Hyperspectral unmixing remains a challenging problem in complex scenes, where the linear model cannot describe the spectral reflectance of mixtures of pure materials. Although nonlinear mixing models have been proposed to address this challenge, existing methods are either supervised, i.e., require endmembers of the dataset as prior information, or are suitable only for datasets containing either pure pixels or near-pure pixels. When pure pixels are unavailable in the dataset, a dataset simplex has to be reconstructed in order to generate virtual endmembers. Unfortunately, the popular minimum simplex volume constraint (MSVC) often used for linear datasets cannot be directly applied to nonlinear datasets. To tackle this challenge, in this work, we propose a novel strategy called linearizing space transformation (LST) that estimates the linear component of a nonlinear dataset by analytically inverting the nonlinear dataset. MSVC can then be applied to this linear component to estimate the endmembers of the nonlinear dataset. LST can be applied to nonlinear datasets that can be expressed as an explicit combination of linear and nonlinear components. The polynomial mixing models are a class of models that fulfill this criterion. In this work, we theoretically demonstrate the effectiveness of the proposed strategy for two popular mixing models from the literature, i.e., the polynomial postnonlinear mixing model (PPNM) and the multilinear mixing model (MLM). In order to estimate endmembers, abundance maps, and nonlinear parameters of the mixing models, an end-to-end deep network called MPGU-Net is proposed. The network consists of three modules: 1) a variational autoencoder (VAE)-based endmember generation network for robust spectral signature estimation; 2) an abundance estimation network enhanced by a convolutional block attention module (CBAM) for accurately estimating abundance maps; and 3) a nonlinearity parameter estimation network for estimating pixelwise nonlinear interaction processes. In contrast to existing methods that model nonlinearity through a nonlinear activation function in the last layer of the network, our approach models nonlinearity explicitly through the nonlinear mixing equation. LST is not a direct component of the MPGU-Net framework, but is incorporated into the loss function, enabling more accurate estimation of endmembers and fractional abundances. By jointly optimizing reconstruction consistency, geometric constraints, endmember consistency, and variational regularization, our MPGU-Net achieves high-accuracy unmixing with strong physical interpretability. Extensive experiments on both synthetic and real hyperspectral datasets demonstrate that our method significantly outperforms existing state-of-the-art (linear and nonlinear) unmixing approaches in terms of reconstruction accuracy, endmember estimation fidelity, and abundance visualization. We release our code at https://github.com/xuanwentao

The automated sorting of shredded black plastics from end-of-life (EOF) industrial waste presents a significant challenge in recycling facilities, primarily due to the limitations of current sensing and analytical approaches. Existing studies predominantly rely on single-point contact-based mid-infrared spectroscopy or laboratory hyperspectral imaging (HSI) setups, which fail to provide the spatially resolved analysis necessary for fast, bulk processing. Moreover, available datasets are laboratory-controlled and focus on intact rather than shredded plastics, hindering further recycling refinement. Black industrial plastics, in particular, are underrepresented, while most classification pipelines depend on manual region selection and rule-based spectral matching, neglecting spatial information and modern deep learning (DL) methods. To address these gaps, we introduce the first publicly available HSI dataset of shredded black plastics from EOF vehicle, comprising four industrial polymers across 13 co-registered RGB, VNIR, SWIR, and MWIR scenes and their segmentation pipeline. We developed a multi-modal spectral-spatial framework that integrates foreground isolation, pixel-wise classification, and object-level majority voting. By adapting advanced hyperspectral transformers from earth observation and incorporating chemometric band selection, we achieve accurate classification of complex black plastics. The study establishes the first comprehensive benchmark using nine processing methods, including chemometric, machine learning, and DL architectures. To ensure reproducibility, the complete dataset and methodologies are publicly released, establishing a benchmark for a hyperspectral object-analysis pipeline in industrial inspection.

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.

