Hyperspectral Unmixing

Linear hyperspectral unmixing aims at retrieving pure material spectra present in an observed scene and their associated abundance fractions in each pixel. In most practical situations, hyperspectral images are affected by spectral variability (SV) also known as intra-class variability, which is caused by different physical phenomena including atmospheric effects, intrinsic variability of the pure materials and illumination or topographic changes. Nevertheless, the standard hyperspectral unmixing methods that rely on the Linear Mixing Model (LMM) do not consider these phenomena. Thus, neglecting them will spread errors throughout the linear hyperspectral unmixing process. To avoid this problem, this paper proposes two hyperspectral unmixing algorithms dedicated to a parametric model called Structured Additive Variability LMM (SAV-LMM). This mixing model handles SV in an additive manner by incorporating two terms into the standard LMM. Moreover, the designed algorithms are based on Nonnegative Matrix Factorization (NMF) and optimize a cost function which integrates additional penalization accounting for SV. Furthermore, a novel improved initialization scheme, which takes SV into account, is proposed. Experiments conducted on both synthetic and real datasets show the effectiveness of the proposed algorithms for linearly unmixing hyperspectral images with SV compared to the tested state-of-the-art methods.

Cameras and the foundation models built on them recognize what a 3D scene contains, but not what it is made of: surfaces of the same colour can be different materials. Hyperspectral unmixing explains each spectrum as a mixture of material signatures, yet in 3D it is applied to rendered images after the views are composited, or tied to slow implicit fields, and no multi-view data with known composition exist to check the result. We present the Spectral World Renderer (SWR), which unifies world generation and unmixing. A coding agent builds executable 3D worlds that are rendered with measured spectra, so every hyperspectral image comes with exact labels and sub-pixel proportions; the resulting SWR-Bench provides eight indoor and outdoor worlds in which decompositions can be verified. SWR then unmixes inside rendering: each Gaussian of a compact 3D representation is decoded into material abundances before compositing, so one render yields spectra and material maps, and any surface can be queried by material name, a clicked pixel or a reference spectrum. Without material labels, SWR identifies materials best in all eight worlds, has the best mean PSNR on real captures, trains 3.7-12.9x faster than unmixing baselines, renders 34.9 labelled views/s and separates same-coloured materials.

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) how do foundation models perform in hyperspectral unmixing?; 2) 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 image (HSI) classification plays a vital role in remote sensing applications, including agriculture, environmental monitoring, and urban analysis. However, its performance remains challenged by high spectral redundancy, noise sensitivity, and the difficulty of jointly modeling local material composition and long-range spectral dependencies. To address this, we propose AGSA-Net, an abundance-guided self-attention network that explicitly integrates spectral unmixing priors into the classification process. AGSA Net first estimates physically meaningful subpixel abundance maps subject to non-negativity and sum-to-one constraints, regularized by hybrid linear-nonlinear reconstruction decoder. The learned abundances are then used to construct an abundance affinity prior that guides a spectral transformer to emphasize class-discriminative interactions, and the resulting transformer features are fused with compact abundance descriptors for final prediction; in contrast to existing approaches that use abundance as auxiliary or concatenated features. Experiments on Indian Pines, Augsburg, and Berlin demonstrate the benefit of incorporating abundance- guided contextual modeling, particularly in heterogeneous urban scenes. The source code and trained models are available at: https://github.com/nnuvi/AGSA-Net

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 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 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 $ρ> 0.90$.

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.

Hyperspectral unmixing (HU) is crucial for analyzing hyperspectral imagery, yet achieving accurate unmixing remains challenging. While traditional methods struggle to effectively model complex spectral-spatial features, deep learning approaches often lack physical interpretability. Unrolling-based methods, despite offering network interpretability, inadequately exploit spectral-spatial information and incur high memory costs and numerical precision issues during backpropagation. To address these limitations, we propose DEQ-Unmix, which reformulates abundance estimation as a deep equilibrium model, enabling efficient constant-memory training via implicit differentiation. It replaces the gradient operator of the data reconstruction term with a trainable convolutional network to capture spectral-spatial information. By leveraging implicit differentiation, DEQ-Unmix enables efficient and constant-memory backpropagation. Experiments on synthetic and two real-world datasets demonstrate that DEQ-Unmix achieves superior unmixing performance while maintaining constant memory cost.

