Hyperspectral Unmixing

Several foundation models dedicated to hyperspectral images have recently been made available. These models are trained on large unlabeled datasets and exhibit strong performance on many hyperspectral imaging tasks, such as classification or denoising. Nonetheless, their performance for hyperspectral unmixing -- the task of separating mixed spectra of overlapping materials in a hyperspectral image -- remain understudied. This might partly be due to the fact that most of them rely on vision transformer backbones, including patchification, leading to a feature resolution problem. While hyperspectral unmixing already arises from the low resolution of hyperspectral images, this patchification step potentially makes the problem even more ill-posed. Therefore, in this work, we aim to answer two questions: 1) \emph{how do foundation models perform in hyperspectral unmixing?}; 2) \emph{how to tackle the feature-level loss of resolution?} To answer the first question, we benchmark foundation models for unmixing, showing that they can reach state-of-the-art performance on four hyperspectral unmixing datasets. To answer the second question, we compare several feature upsampling approaches and empirically show that using a simple one can lead to high performance results. The code is available at https://gitlab.telecom-paris.fr/ring/hfm-hsu.git.

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 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.

Hyperspectral unmixing is a key task in remote sensing that aims to decompose mixed pixels in hyperspectral images into their constituent material signatures, or endmembers, and their fractional abundances. Conventional modular approaches estimate the scene composition through successive model-order estimation, endmember extraction, and abundance estimation stages, whose errors can lead to redundant or ambiguous candidate components and ultimately affect the recovered decomposition. We introduce an algorithm-agnostic, large vision-language model (LVLM)-driven agentic framework that refines the outputs of such pipelines rather than replacing their underlying numerical algorithms. Starting from an initial decomposition, the agent iteratively gathers complementary spectral and spatial evidence through dedicated tools, including spectral-library retrieval and abundance-map visualization, and modifies the active endmember set through merge and discard operations followed by abundance re-estimation. We apply the same refinement procedure to several modular pipelines combining different model-order, extraction, and abundance-estimation methods, and evaluate it on HYDICE Urban, Jasper Ridge, and Stonewall Playa. Experiments show that the proposed agent consistently improves endmember cardinality and generally improves the recovered spectral signatures and abundance maps across heterogeneous modular pipelines, while remaining competitive with integrated end-to-end unmixing methods, including CNN-AE, uDAS, and R-CoNMF. These results highlight the potential of tool-using LVLM agents to combine spectral and spatial evidence for algorithm-agnostic refinement of physically grounded hyperspectral unmixing decompositions. Code is publicly available at https://anonymous.4open.science/r/agentic-hu.

Hyperspectral image super-resolution aims to reconstruct high-resolution imagery while preserving dense spectral information. Recently, Mamba-based models have shown promising potential for this task by capturing long-range dependencies with linear computational complexity. Nevertheless, their causal sequence modeling requires two-dimensional hyperspectral features to be unfolded along predefined scanning orders, which disrupts spatial adjacency and restricts the effective propagation of contextual information. Moreover, state-space parameterization of existing models is predominantly derived from generic learned representations, without explicit alignment with the intrinsic characteristics of the hyperspectral image. To address this issue, we propose an Unmixing-derived Spectral and Structural Prompting Mamba framework, termed USP-Mamba, which adapts Mamba state evolution through composition-aware spectral priors and image-dependent structural prompts. Specifically, an unmixing-informed spectral prompt captures the global material composition of the input image and provides persistent conditioning throughout reconstruction. Injected into the Mamba sequence and progressively adapted across layers, it steers state evolution toward composition-consistent reconstruction. We introduce feature-level structural prompts comprising spatial and frequency components to provide image-dependent local guidance. The spatial prompt promotes structure-sensitive state encoding for local detail preservation, while the frequency prompt enables region-adaptive transitions between homogeneous regions and high-frequency details. Finally, complementary Hilbert and Semantic-Guided Neighboring scans preserve spatial continuity and strengthen non-local semantic dependency modeling. Extensive experiments on different datasets demonstrate that the proposed method consistently outperforms representative approaches.