Characterizing mortars in the context of conservation is essential for preserving historic façades, yet laboratory analysis is invasive and often impractical in situ. Lime mortars are preferred for compatibility, but undocumented cement additions are common and may compromise durability. Determining not only the presence but also the proportion of cement is therefore critical, as conservation architects must understand the existing material composition to design a tailored and compatible restoration approach. Using longwave ultraviolet to shortwave infrared spectrometer data (350-2500 nm), we evaluate regression models to predict lime-cement ratios in laboratory-prepared mortars and introduce monotonicity (via Spearman rank correlation) as a complementary reliability criterion. Linear regression, despite its simplicity, attains near-perfect monotonicity ($\rho_{\text{Spearman}}>0.99$) while maintaining accuracy comparable to polynomial Support Vector Regression (SVR). Emphasizing trend preservation supports interpretability and aligns with conservation needs. The results show that regression, augmented with monotonicity analysis, offers a robust, non-destructive pathway for assessing mortars in heritage monitoring.

Leaf Water Thickness, often described as equivalent water thickness, is an important trait in plant physiology and can be estimated non-destructively using the leaf's spectral reflectance. Leaf water thickness is defined as the depth of the water layer if all the water contained in a plant leaf were uniformly distributed over a given area. In this study, we propose a supervised machine learning approach based on polynomial regression, combined with our method, NRAL, to estimate leaf water thickness. The results are compared against those obtained using the PROSPECT model, a well-established physical model for simulating leaf optical properties. This methodology is evaluated on the LOPEX dataset, along with three additional hyperspectral datasets. In all cases, the proposed approach achieves a lower root mean squared error (RMSE) compared to the PROSPECT model. These findings highlight the potential of hybrid machine learning methods to outperform traditional models in accurately estimating leaf biophysical parameters.

Understanding how moisture interacts with porous building stones is essential for preserving heritage structures. Due to the strong absorption bands of molecular water in the shortwave infrared (SWIR) range, the spectral reflectance of moist samples is heavily influenced by water, enabling non-invasive monitoring via hyperspectral imaging. A recent dataset captured the spectral behavior of six types of stone at multiple moisture levels using high-resolution SWIR imaging. While the Normalized Relative Arc Length (NRAL) method effectively estimated moisture content in most samples, notable inaccuracies emerged for two specific limestones with strong internal heterogeneity, Euville and Savonnières. Petrographic thin-section analysis confirmed that a single hyperspectral pixel can indeed span both a large pore (wet region) and the surrounding stone matrix (dry region). To tackle this challenge, in this study, we present NRAL+, an enhanced method for modeling spectral reflectance as a mixture of dry and wet components at the sub-pixel level. The experimental results demonstrate the potential of the proposed approach.

The global challenge of sustainable recycling demands automated, fast, and accurate material detection systems that act as a bedrock for a circular economy. Integrating front-tier technologies into advanced recycling systems democratizes access to AI-driven sustainability, and transforms waste analysis from isolated research efforts into real-time, scalable industrial practice. This integration not only accelerates material recovery but also strengthens the technological backbone required to achieve large-scale recycling and alignment with the Green Deal ambitions. In response, we introduce Electrolyzers-HSI, a new multimodal benchmark dataset designed to accelerate the recovery of critical raw materials through accurate electrolyzer materials classification. The dataset comprises 55 co-registered high-resolution RGB images and hyperspectral imaging (HSI) data cubes spanning the 400–2500 nm spectral range. This enables non-invasive analysis of shredded electrolyzer samples, facilitating quantitative material classification. We evaluate various analytical methods, including state-of-the-art (SOTA) Transformer-based deep learning (DL) architectures, to validate the dataset for robust electrolyzers identification. The openly accessible dataset and codebase promote reproducible research and facilitate broader adoption of smart and sustainable E-waste recycling.

