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

Hyperspectral unmixing decomposes mixed pixels into material endmembers and their abundances from contiguous spectral observations. In modular sensing pipelines, endmembers are often first identified and then treated as fixed during abundance estimation. When this fixed endmember prior is inaccurate, spatially structured mismatch arising from illumination changes, sensor artifacts, or material boundaries may be incorrectly captured by the abundance variables, leading to unstable decompositions. This study presents an interpretable stage-wise hyperspectral unmixing framework (I-HyperSU) under fixed endmember priors, which is explicitly decomposed into a fixed endmember matrix $\mathbf{A}$, an abundance block $\mathbf{X}$, and a structural residual refinement block $\mathbf{S}$. The X-block estimates abundances using FISTA with nonnegativity and sparsity enhancement, and a soft penalty that approximately enforces sum-to-one constraints. The S-block jointly applies low-rank SVD structural regularization and a lightweight deep image prior (DIP) to refine structured residuals. This staged design makes the interaction between abundance and residual components transparent and interpretable. Experiments on Samson, Urban, and Jasper Ridge datasets demonstrate that, under fixed and imperfect endmember priors, soft abundance relaxation consistently outperforms hard simplex projection. Under the default N-FINDR endmember prior, the proposed framework reduces the joint reconstruction error by 61.7%--69.5% compared with a fixed-$\mathbf{A}$ UCLS baseline, while keeping the abundance RMSE nearly unchanged, indicating that the residual refinement branch accounts for structured model mismatch without degrading the abundance estimates. For example, on Urban, the reconstruction SAM decreases from $5.99^\circ$ for the X-only model to $1.92^\circ$ for the full model.

Hyperspectral image (HSI) restoration is crucial for reliable analysis, as real-world HSIs suffer from noise, blur, and resolution loss. However, existing models trained on source data often fail on target domains lacking clean references, a common real-world scenario. To address this, we present HIR-ALIGN, a plug-and-play target-adaptive augmentation framework that enhances HSI restoration by augmenting limited training images with synthetic data matching the target distribution, without extra clean target-domain HSI data. It has three stages: (i) proxy generation, where off-the-shelf restoration models are applied to degraded target observations to produce semantics-preserving proxy HSIs that approximate clean target-domain images; (ii) distribution-adaptive synthesis, where a blur-robust unCLIP diffusion model generates target-aligned RGBs from proxy RGBs with prompt conditioning and embedding-space noise initialization. The warp-based spectral transfer module then synthesizes HSIs by aligning each generated RGB with its proxy RGB, estimating soft patch-wise transport weights, and applying these weights and learnable local interpolation kernels to the proxy HSI; and (iii) aligned supervised finetuning, where restoration networks pretrained on the source distribution are finetuned with proxy HSIs and synthesized target-aligned HSIs, then deployed on degraded target images. We also provide theoretical analysis showing that, under stated assumptions, the proposed augmentation-based finetuning obtains a tighter target-domain restoration-risk upper bound by jointly improving target-distribution coverage and controlling spectral bias. Experiments on simulated and real datasets across denoising, super-resolution, and other restoration tasks demonstrate that HIR-ALIGN is superior to proxy-only target-adaptation baselines and outperforms representative unsupervised methods in most cases.

Reconstructing a three-dimensional hyperspectral cube from a two-dimensional compressed measurement is a severely ill-posed inverse problem. Existing deep unfolding networks (DUNs) retain fidelity to the imaging model, but regression-trained denoisers can suppress spatial detail and smooth spectral structure under strong modulation. This paper proposes \emph{FMU}, a deep unfolding framework that couples a measurement-conditioned flow-matching prior with a sensing-model-guided measurement update. A two-phase scheme first learns a compact clean-HSI latent target and then trains a conditional velocity field to generate this target from Gaussian noise. A mean-velocity regularizer additionally penalizes the first-moment error of the learned field. On the KAIST 10-scene benchmark under the optical-filter setting, FMU obtains 42.13,dB PSNR and 0.9900 SSIM, outperforming LADE-DUN by 1.16,dB in PSNR under the same training data, sensing mask, and evaluation protocol. Under the same optical-filter operator, FMU is further evaluated on held-out KAIST and ICVL scenes without fine-tuning. We also report quantitative simulated-CASSI results and qualitative reconstructions of real CASSI measurements.