Machine olfaction for gas unmixing is an underconstrained inverse problem in which gas compositions must be inferred from low-dimensional, delayed, and entangled sensor responses produced by interacting chemical transport, surface adsorption, and sensor transduction. One of the key obstacles is physics closure misspecification, where a neural network is designed to fit sensor traces rather than infer a physically closed olfactory process. In this work, we formulate gas unmixing as a multi-physics-constrained inverse problem governed by Maxwell--Stefan multicomponent transport PDEs, competitive adsorption ODEs, and nonlinear sensor transduction ODEs. Directly solving such a high-dimensional coupled system is computationally expensive and often numerically unstable. To this end, we propose UnMixNet, a physics-closed graph neural solver that embeds this multi-physics forward process into end-to-end gas unmixing. UnMixNet discretizes Maxwell--Stefan cross-diffusion on spatial graphs and formulates the multicomponent flux on each edge. This design enables local, differentiable, and flux-conservative inference for multicomponent cross-diffusion. Evaluations on SmellNet show improved single-odor recognition, seen-mixture unmixing, and unseen-mixture generalization. In addition, an external validation on UCI Dynamic Gas Mixtures shows that the inferred concentration process agrees with ground truth concentration set points under dynamic transitions. Process-consistency diagnostics further show that the proposed model learns transferable dynamic physical fingerprints that better satisfies transport, conservation, adsorption, and readout closure.

Due to the optical diffraction limit and long imaging distances, Closely-Spaced Infrared Small Targets (CSIST) typically exhibit energy overlap, manifesting as indistinguishable blobs in infrared images. This ambiguity invalidates the one-to-one mapping assumption of traditional detection, thereby necessitating a paradigm shift towards CSIST Unmixing, which decomposes these blobs into discrete sub-targets. However, the dominant paradigm deep unfolding networks are shackled by the high latency and structural inflexibility intrinsic to their repetitively iterative architecture. To this end, we propose the Fast One-stage CSIST Unmixing Scheme (FOCUS), a one-stage lightweight paradigm which demonstrates that deep unfolding is not necessary. Motivated by the key observation that image super-resolution (SR) and CSIST Unmixing share an isomorphic degradation model, our insight is that it is possible to achieve a paradigm shift from image SR to CSIST Unmixing via completely transforming the label space, loss functions, and evaluation criteria. Specifically, to avoid entangling geometric recovery with artifact suppression, FOCUS adopts a single pass mapping with an internal coarse-to-fine flow that progressively refines target localization from coarse spatial distributions to finer sub-pixel precision. While sparsity regularization suppresses background clutter, it also attenuates target intensities. To compensate for this attenuation of valid signals, flux conservation is introduced as a competing constraint that restores signal energy back to target centers. To the best of our knowledge, this work is the first attempt to address this task via a lightweight one-stage framework without the DUN paradigm. Experiments demonstrate that our method matches or surpasses the state-of-the-art unfolding approaches in both localization and unmixing accuracy, while boosting the inference speed by 60x.

Music source restoration (MSR) requires jointly addressing source unmixing and the inversion of non-linear production effects. Current methods struggle to achieve accurate target signal reconstruction while maintaining semantic consistency. To address this limitation, we propose DTT-BSR+, a two-stage cascade MSR system that decouples distribution fitting from signal reconstruction into separate stages. A generative DTT-BSR separator in the first stage produces stems matching the prior of clean sources, and a modified Demucs network in the second stage enhances the first stage output using time-domain and multi-resolution spectral losses. DTT-BSR+ improves multi-mel signal-to-noise ratio (MMSNR) over the single-stage DTT-BSR across all stems, and surpasses the state-of-the-art X-LANCE MSR system on five stems. We also reveal through Fréchet Audio Distance (FAD) decomposition an implicit trade-off between signal reconstruction accuracy and semantic distribution fitting across stems.

Hyperspectral 3D imaging enables the capture of dense spectral information and scene geometry but has traditionally been confined to narrow spectral windows, typically the visible range. In this work, we introduce a broadband hyperspectral 3D imaging (BH3D) method to extend this capability across the full visible-near-infrared and short-wavelength infrared (SWIR) spectrum (450-1500 nm). This broad coverage is critical as it captures complementary physical cues: visible wavelengths reveal surface appearance, while SWIR bands provide insight into subsurface properties and material composition. However, realizing BH3D is challenging due to fundamental sensor constraints between visible-spectrum silicon and SWIR-spectrum InGaAs sensors, which necessitate complex multi-spectrograph designs. Here we propose a single-spectrograph BH3D system, using a stereo setup comprising visible and SWIR cameras, that reconstructs dense broadband hyperspectral reflectance together with accurate 3D geometry. Our key idea is to extend dispersed structured light to the broadband regime using a single spectrograph. We model the image formation of broadband dispersed structured light, and estimate hyperspectral reflectance and depth. We validate our approach on diverse real-world scenes, demonstrating accurate reconstruction with a mean spectral angle mapper of 0.13 rad, root mean square error of 0.03, and mean depth error of 4.5 mm. We further demonstrate identifying metameric materials, performing imaging through opaque layers, uncovering hidden features on banknotes, and revealing blood vessels.

