset for high-fidelity image compression containing 70 source images selected from 2,787 candidates using semantic clustering, inter-metric disagreement among objective image quality assessment (IQA) methods, and manual inspection and refinement. The dataset covers a wide range of compression artifacts produced by eight conventional and four learning-based codecs across 17 coding configurations. Each source image is encoded using seven codecs. For each source-codec pair, decoded images are provided at 20 perceptually spaced distortion levels, corresponding approximately to 0.2-4.0 just-noticeable difference (JND) units using the ColorVideoVDP (CVVDP) metric for distortion estimation, yielding 9,618 distorted images. This fine-grained sampling enables analysis of rate-distortion behavior and objective metric evaluation for subtle quality differences across a wide range of compression artifacts. We report an extensive objective analysis using 24 conventional and 12 learning-based IQA methods. The results show substantial disagreement among current IQA methods for fine-grained quality differences, particularly for artifacts introduced by learning-based codecs. The complete dataset is publicly available at https://doi.org/10.18419/DARUS-6156.

Implicit Neural Representations (INRs) have recently emerged as a promising paradigm for image compression, offering a fundamentally different approach from traditional and learned codecs. Nevertheless, INR-based methods for image compression suffer from long encoding times and a consistent performance gap in classic quality metrics such as PSNR. In this work, we explore the potential of purely INR-based compression methods and we propose PaaF (Picture as a Function), a novel INR-based image codec that introduces improved architectural design, adaptive quantization, and an efficient entropy coding scheme. These components are designed to enhance rate-distortion performance while preserving the simplicity and parallelizability of INR-based decoding. Experimental results demonstrate consistent improvements over existing INR-based methods in both quantitative metrics and perceptual quality. These findings highlight the potential of INR-based approaches and contribute to narrowing the gap between functional representations and more established compression paradigms.