Although hyperspectral image (HSI) classification is critical for supporting various environmental applications, it is a challenging task due to the spectral-mixture effect, the spatial-spectral heterogeneity and the difficulty to preserve class boundaries and details. This letter presents a novel unmixing-guided spatial-spectral Mamba with clustering tokens for improved HSI classification, with the following contributions. First, to disentangle the spectral mixture effect in HSI for improved pattern discovery, we design a novel spectral unmixing network that not only automatically learns endmembers and abundance maps from HSI but also accounts for endmember variabilities. Second, to generate Mamba token sequences, based on the clusters defined by abundance maps, we design an efficient Top-K token selection strategy to adaptively sequence the tokens for improved representational capability. Third, to improve spatial-spectral feature learning and detail preservation, based on the Top-K token sequences, we design a novel unmixing-guided spatial-spectral Mamba module that greatly improves traditional Mamba models in terms of token learning and sequencing. Fourth, to learn simultaneously the endmember-abundance patterns and classification labels, a multi-task scheme is designed for model supervision, leading to a new unmixing-classification framework that outputs not only accurate classification maps but also a comprehensive spectral-library and abundance maps. Comparative experiments on four HSI datasets demonstrate that our model can greatly outperform the other state-of-the-art approaches. Code is available at https://github.com/GSIL-UCalgary/Unmixing_guided_Mamba.git

Due to the large footprint of pixels in remote sensing imagery, hyperspectral unmixing (HU) has become an important and necessary procedure in hyperspectral image analysis. Traditional HU methods rely on a prior spectral mixing model, especially for nonlinear mixtures, which has largely limited the performance and generalization capacity of the unmixing approach. In this paper, we address the challenging problem of hyperspectral nonlinear unmixing (HNU) without explicit knowledge of the mixing model. Inspired by the principle of generative models, where images of the same distribution can be generated as that of the training images without knowing the exact probability distribution function of the image, we develop an invertible mixing-unmixing process via a bi-directional GAN framework, constrained by both the cycle consistency and the linkage between linear and nonlinear mixtures. The combination of cycle consistency and linear linkage provides powerful constraints without requiring an explicit mixing model. We refer to the proposed approach as the linearly-constrained CycleGAN unmixing net, or LCGU net. Experimental results indicate that the proposed LCGU net exhibits stable and competitive performance across different datasets compared with other state-of-the-art model-based HNU methods.

Semantic segmentation and hyperspectral unmixing are two central problems in spectral image analysis. The former assigns each pixel a discrete label corresponding to its material class, whereas the latter estimates pure material spectra, called endmembers, and, for each pixel, a vector representing material abundances in the observed scene. Despite their complementarity, these two problems are usually addressed independently. This paper aims to bridge these two lines of work by formally showing that, under the linear mixing model, pixel classification by dominant materials induces polyhedral-cone regions in the spectral space. We leverage this fundamental property to propose a direct segmentation-to-unmixing pipeline that performs blind hyperspectral unmixing from any semantic segmentation by constructing a polyhedral-cone partition of the space that best fits the labeled pixels. Signed distances from pixels to the estimated regions are then computed, linearly transformed via a change of basis in the distance space, and projected onto the probability simplex, yielding an initial abundance estimate. This estimate is used to extract endmembers and recover final abundances via matrix pseudo-inversion. Because the segmentation method can be freely chosen, the user gains explicit control over the unmixing process, while the rest of the pipeline remains essentially deterministic and lightweight. Beyond improving interpretability, experiments on three real datasets demonstrate the effectiveness of the proposed approach when associated with appropriate clustering algorithms, and show consistent improvements over recent deep and non-deep state-of-the-art methods. The code is available at: https://github.com/antoine-bottenmuller/polyhedral-unmixing

