WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression

Large language model (LLM)-based lossless image compression methods typically represent pixel data through the native text interface of a pretrained model, converting pixel values into token sequences that the LLM processes through its vocabulary head. This design shows that pretrained language models can provide probability estimates for image coding, but it also couples compression to tokenizer behavior, vocabulary-specific numeric tokens, and model-family-specific adaptation. In this paper, we present LUMI (LLM-based Unified Model-agnostic lossless Image compression), a tokenizer-agnostic framework for lossless RGB image compression with frozen LLM backbones. LUMI replaces pixel-as-text tokenization with a pixel embedding module that maps raw intensity and channel information into the continuous embedding space of the LLM. It further introduces intra-patch position encoding to retain two-dimensional spatial structure after flattening, and uses a 256-way prediction head to produce probabilities over the native pixel alphabet. Only the pixel embedding, position encoding, soft-prefix parameters, and prediction head are trained, while the LLM backbone remains fixed. Experiments on natural, medical, and remote-sensing image benchmarks with LLaMA, Qwen, and Gemma backbones show that LUMI provides a unified interface across tokenizer families, achieves competitive compression rates, and improves cross-domain robustness over tokenizer-based LLM compression baselines. These results formulate LLM-based lossless image compression as pixel-space adaptation of frozen foundation models rather than tokenizer-specific language-symbol modeling.

State-of-the-art learned image compression (LIC) schemes are increasingly based on hybrid CNN-transformer architectures. To further improve rate-distortion performance, we introduce channel-wise wavelet transforms into both the transformer and entropy-coding components. First, we propose a channel-wise wavelet-domain transformer attention (ChWDTA) mechanism. ChWDTA keeps the efficient windowed spatial self-attention used in modern LIC backbones, but computes the Q/K/V projections on channel-wise wavelet-transformed features before mapping the attention output back with the inverse transform. The resulting Channel-wise Wavelet-Domain Transformer Block (ChWDTB) therefore preserves the spatial tokenization pattern of windowed attention while sparsifying the channel covariance seen by the attention projections. Second, in the entropy-coding stage, we introduce a channel-wise wavelet packet (ChWP) decomposition that produces four equal-sized subbands, which better fit channel-wise slice-based autoregressive entropy modeling. When each channel-wise subband is divided into two slices, we use eight slices for entropy coding. With this configuration, the proposed scheme obtains BD-rate reductions of -17.82%, -19.15%, and -22.56% on the Kodak, CLIC Professional Validation, and Tecnick test sets, respectively. Even when each channel-wise subband is coded as a single slice, the scheme still retains most of the coding gains with lower complexity. The results confirm the advantage of introducing wavelet transform in CNN-transformer-based LIC schemes.

Entropy coding is widely used in typical learned image compression (LIC) that converts latents into a compact bitstream. However, entropy coding is typically sequential and becomes the coding latency bottleneck. To overcome it, we present Entropy-Coding Free Learned Image Compression (EF-LIC), a multi-rate framework that generates compact representation by removing statistical and correlation redundancy with low coding latency. First, we introduce unconstrained vector quantization and prove that its index distribution approaches the maximum-entropy bound, yielding minimal statistical redundancy. Second, we propose a context-conditioned autoregressive transform that directly reparameterizes the latents to reduce inter-dependency. Theoretical analysis shows that EF-LIC can remove correlation redundancy as effectively as typical LIC with entropy coding, leading to comparable compression performance. Experiments show EF-LIC achieves up to 67.86% bitrate reduction over MS-ILLM on Kodak with LPIPS. Ablation studies further show EF-LIC matches the compression performance of its entropy-coding based variant while achieving over $3\times$ faster encoding and $5\times$ faster decoding.