Taming Hierarchical Image Coding Optimization: A Spectral Regularization Perspective

Hierarchical coding offers distinct advantages for learned image compression by capturing multi-scale representations to support scale-wise modeling and enable flexible quality scalability, making it a promising alternative to single-scale models. However, its practical performance remains limited. Through spectral analysis of training dynamics, we reveal that existing hierarchical image coding approaches suffer from cross-scale energy dispersion and spectral aliasing, resulting in optimization inefficiency and performance bottlenecks. To address this, we propose explicit spectral regularization schemes for hierarchical image coding, consisting of (i) intra-scale frequency regularization, which encourages a smooth low‑to‑high frequency buildup as scales increase, and (ii) inter-scale similarity regularization, which suppresses spectral aliasing across scales. Both regularizers are applied only during training and impose no overhead at inference. Extensive experiments demonstrate that our method accelerates the training of the vanilla model by 2.3$\times$, delivers an average 20.65\% rate–distortion gain over the latest VTM-22.0 on public datasets, and outperforms existing single-scale approaches, thereby setting a new state of the art in learned image compression.