Moisture poses a major threat to built heritage through processes such as frost damage, salt crystallization and biological growth, which accelerate stone deterioration. Stone moisture content can be determined non-destructively by spectral reflectance in the shortwave infrared (SWIR) wavelength range. To validate this, large cubic and small cylindrical samples from six stone types, Brick, Euville, Massangis, Neubrunn, Obernkirchen, and Savonnières, with different controlled moisture levels were prepared, and a comprehensive SWIR hyperspectral image dataset was created. The acquired hyperspectral images were processed using the Normalized Relative Arc Lengths (NRAL) method to generate moisture maps that illustrate the spatial distribution of water within each sample. Because moisture distribution is influenced by pore characteristics and grain arrangement, the moisture maps were validated through petrographic examination. For quantitative validation, the mean moisture content of each sample was compared with the corresponding gravimetric moisture content. The results demonstrated strong agreement between the estimated and gravimetric moisture values, with root mean square errors ranging from 1 and 2 g/g × 100.

Because of its significant absorption power, especially in the shortwave infrared optical region, water dominates the optical reflectance properties of water-bearing materials. This allows us to study a material’s water-related features, such as its moisture content, from optical reflectance. In this study, we proposed a framework to estimate soil moisture content from PRISMA hyperspectral remote sensing data. The proposed framework requires a dry endmember spectrum and an endmember spectrum of high soil moisture along with ground truth moisture content, obtained from ground measurements. The method takes into account the complex interaction of light with soils, the large variation of environmental conditions, leading to spectral variability and the soil-specific behavior of water. The framework is extensively validated using ground-measured soil moisture data from the International Soil Moisture Network database. A total of 1418 PRISMA images corresponding to 151 ground stations were analyzed. From 518 retained images, a total root-mean-squared error of 8.682 % and $R^{2}$ of 0.385 was obtained.

Hyperspectral unmixing has been widely used as a technique to interpret hyperspectral data, and to uncover information regarding pure materials and their distribution in an image. A major challenge when unmixing these images is the variability in the spectra of the pure materials (endmembers). Under the linear mixing assumption, several models have been proposed to mitigate this effect, such as the scaled linear mixing model (SLMM) and the extended linear mixing model (ELMM). While the SLMM is often an oversimplified model, leading to significant modeling errors, the ELMM leads to highly nonconvex optimization problems with many non-unique solutions, making it difficult to solve. In this paper, we propose a new two-step linear mixing model (2LMM), which is rich enough to describe hyperspectral variability in a wide variety of cases, while leading to only mildly nonconvex optimization problems that are easier to solve. Using an off-the-shelf interior-point solver, we show that the model performs well and produces better abundance estimates than both the SLMM and ELMM. A MATLAB and Julia demo of the proposed method can be found at github.com/XanderHaijen/two_step_lmm.

Hyperspectral unmixing, an essential and fundamental task in remote sensing, focuses on estimating endmembers (spectrally pure components) and their fractional abundances within each mixed pixel of a hyperspectral image. With the advent of deep learning (DL), the field of hyperspectral unmixing has made significant progress. Among DL approaches, autoencoder-based models have shown promising results. However, most unmixing methods estimate the endmembers by the weights of the linear layers in the decoder of their networks, making their performance highly dependent on weight initialization. Moreover, noise is not explicitly accounted for in most recent methods that use spectral angle distance (SAD) loss. To avoid the initialization problems, we developed an innovative inversion strategy to directly estimate the endmembers. Moreover, to optimally account for noise, an end-to-end network is proposed, which integrates both denoising and unmixing. Finally, for an improved feature extraction, a novel spectral-spatial attention module (SSAM) is integrated into the network. Extensive experiments on synthetic and three real datasets show that the proposed method significantly and consistently outperforms the compared state-of-the-art methods. The full code is available at https://github.com/xuanwentao for public evaluation.

This paper introduces the Checkerboard dataset, a new benchmark for linear unmixing of hyperspectral images that incorporates spectral variability and provides reliable ground truth. This dataset addresses the critical need for realistic evaluation data, as existing real hyperspectral images often lack ground truth and synthetic data generation faces challenges in terms of realism. The Checkerboard dataset contains linear mixtures of four endmembers and includes spectral variability. We validate several aspects of the unmixing process on this dataset, specifically endmember extraction and abundance estimation. This work aims to provide a valuable resource for researchers to thoroughly evaluate and compare newly proposed unmixing methods, particularly those designed to handle spectral variability. The dataset is publicly available via Zenodo: https://doi.org/10.5281/zenodo.15632214.

