Joint Compression and Denoising Methods

• The article introduces joint methodologies that integrate denoising with compression pipelines to optimize rate-distortion performance and reduce noise-induced bit misallocation.
• It details multi-branch and latent-space strategies where parallel streams and feature partitioning enable targeted noise filtering and efficient signal reconstruction.
• Empirical results demonstrate significant improvements in PSNR, MS-SSIM, and BD-rate savings, alongside enhanced computational efficiency using contrastive and attention mechanisms.

Joint Compression and Denoising Methodology

Joint compression and denoising methods address the intertwined challenges of efficiently representing data that is corrupted by noise while simultaneously reducing that noise. Such methodologies are motivated by the inherent difficulty of distinguishing noise from signal in high-entropy data: the presence of noise generally leads to suboptimal compression ratios, as conventional codecs allocate unnecessary bits to encode stochastic variations. By integrating denoising into the compression pipeline—either in feature, latent, or domain space—recent research has demonstrated significant gains in rate-distortion (RD) performance, generalization to diverse noise types, and computational efficiency. This article provides a comprehensive treatment of the technical principles, architectures, optimization strategies, and empirical findings of state-of-the-art joint compression and denoising approaches.

1. Technical Motivations and Problem Definition

Compression codecs are designed to encode visual, audio, or textual data using the minimum number of bits subject to distortion constraints. When input data is noisy—due to sensor limitations, transmission errors, or acquisition artifacts—classical lossy compressors struggle, often preserving noise alongside signal in the encoded representation. This bit misallocation results in amplified reconstruction errors after decoding and impedes downstream restoration tasks.

Practitioners seek to minimize the RD cost: $$\mathcal{L}_\text{RD} = R(\hat{y}) + R(\hat{z}) + \alpha D(x, \hat{x})$$ where $R(\hat{y})$ and $R(\hat{z})$ represent the bitrates of the main and side information streams, $D$ quantifies distortion (commonly MSE or multiscale perceptual loss), and $\alpha$ controls the rate-distortion tradeoff (Xie et al., 2024). For joint methodologies, the loss is augmented by terms that directly supervise feature denoising and/or enforce guidance from clean exemplars: $$\mathcal{L}_\text{total} = \mathcal{L}_\text{RD} + \gamma \mathcal{L}_G + \beta \mathcal{L}_\text{CL}$$ where $\mathcal{L}_G$ is the guidance loss (feature-level clean-noisy correspondence), and $\mathcal{L}_\text{CL}$ is a contrastive loss that promotes separation between noise and signal in representations.

2. Core Architectures: Multi-Branch and Latent-Space Strategies

Recent methods employ multi-branch architectures that process noisy and clean data in tandem, explicitly sharing encoder weights to align feature spaces (Cheng et al., 2022, Xie et al., 2024, Cai et al., 2024). Typically, systems comprise:

• Main denoising branch: Input noisy data; outputs denoised features ($y_0', y_1$) via multi-stage residual blocks and attention modules.
• Guidance branch: Clean reference data during training, producing “ground-truth” features for supervision.
• Auxiliary (e.g., contrastive/SNR-aware) branches: Encode statistical priors or adapt features based on local SNR maps or contrastive objectives.

In latent-space approaches, the encoder’s output is partitioned into base and enhancement subsets. The base latent contains signal-relevant features, while enhancement channels carry noise (Alvar et al., 2022). Only the base is required for clean reconstruction—enabling efficient denoising—and the full latent (base+enhancement) can be decoded for full noisy image recovery: $z = [z_{\text{base}}, z_{\text{enh}}]$ Training is formulated to ensure that the entropy model “filters” noise into enhancement channels, minimizing the base bitrate and maximizing scalability.

Self-Organizing Operational Neural Networks (Self-ONNs) are leveraged for multi-scale denoising in feature space. The per-channel generative neuron implements a truncated Taylor expansion of the activation function: $f(x) \approx \sum_{n=0}^{Q} W_n * x^n + W_0$ which supports richer nonlinear feature representations than conventional CNNs and improves denoising robustness (Xie et al., 2024).

3. Contrastive and Attention Mechanisms

Contrastive learning is integrated to enhance discrimination between high-frequency image details and noise. The method projects noisy and clean feature representations through a shallow MLP and maximizes cosine similarity for positive pairs (from the same image under augmentation), while minimizing it for all others (Xie et al., 2024): $$\mathcal{L}_\mathrm{CL} = -\frac{1}{N}\sum_{i=1}^{N} \log \frac{\exp(\mathrm{sim}(z_{o,i}, z_{\text{aug}, i}^+)/\tau)}{\sum_{j=1}^{N}\exp(\mathrm{sim}(z_{o,i}, z_{\text{aug}, j}^-)/\tau)}$$ where $\tau$ is a temperature hyperparameter, and “sim” denotes cosine similarity.

Hybrid-attention transformer blocks (HATB) combine channel-wise group attention (to aggregate broad content information) and spatially decoupled attention (to capture local degradation structures), supporting restoration of images corrupted by a wide variety of degradations including haze, rain, snow, and noise (Zeng et al., 5 Feb 2025).

