Self-Calibrated Subspace Robust PCA for Parameter-Free Removal of Mixed Noise and Line Stripes in Hyperspectral Images

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.

The core challenge of hyperspectral image denoising is striking the right balance between data fidelity and noise prior modeling. Most existing methods place too much emphasis on the intrinsic priors of the image while overlooking diverse noise assumptions and the dynamic trade-off between fidelity and priors. To address these issues, we propose a denoising framework that integrates noise prior reduction and a spatial-spectral adaptive fidelity term. This framework considers comprehensive noise priors with fewer parameters and introduces an adaptive weight tensor to dynamically balance the fidelity and prior regularization terms. Within this framework, we further develop a fast and robust pixel-wise model combined with the representative coefficient total variation regularizer to accurately remove mixed noise in HSIs. The proposed method not only efficiently handles various types of noise but also accurately captures the spectral low-rank structure and local smoothness of HSIs. An efficient optimization algorithm based on the alternating direction method of multipliers is designed to ensure stable and fast convergence. Extensive experiments on simulated and real-world datasets demonstrate that the proposed model achieves superior denoising performance while maintaining competitive computational efficiency.

Hyperspectral image super-resolution (HSI-SR) aims to recover spatial detail while preserving the spectral shape on which quantitative analysis relies. Recent HSI-SR methods, from repurposed RGB super-resolution backbones to dedicated spectral-spatial architectures, have greatly improved spatial reconstruction. However, overlooking the compact spectral structure of hyperspectral data leaves residual spectral errors, while binding the spectral treatment to each architecture forces it to be rebuilt for every new backbone. Yet the low-dimensional structure of spectra belongs to the data, not to any backbone. Backbones differ in the errors they leave, but not in the structure of the true spectra. One rectifier design can therefore serve any backbone. Building on this insight, we propose the Spectral Rectification Super-Resolution Network (\textbf{SR$^{2}$-Net}), a model-agnostic rectifier that needs nothing from the backbone but its output, leaves its internal architecture untouched, and is trained per backbone. SR$^{2}$-Net follows an enhance-then-rectify pipeline in which Hierarchical Spectral-Spatial Synergy Attention (\textbf{H-S$^{3}$A}) reinforces cross-band interactions, while Mode-Constrained Rectification (MCR) confines the correction to a learned compact spectral subspace. A degradation-consistency constraint further ties the output to the observed low-resolution input. Experiments with five backbones spanning CNN, Transformer, and diffusion families show that one fixed configuration improves spectral fidelity in every reported setting while preserving or improving spatial quality. Averaged over thirty in-domain settings, SR$^{2}$-Net removes 22.6% of the residual spectral error at a backbone-independent cost of 0.048M parameters.