Characterization of mortar samples from spectral reflectance is essential for both the conservation of historical buildings and modern construction practices. We propose an approach to estimate the composition of mortar by spectral unmixing. Changes in the spectral reflectance of raw powder mixtures after chemical reactions with water complicate the problem. The challenge becomes even more pronounced when the endmember spectra of the cured pure components are unavailable for unmixing. The proposed approach mitigates spectral variability by projecting the dataset onto the unit hypersphere on which the endmembers are estimated using a minimum volume optimization technique. The endmembers are then manually assigned to the pure components and the original composition of the mortar samples is determined by minimizing the reconstruction error between the measured and reconstructed spectra. The methodology was validated using spectral reflectance data from 93 different mortar samples. Experimental results demonstrate the potential of the proposed approach.

The conservation of cultural built heritage is crucial because of its historical, cultural and architectural significance. Water or moisture can cause severe damage, which can lead to deterioration. Therefore, estimating moisture content (MC) using non-destructive techniques is essential to ensure the conservation of these sites. Hyperspectral imaging (HSI) has been widely used in various fields, but its application in estimating MC in cultural built heritage materials has received limited research. This exploratory study investigates the potential of HSI for estimating MC by preparing a comprehensive hyperspectral dataset in the Short-Wave Infrared (SWIR) from six natural and historical stones at five different saturation levels. To estimate MC, a recently developed quantitative approach, the Normalized Relative Arc Length method was applied. The results showed high accuracy (RMSE of less than 5%) in the estimated MC, underscoring the reliability of HSI in this context.

This paper introduces a novel preprocessing method to reduce the redundancy of spectral data with the purpose of improving the accuracy of hyperspectral unmixing techniques. The approach is based on Fast Fourier Transform (FFT) component selection using a genetic algorithm. The method is tested on a real-world hyperspectral dataset, showing significant reductions in error for multiple unmixing models. Additionally, the method's robustness to noise is evaluated, demonstrating stability under moderate noise levels.

In this work, we propose a supervised framework for spectral unmixing of binary intimate mixtures. The core idea is based on geodesic distance measurements and regression to estimate the fractional abundances. The main assumption is that spectral reflectances of binary mixtures form a curve between the two endmembers, and the mixture's relative position on this curve serves as an indicator of its fractional abundances. We propose four novel approaches to approximate this relative position. From this, the fractional abundances are obtained using Gaussian process regression. The proposed framework simultaneously copes with the spectral variability by hypersphere and high-dimensional simplex projections. The approach is extensively validated on real datasets, including binary mineral mixtures and industrial clay powder mixtures produced in a laboratory setting, comprising 60 binary mixtures derived from five types of clay powders: Kaolin, Roof clay, Red clay, mixed clay, and Calcium hydroxide, measured by a variety of hyperspectral sensors in the VNIR-SWIR and mid-and longwave infrared regions. A comparison with the linear mixing model and several nonlinear mixing models demonstrates the superiority of the proposed approach.

Hyperspectral unmixing is a crucial technique in remote sensing data processing that aims to estimate component information from mixed pixels in hyperspectral images. Most existing deep learning-based hyperspectral unmixing models employ autoencoder (AE) networks to reconstruct hyperspectral images and estimate abundance maps. Here, the weight between the reconstructed and the softmax layers is used to extract/estimate endmember signatures. However, AEs are heavily dependent on initial weights, which introduces inherent randomness, potentially compromising unmixing accuracy. To address this issue, in this article, we present a new dual-feature fusion network (DFFN) for enhanced hyperspectral unmixing. Our DFFN mainly consists of four modules: 1) a feature fusion module (FFM); 2) an abundance estimation module (AEM); 3) an endmember estimation module (EEM); and 4) a reconstruction module (RM). First, FFM calculates spectral and spatial similarities and then enhances the hyperspectral image by matrix multiplications with similarity matrices. Second, AEM takes the enhanced hyperspectral image as input and uses convolutional layers to estimate abundances and reconstruct the image. Next, the reconstructed image is fed into EEM to automatically estimate endmembers. RE performs the final reconstruction through matrix multiplication of the estimated endmembers and abundances. Experiments on synthetic and real hyperspectral datasets, together with a comparison with state-of-the-art techniques, demonstrate the superiority of our newly proposed DFFN. The full code is released at https://github.com/xuanwentao for public evaluation.