Hyperspectral imagery encodes rich material properties that can improve tracking robustness under appearance ambiguity, illumination change, and background clutter. However, due to the limited availability of hyperspectral video data, many existing methods adapt pretrained RGB trackers via spatial or channel fusion strategies, largely neglecting the intrinsic material information in hyperspectral imagery. Moreover, the few material-aware approaches typically rely on external spectral unmixing pipelines that are decoupled from the tracking objective, limiting effective optimization of material representations for target localization. To address these limitations, we formulate hyperspectral object tracking as a joint optimization problem of material decomposition and target localization, coupling the two tasks via a weighted target-oriented unmixing loss that explicitly aligns material representations with localization accuracy. Specifically, we propose a material representation decomposition module for deep learning-based spectral unmixing with adaptive frequency decomposition. Building on the decomposed material representations, we further introduce a dual-branch wavelet-enhanced material prompt module that learns low- and high-frequency material prompts through efficient spatial-material interactions in the frequency domain. The framework is model-agnostic and can be seamlessly generalized to different unmixing backbones. Extensive experiments on standard hyperspectral tracking benchmarks demonstrate state-of-the-art performance and validate the effectiveness of the proposed end-to-end material-aware tracking framework. Code is available at https://github.com/han030927/E2EMPT.

The accurate recovery of constituent-level optical properties from integrating sphere measurements is a central analytical challenge in pharmaceutical analysis, food science, and biomedical diagnostics. Neural network autoencoders can extract spectrally resolved absorption and scattering coefficients for each constituent without prior knowledge, but their fully connected encoders bind learned features to absolute wavelength indices, causing accuracy loss under spectrometer calibration drift or hardware exchange. This work introduces the Bin Latent Transformer (BiLT)-Autoencoder, in which the dense encoder is replaced by a cross-attention scanner: 16 learnable probe vectors query a convolutional feature map, aggregating morphological spectral information independently of absolute wavelength position. A physics-constrained linear decoder with enforced absorption/scattering separation and a three-phase curriculum augmentation strategy complete the architecture. On a liquid phantom benchmark (intralipid and two ink absorbers; 496 samples), the model achieves $R^2 = 0.979$ and $0.975$ for $μ_a(λ)$ and $μ_s'(λ)$, respectively, on held-out test spectra, maintaining $R^2 > 0.90$ for $μ_a$ and $R^2 \approx 0.99$ for $μ_s'$ across the full tested shift range of $\pm 10$ spectral bands. The model generalises to a simulated spectrometer with a broader instrument line shape (${\approx}24$nm FWHM) without retraining, retaining $R^2 \approx 0.96$ and $0.974$ for the two channels. Attention map analysis reveals a physically interpretable two-component probe strategy: sparse anchor probes at absorption-edge wavelengths combined with a diffuse, SNR-driven ensemble at the high-transmittance long-wavelength region, which recruits additional probes dynamically under noise to provide implicit spectral averaging.

The Linear Mixing Model (LMM) dominates spectral unmixing for its simplicity, but fails under multiple scattering; existing nonlinear models compensate by applying a fixed regime uniformly across entire scenes. We propose Physics-Guided Regime Unmixing (PGRU), which estimates a pixel-wise scalar $ξ_i \in [0,1]$ from observable physical features to activate nonlinear mixing only where justified. Residuals from the Generalized Bilinear Model (GBM), the Post-Nonlinear Mixing Model (PPNM), and Hapke are combined via learned attention, yielding interpretable regime maps. Experiments on Samson, Jasper Ridge, and Urban show consistent improvements over baselines, with physical coherence $ρ> 0.90$.

