Framelet-WCD: A Novel Paradigm for Ultra-Efficient AI-Driven Data Compression and High-Fidelity Reconstruction

This work proposes Framelet-WCD a novel AI-driven data compression framework that combines *multiscale basis decomposition* with *semantic-aware sparsity*. Conventional neural compression techniques rely heavily on opaque latent representations and end-to-end optimization, sacrificing interpretability and controllability. Framelet-WCD introduces a new paradigm through Weighted Combinatorial Decomposition (WCD) — a logic-aligned sparsity prior that dynamically selects structured basis groups aligned with semantic tags. We demonstrate that Framelet-WCD achieves:- **5.8× decoding speedup** over neural codecs,- **42% gain in OOD robustness**,- **Dice score of 0.92** on tumor segmentation (BraTS 2023),- **<0.5m LIDAR ranging error** at 50m (KITTI),- and **≥90% semantic group coherence**, all with interpretable structure. This framework not only bridges the gap between classical transform coding and deep learning but also aligns with key industrial standards like ISO 26262 and DICOM — enabling direct deployment in safety-critical domains. Revision History v1.0Initial release. Included a major title typo (“Flemlet”) and an early draft structure. v1.1Corrected the title spelling to “Framelet.” Minor cleanup of wording, references, and consistency. v2Major revision of the manuscript. The paper structure was substantially reorganized, including rewritten Introduction and Background sections, a clarified formulation of Framelet-WCD, a reframed theoretical analysis with more precise claim scope, expanded experimental validation across MRI, LIDAR, OOD robustness, and interpretability, and reorganized appendices. The revised version also positions Framelet-WCD more clearly as an interpretable and semantically stable compression framework, rather than a codec optimized only for peak in-distribution PSNR.