SNR-aware feature fusion adaptively weights local and non-local features using analytic SNR maps: $$s_\text{out} = f_s \odot s' + f_\ell \odot (1 - s')$$ where $f_s$ and $f_\ell$ are short-range and long-range features, and $s'$ is the scaled SNR map (Cai et al., 2024).

4. Training Protocols, Loss Functions, and Optimization

End-to-end training employs large-scale synthetic and real datasets, with explicit noise modeling (e.g., uniform sampling of read/shot noise or AWGN/Poisson noise) (Xie et al., 2024, Alvar et al., 2022). The typical pipeline utilizes Adam optimization with progressive learning rate scheduling and batch sizes 16–32.

For joint supervision, the loss is composed of RD and guidance/contrastive components:

• Guidance loss at multiple feature scales: $$L_G = \|y_0 - y_{\text{gt}}\|_1 + \|y_1 - y_{\text{gt}}\|_1$$
• Rate is directly computed from learned entropy models: arithmetic encoding conditioned on hyperprior latent statistics.
• Multi-scale supervision ensures robustness to unseen noise levels and different degradations (Cheng et al., 2022, Zeng et al., 5 Feb 2025).

Contrastive weights ($\beta$), guidance weights ($\gamma$), and hyperparameters such as temperature ($\tau$) are determined by grid search, typically ($\gamma=3, \beta=1.5, \tau=0.1$) (Xie et al., 2024).

5. Empirical Performance, Ablation, and Generalization

Extensive experiments on standard benchmarks (Kodak, CLIC, SIDD) with synthetic and real noise reveal the advantages of joint methods over sequential pipelines. Rate-distortion and PSNR/MS-SSIM curves demonstrate:

• At high noise, joint models yield up to 23.8–27.9% BD-rate savings (noise level 4: PSNR ↑ by ∼0.7 dB at low bpp, MS-SSIM ↑ by up to 0.02) (Xie et al., 2024).
• Ablations show that omitting contrastive learning degrades PSNR by ~0.16 dB, replacing Self-ONN with CNN loses ~0.1 dB, and removing multi-scale structure loses another ~0.05 dB (Xie et al., 2024).
• SNR-aware fusion nets outperform all baselines and prior joint schemes by up to 1.0 dB at highest noise (Cai et al., 2024).
• Latent-space scalable codecs achieve 70–80% BD-rate savings over cascaded denoiser+compressor setups in high-noise regimes, while providing a single bitstream for both clean and noisy reconstruction (Alvar et al., 2022).
• Transformer-based approaches incorporating latent refinement and prompt injection realize denoising at only a modest model cost (+11–28%), matching fully fine-tuned decoder quality under matched noise, and exhibiting superior cross-noise generalization (Chen et al., 2024).

Computational complexity gains are observed: multi-scale Self-ONN and attention blocks permit encoding and decoding 3–6% faster than prior joint architectures despite modest parameter overhead (Xie et al., 2024).

6. Limitations, Open Challenges, and Future Work

Current joint compression–denoising frameworks face specific limitations:

• At low noise levels, gains are modest as noise contributes minimally to entropy.
• Synthetic noise models cannot fully encompass the complexity of real sensor noise, which may include structured and spatially-dependent artifacts (Xie et al., 2024, Alvar et al., 2022).
• Parameter overhead from multi-scale denoising or high-dimensional transformer blocks may constrain deployment in resource-constrained environments.
• Generalization to multimodal data (e.g., raw-to-RGB workflows, cross-sensor adaptation) requires further study, though raw-domain joint denoising+demosaicing has shown substantial improvements in RD and computational efficiency (Brummer et al., 15 Jan 2025).
• Blind quality factor estimation for block-transform codecs (JPEG/HEVC) remains a bottleneck for real-time joint restoration (Shu et al., 2016).
• Extension of contrastive learning to deeper layers and more modalities may further improve robustness across unseen conditions (Xie et al., 2024, Zeng et al., 5 Feb 2025).

7. Domain-Specific Variants and Applications

Wavelet-domain joint compression-denoising algorithms (e.g., POAC, Ro3) project detail subbands onto approximation coefficients and discard high-frequency bands, reducing both noise and representation size, with compression ratios up to 5:1 and PSNR comparable to thresholding methods (Mastriani, 2016, Mastriani, 2014). Regularized residual quantization employs a multi-layer VQ network, yielding denoising at compression by projecting noisy inputs onto learned clean-image manifolds, outperforming JPEG-2000 and BM3D at low bitrates and moderate noise (Ferdowsi et al., 2017). Joint denoising/compression on image contours leverages dynamic programming with rate-constrained MAP estimation and context trees, demonstrating that the joint approach strictly dominates the separate two-stage pipeline in terms of RD tradeoff and smoothness of reconstructed shapes (Zheng et al., 2017). Compression-based denoising for discrete memoryless channels optimizes the distortion measure to match the channel, yielding an exact characterization of achievable loss and Markovity of reconstructed triples (Song et al., 16 Dec 2025).

The rapid evolution of joint compression and denoising frameworks, driven by synergistic advances in representation learning, attention mechanisms, latent scalability, and channel-matched optimization, is establishing new upper bounds on rate-distortion performance and restoration quality across modality, noise level, and bandwidth constraints.