This paper proposes a semisupervised geometric unmixing approach called minimum simplex semisupervised unmixing (MiSiSUn). The geometry of the data was incorporated for the first time into library-based unmixing using a simplex-volume-flavored penalty based on an archetypal analysis-type linear model. The experimental results were performed on two simulated datasets considering different levels of mixing ratios and spatial instruction at varying input noise. MiSiSUn considerably outperforms state-of-the-art semisupervised unmixing methods. The improvements vary from 1 dB to over 3 dB in different scenarios. The proposed method was also applied to a real dataset where visual interpretation is close to the geological map. MiSiSUn was implemented using PyTorch, which is open-source and available at https://github.com/BehnoodRasti/MiSiSUn. Moreover, we provide a dedicated Python package for Semisupervised Unmixing, which is open-source and includes all the methods used in the experiments for the sake of reproducibility.

Weak spectral responses in hyperspectral images are often obscured by dominant endmembers and sensor noise, resulting in inaccurate abundance estimation. This paper introduces WS-Net, a deep unmixing framework specifically designed to address weak-signal collapse through state-space modelling and Weak Signal Attention fusion. The network features a multi-resolution wavelet-fused encoder that captures both high-frequency discontinuities and smooth spectral variations with a hybrid backbone that integrates a Mamba state-space branch for efficient long-range dependency modelling. It also incorporates a Weak Signal Attention branch that selectively enhances low-similarity spectral cues. A learnable gating mechanism adaptively fuses both representations, while the decoder leverages KL-divergence-based regularisation to enforce separability between dominant and weak endmembers. Experiments on one simulated and two real datasets (synthetic dataset, Samson, and Apex) demonstrate consistent improvements over six state-of-the-art baselines, achieving up to 55% and 63% reductions in RMSE and SAD, respectively. The framework maintains stable accuracy under low-SNR conditions, particularly for weak endmembers, establishing WS-Net as a robust and computationally efficient benchmark for weak-signal hyperspectral unmixing.

Unregistered hyperspectral image (HSI) super-resolution (SR) typically aims to enhance a low-resolution HSI using an unregistered high-resolution reference image. In this paper, we propose an unmixing-based fusion framework that decouples spatial-spectral information to simultaneously mitigate the impact of unregistered fusion and enhance the learnability of SR models. Specifically, we first utilize singular value decomposition for initial spectral unmixing, preserving the original endmembers while dedicating the subsequent network to enhancing the initial abundance map. To leverage the spatial texture of the unregistered reference, we introduce a coarse-to-fine deformable aggregation module, which first estimates a pixel-level flow and a similarity map using a coarse pyramid predictor. It further performs fine sub-pixel refinement to achieve deformable aggregation of the reference features. The aggregative features are then refined via a series of spatial-channel abundance cross-attention blocks. Furthermore, a spatial-channel modulated fusion module is presented to merge encoder-decoder features using dynamic gating weights, yielding a high-quality, high-resolution HSI. Experimental results on simulated and real datasets confirm that our proposed method achieves state-of-the-art super-resolution performance. The code will be available at https://github.com/yingkai-zhang/UAFL.

Spectroscopic imaging (SI) has become central to heritage science because it enables non-invasive, spatially resolved characterisation of materials in artefacts. In particular, attenuated total reflection Fourier transform infrared microscopy (ATR-$μ$FTIR) is widely used to analyse painting cross-sections, where a spectrum is recorded at each pixel to form a hyperspectral image (HSI). Interpreting these data is difficult: spectra are often mixtures of several species in heterogeneous, multi-layered and degraded samples, and current practice still relies heavily on manual comparison with reference libraries. This workflow is slow, subjective and hard to scale. We propose an unsupervised CNN autoencoder for blind unmixing of ATR-$μ$FTIR HSIs, estimating endmember spectra and their abundance maps while exploiting local spatial structure through patch-based modelling. To reduce sensitivity to atmospheric and acquisition artefacts across more than 1500 bands, we introduce a weighted spectral angle distance (WSAD) loss with automatic band-reliability weights derived from robust measures of spatial flatness, neighbour agreement and spectral roughness. Compared with standard SAD training, WSAD improves interpretability in contamination-prone spectral regions. We demonstrate the method on an ATR-$μ$FTIR cross-section from the Ghent Altarpiece by the Van Eyck brothers.

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.