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AXS-Net: Interpretable Deep Unfolding for Hyperspectral Image Denoising via Spectral Basis Unmixing and Structured Noise Refinement

Ziyi Guan, Jianping Zhang, Zheng Yang

arXiv:2609.08777v1cs.CV

TL;DR

Hyperspectral denoisers often entangle structured corruption with the clean image, despite mixed noise also distorting spectral characteristics. AXS-Net unrolls an A-X-S decomposition with learned abundance and structured-noise operators. It reports strong in-domain performance and effective transfer to unseen datasets, while exposing interpretable intermediate estimates.

  • Problem

    Many deep denoisers regress a single clean image, entangling signal and structured noise without an explicit handle on stripes or impulses, which can distort per-pixel spectra.

    Source: §1 · p. 2

  • Method

    AXS-Net unrolls an alternating A-X-S decomposition, separating a low-rank unmixing-style clean component from structured noise with learned abundance and residual operators.

    Source: §1 · p. 2

  • Results

    AXS-Net achieves top in-domain performance on ICVL and generalizes effectively to unseen CAVE and Harvard, with the largest margins on Harvard.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The decomposition exposes AX as the denoised output and retains structured corruptions as a separately inspectable estimate.

    Source: §2.1 · p. 3

    The formulation assumes clean pixels are non-negative combinations of a small set of shared spectral signatures, with non-negative abundances and normalized basis columns.

    Source: §2.1 · p. 3

Abstract

from arXiv · show

Hyperspectral images (HSIs) are often degraded by mixed noise, including band-dependent Gaussian perturbations and structured artifacts such as stripes, dead-lines, and impulse noise. Most deep denoisers regress the clean image directly, entangling signal and structured noise. We instead model HSI denoising as $\Y=\A\X+\Snoise+\Nnoise$, where $\A\X$ is a low-rank spectral-subspace (unmixing) reconstruction, $\Snoise$ is structured sparse noise and $\Nnoise$ is residual Gaussian noise. The resulting regularized optimization problem is unrolled into AXS-Net, a $K$-stage alternating proximal-point framework. Each stage combines an analytic spectral-basis gradient step, an SSX-Block proximal operator for abundance coefficients, and an SBlock proximal operator for the structured residual with column-consistent and sparse priors. This optimization correspondence exposes interpretable endmembers, abundance maps, and structured-noise estimates. Across ICVL, CAVE, and Harvard datasets and five noise configurations, the proposed AXS-Net achieves strong in-domain accuracy and competitive zero-shot transfer, with consistent gains across all five noise regimes on ICVL and Harvard. The recovered structured-noise closely follows the synthetic reference, and the recovered spectral basis is smooth and band-ordered rather than an arbitrary set of latent channels.

1 Introduction

Mixed Gaussian and structured noise degrades hyperspectral images and distorts their spectral characteristics. AXS-Net unrolls a low-rank-plus-sparse decomposition, and the reported results combine strong benchmark performance with interpretable noise and spectral estimates.

1 Introduction

  • Mixed-noise removal matters because stripes, dead-lines, and impulses reduce visual quality and distort per-pixel spectral characteristics.HSIs also contain band-dependent Gaussian perturbations and structured corruptions.Source: §1 · pp. 1–2
  • Most deep denoisers regress a single clean image, entangling signal and structured noise without an explicit handle on stripes or impulses.Existing unfolded denoisers also optimize a single clean-image variable, while classical priors and iterative solvers can limit accuracy and efficiency.Source: §1 · p. 2
  • AXS-Net unrolls an alternating low-rank-plus-sparse decomposition, using an analytic spectral-basis update, SSX-Block for abundance estimation, and SBlock for structured-residual refinement.The formulation separates an unmixing-style clean component AX from a dedicated structured-noise estimate S.Source: §1 · p. 2
  • AXS-Net achieves top in-domain performance on ICVL and generalizes effectively to unseen CAVE and Harvard, with the largest margins on Harvard.Its recovered structured noise closely follows synthetic ground truth, and its stage-wise decomposition remains spectrally organized and interpretable.Source: §1 · p. 2

2 Methodology

AXS-Net formulates HSI restoration as a low-rank unmixing reconstruction plus structured sparse and residual Gaussian noise, then unfolds alternating updates into a fixed-depth network.

2.1 Problem Formulation

  • The observation is decomposed into a low-rank clean reconstruction AX, structured sparse noise S, and residual Gaussian noise N.The clean component is treated as the denoised output, while S remains separately inspectable; nonnegative A and X constraints support their endmember and abundance interpretations.Source: §2.1 · p. 3

2.2 Overall Unfolding Framework

  • Six stages unroll alternating updates into a feed-forward network, retaining an analytic A-step while learning proximal updates for X and S.Stage parameters are distinct, and K=6 balances restoration performance against added latency.Source: §2.2 · pp. 4–5, Figure 1 · p. 4

2.3 Endmember Update: Analytic Spectral Basis Step

  • The spectral basis A is updated by a projected gradient step, preserving nonnegativity and unit-norm columns rather than learning the update as a module.The A-update is held fixed for the first 10 epochs, then activated.Source: §2.3 · p. 5