Accurate estimation of the fractional abundances of intimately mixed materials from spectral reflectances is generally hard due to a highly nonlinear relationship between the measured spectrum and the composition of the material. Changes in the acquisition and the illumination conditions cause variability in the spectral reflectance, further complicating the spectral unmixing procedure. In this work, we propose a methodology for unmixing intimate mixtures that can tackle both nonlinearity and spectral variability. A supervised approach is proposed that characterizes the nonlinear data manifolds by high-dimensional Bezier surfaces. To deal with spectral variability, a manifold transformation procedure is designed. To generate Bezier surfaces, training samples are required that are uniformly distributed throughout the data manifold. For this, we recently generated a hyperspectral dataset of intimate mineral powder mixtures by homogeneously mixing five different clay powders (Kaolin, Roof clay, Red clay, mixed clay, and Calcium hydroxide) in laboratory settings. In total 330 samples (325 mixtures and five pure materials) were prepared. The ground fractional abundances of these mixtures uniformly cover the 5-D probability simplex. The spectral reflectances of these samples were acquired by multiple sensors with a large variation in sensor types, platforms, and acquisition conditions. Experiments are conducted both on simulated and real intimate mineral powder mixtures. Comparison with a number of unsupervised unmixing methods demonstrates the potential of the proposed approach.

Optical hyperspectral cameras capture the spectral reflectance of materials. Since many materials behave as heterogeneous intimate mixtures with which each photon interacts differently, the relationship between spectral reflectance and material composition is very complex. Quantitative validation of spectral unmixing algorithms requires high-quality ground truth fractional abundance data, which are very difficult to obtain. In this work, we generated a comprehensive laboratory ground truth dataset of intimately mixed mineral powders. For this, five clay powders (Kaolin, Roof clay, Red clay, mixed clay, and Calcium hydroxide) were mixed homogeneously to prepare 325 samples of 60 binary, 150 ternary, 100 quaternary, and 15 quinary mixtures. Thirteen different hyperspectral sensors have been used to acquire the reflectance spectra of these mixtures in the visible, near, short, mid, and long-wavelength infrared regions (350-15385) nm. Overlaps in wavelength regions due to the operational ranges of each sensor and variations in acquisition conditions resulted in a large amount of spectral variability. Ground truth composition is given by construction, but to verify that the generated samples are sufficiently homogeneous, XRD and XRF elemental analysis is performed. We believe these data will be beneficial for validating advanced methods for nonlinear unmixing and material composition estimation, including studying spectral variability and training supervised unmixing approaches. The datasets can be downloaded from the following link: https://github.com/VisionlabHyperspectral/Multisensor_datasets.

This study aims to enhance the robustness and real-time applicability of polymers classification for more efficient and sustainable recycling practices. By utilizing a hyperspectral imaging (HSI) plastic dataset in the visible/near and the short wave infrared acquired at the Helioslab at the Helmholtz In-stitute Freiberg for Resource Technology, we assess multiple state-of-the-art (SOTA) machine learning (ML) models in-cluding single and multi-modality Transformers-based models like Vision Transformer, SpectralFormer, and Multimodal Fusion Transformer for polymer identification in challenging industrial scenarios. We investigate the impact of different wavelength ranges on the models' performance by ex-amining four wavelength ranges related to the polymers' ab-sorption features. We propose an enhanced HSI data prepro-cessing pipeline targeting close and long-range hyperspectral applications to handle large hyperspectral data and its aug-mented version. The comprehensive experiments and fine-tuning demonstrate the proposed pipeline's efficiency, signif-icantly enhancing the SOTA performance. The work will be available at https://github.com/hifexplo.