Raman spectra obtained in real world applications are often a noisy combination of several spectra of various substances in a tested sample. Unmixing such spectra into individual components corresponding to each of the substances is of great value and has been a longstanding challenge in Raman spectroscopy. Existing unmixing methods are predominantly designed to invert an overdetermined mixed model and therefore require multiple mixed spectra as input. However, open domain and/or non-cooperative detection applications in Raman spectroscopy such as controlled substance detection, call for single-channel solutions which can identify individual components from thousands of candidates by analyzing only a single noisy mixed spectrum. To our knowledge, sparse regression is the only existing solution which can cope with this scenario, yet it has very low tolerance to noises and can hardly be applicable in practice. To address these limitations, we introduce a novel neural approach for single-channel Raman spectrum unmixing inspired by speech separation. It aims at solving underdetermined systems and can decompose a noisy mixed spectrum from a library of thousands of components (substances). The core of our method is a deep separation neural network (RSSNet) which takes a mixed spectrum as input and outputs spectra of pure components. We created two synthetic datasets of single-channel Raman spectra unmixing and demonstrated feasibility and superiority of RSSNet on these datasets (outperform competing methods by >4dB). Furthermore, we verified that RSSNet, trained solely on synthetic data, can successfully unmix real-world mixed spectra of mixtures of mineral powders, exhibiting strong generalization. Our approach represents a new paradigm for Raman unmixing and enables new possibilities for fast detection of Raman mixtures.

Traditional glass-based optics are typically optimized for narrow spectral bands, such as the visible (400-700nm) or shortwave infrared (1000-1800nm). While the emergence of VIS-SWIR sensors (400-1700nm) offers transformative potential, refractive optics struggle to focus this entire range simultaneously. Mirrors represent a promising achromatic alternative; however, they are often sidelined by field curvature, and off-axis aberrations. This paper introduces Computational Mirrors, a framework that enables high-resolution, wide-field-of-view imaging across the complete VIS-SWIR spectrum using a single sensor. Our method is built on the observation that distinct regions of the field of view reach focus at varying distances from the mirror. By capturing a minimal focal stack (2-4 images), we utilize a computational backend to recover a sharp, all-in-focus image. A key contribution of this work is SeidelConv, a novel, physics-inspired, spatially-varying point spread function (PSF) model designed to accurately characterize and correct the off-axis aberrations inherent in simple concave mirrors. We demonstrate the efficacy of our approach using a first-of-its-kind 50mm F/1 optical system equipped with a VIS-SWIR sensor. Our system produces sharp images across RGB, NIR, and SWIR wavelengths without requiring refocusing, revealing material details invisible within individual spectral bands. We further validate the scalability of our approach with a 100mm F/2 system optimized for long-range imaging.

Unmixing reveals the spatial distribution and spectral details of different constituents, called endmembers, in a hyperspectral image. Because unmixing has limited ground truth requirements, can accommodate mixed pixels, and is closely tied to light propagation, it is a uniquely powerful tool for analyzing hyperspectral images. However, spectral variability inhibits unmixing performance, the proper way to determine the number of endmembers is ambiguous, and the clarity of the endmembers degrades as more are included. Hierarchical structure is a possible solution to all three problems. Here, hierarchical unmixing is defined by imposing a hierarchical abundance sum constraint on Deep Nonnegative Matrix Factorization. Binary Linear Unmixing Tactile Hierarchies (BLUTHs) solve the hierarchical unmixing problem with a simple network architecture. Sparsity modulation unmixing growth tailors the topology of a BLUTH to each scene. The structure imposed by BLUTHs allows endmembers with varying levels of spectral contrast to be revealed, mitigating the challenge of spectral variability. The performance of BLUTHs exceeds state-of-the-art unmixing algorithms on laboratory scenes, particularly with regard to abundance estimation, while their performance remains competitive on remote sensing scenes. In addition, ocean color unmixing by BLUTHs is demonstrated on hyperspectral scenes from the HYPSO and PACE satellites.

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its solutions are typically not unique. To address these two issues, additional constraints or assumptions are often used. In particular, separability assumes that the basis vectors in the NMF are equal to some columns of the input matrix. In that case, the problem is referred to as separable NMF (SNMF) and can be solved in polynomial-time with robustness guarantees, while identifying a unique solution. However, in real-world scenarios, due to noise or variability, multiple data points may lie near the basis vectors, which SNMF does not leverage. In this work, we rely on the smooth separability assumption, which assumes that each basis vector is close to multiple data points. We explore the properties of the corresponding problem, referred to as smooth SNMF (SSNMF), and examine how it relates to SNMF and orthogonal NMF. We then propose a convex model for SSNMF and show that it provably recovers the sought-after factors, even in the presence of noise. We finally adapt an existing fast gradient method to solve this convex model for SSNMF, and show that it compares favorably with state-of-the-art methods on both synthetic and hyperspectral datasets.