2.4 Abundance Update: Spatial–Spectral Proximal Block

  • SSX-Block applies a learned proximal update to abundances, combining window-based spatial attention with spectral attention over channel dependencies.Its inputs include the gradient-corrected estimate, prior abundance, residual information, and momentum feature; the output uses a nonnegative residual readout.Source: §2.4 · pp. 6–7, Figure 2 · p. 6

2.5 Structured-noise Update: Structure-Aware Residual Block

  • SBlock processes the reconstruction residual with directional and local branches, combines structured priors, and applies adaptive thresholding to estimate sparse structured noise.The directional branch targets stripe and dead-line structures, while the local branch preserves texture; the column-consistency and median-residual priors address stripe/dead-line and impulse noise, respectively.Source: §2.5 · pp. 7–8, Figure 3 · p. 7

2.6 Training Loss

  • Training applies deep supervision across unrolled stages, supervising clean-image intensity, spectral fidelity, structured noise, and consistency with the observation model when noise ground truth is available.Without ground-truth noise components, structured-noise and consistency losses are omitted, leaving clean-image supervision.Source: §2.6 · p. 8

3 Experiments

Experiments compare AXS-Net with learned denoisers on ICVL and zero-shot CAVE and Harvard, then examine decomposition fidelity and component ablations. Results show strong benchmark performance and interpretable structured-noise estimates, with computational and supervision trade-offs.

3.1 Experimental Setup

  • ICVL-trained models are evaluated on 50 ICVL scenes and zero-shot on 32 CAVE and 26 Harvard scenes, using five noise settings and identical pre-generated noisy cubes.The comparison covers MPSNR, MSSIM, SAM, ERGAS, and RMSE; learned baselines use official weights and native inference pipelines without retuning or test-time augmentation.Source: §3.1 · p. 9

3.2 Comparison with State-of-the-Art

  • AXS-Net leads all ICVL metrics across five noise settings and all Harvard metrics plus CAVE MSSIM, but SSUMamba has higher CAVE MPSNR on stripe and mixture noise.Paired tests report 107 wins/8 ties/5 losses on ICVL and 106/9/5 on Harvard; CAVE is more balanced at 62/29/29.Source: §3.2 · pp. 9–10, Table 1 · p. 10, Table 2 · p. 10
  • AXS-Net uses 1.80 M parameters and takes 14.42 s on a 1392 × 1300 × 31 tensor, slower than SSUMamba, HSDT, and T3SC but faster than MAC-Net.The reported deployment-time figures use each method’s native inference configuration, not a hardware-normalized complexity ranking.Source: §3.2 · p. 10

3.3 Interpretability and Structured-Noise Recovery

  • Recovered bases are smooth and band-ordered, abundance maps retain spatial structure, and the reconstruction sharpens from k=1 to k=6 as the residual concentrates on stripes.The paper does not claim that recovered endmembers identify physical materials.Source: §3.3 · pp. 10–11
  • Across 50 ICVL mixture scenes, estimated structured-noise profiles have median Pearson correlation 0.84 and RMSE 0.096 ± 0.002 against synthetic references.The reported metrics quantify consistency under synthetic supervision and the experimental setting.Source: Figure 6 · p. 11, §3.3 · p. 12

3.4 Ablation Study

  • Removing structured-noise supervision improves mixture-noise MPSNR by 0.70 dB and SAM by 0.92, but the supervised model retains an interpretable S estimate comparable to the reference profile.The reported main model keeps supervision to tether S to the reference.Source: §3.4 · p. 13
  • On ICVL mixture noise, removing the structured-noise branch costs 8.15 dB MPSNR, freezing the PCA basis costs 10.02 dB, and halving depth costs 5.22 dB.The structured-noise branch costs 0.12 dB on pure Gaussian, 2.38 dB on stripe, and 8.15 dB on mixture noise; SSX spatial attention most benefits Gaussian and mixture settings, while component omissions markedly hurt impulse-noise performance.Source: §3.4 · p. 12, Table 4 · p. 13
  • Removing the impulse prior costs 1.06 dB MPSNR, while removing the stripe prior or local branch leaves image MPSNR essentially unchanged.The stripe prior is retained because it is parameter-free, and the local branch supplies isotropic features that the directional branch alone cannot represent; image-space metrics do not capture their effects on recovered S.Source: Table 4 · p. 13, §3.4 · p. 13

4 Conclusion

AXS-Net unrolls an A–X–S decomposition with analytic and learned updates, producing strong in-domain and zero-shot results while exposing spectrally structured variables. Its evaluation and structured-noise estimates remain bounded by synthetic supervision and synthetic corruption.

  • AXS-Net unrolls an A–X–S decomposition using an analytic basis step and learned abundance and structured-noise operators.Source: §4 · p. 13
  • The method achieves strong in-domain and zero-shot results while exposing spectrally structured intermediate variables.Source: §4 · p. 13
  • The study relies on synthetic S supervision and evaluates only synthetically corrupted data; real-noise HSI validation and unsupervised structured-noise estimation remain future work.Source: §4 · p. 13
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