Nonlinear Unmixing Method Research Articles

Cascaded hybrid convolutional autoencoder network for spectral-spatial nonlinear hyperspectral unmixing

ABSTRACT Due to the complex interaction of photons between materials, linear hyperspectral unmixing (HU) is limited in real scenarios, making nonlinear unmixing a promising alternative. With the advancement of deep learning (DL), nonlinear unmixing methods based on the convolutional autoencoder (CAE) have gained considerable traction in HU. However, these unmixing methods struggle to integrate spectral and spatial information while reducing the loss of material details during the unmixing process. Therefore, we propose a cascaded hybrid CAE nonlinear unmixing network, called CHCANet, which effectively leverages convolutional combinations to deeply explore the spectral-spatial information from hyperspectral data and preserve the material details through self-perception. Specifically, each CAE in CHCANet combines 1-D and 2-D convolutions, fully utilizing the flexibility and simplicity of 1-D convolutions to capture spectral features and the spatial correlation handling capability of the 2-D convolution. Moreover, we apply the self-perception mechanism to the nonlinear HU task, which can establish the cycle consistency of the network, strengthen mutual connections between encoders, and effectively preserve high-level semantic information. Following this, the optimized self-perception loss further enhances CHCANet’s perception capability of nonlinear components and strengthens the connection between the decoder directly associated with image reconstruction. Extensive experiments on synthetic and real datasets demonstrate the effectiveness of CHCANet and show excellent competitiveness compared to state-of-the-art unmixing methods.

Geometrical projection improved multi-objective particle swarm optimization for unsupervised nonlinear hyperspectral unmixing

ABSTRACT In recent years, a series of bilinear mixture models (BMMs) have been well studied, based on which nonlinear unmixing algorithms for hyperspectral images have been proposed. However, the performance of unsupervised nonlinear spectral unmixing can be largely affected by the collinearity and the nonconvex unmixing problem’s inherent complexity. To solve the problems, this paper proposes a geometrical projection improved multi-objective particle swarm optimization (GPMOPSO) method for nonlinear unmixing, which consists of two dynamically updating procedures. First, under the assumption of the BMMs, observed pixels are geometrically projected to their approximate linear mixture components to alleviate the collinearity. Second, the linear mixture components are efficiently decomposed to refined endmembers and abundances in an improved linear unmixing framework using multi-objective particle swarm optimization. Two advanced multi-objective optimization strategies are adopted to balance the influence of an endmember distance constraint and an abundance sparsity constraint on the achieved unsupervised linear unmixing process, respectively. Then, accurate unmixing variables can be fed back to the geometrical projection procedure to produce more reliable linear mixture components which facilitate the execution of the former in turn. Experimental results of both simulated data and real hyperspectral remote sensing data verify the superior nonlinear unmixing performance of the proposed method.

Unsupervised Nonlinear Hyperspectral Unmixing with Reduced Spectral Variability via Superpixel-Based Fisher Transformation

In hyperspectral unmixing, dealing with nonlinear mixing effects and spectral variability (SV) is a significant challenge. Traditional linear unmixing can be seriously deteriorated by the coupled residuals of nonlinearity and SV in remote sensing scenarios. For the simplification of calculation, current unmixing studies usually separate the consideration of nonlinearity and SV. As a result, errors individually caused by the nonlinearity or SV still persist, potentially leading to overfitting and the decreased accuracy of estimated endmembers and abundances. In this paper, a novel unsupervised nonlinear unmixing method accounting for SV is proposed. First, an improved Fisher transformation scheme is constructed by combining an abundance-driven dynamic classification strategy with superpixel segmentation. It can enlarge the differences between different types of pixels and reduce the differences between pixels corresponding to the same class, thereby reducing the influence of SV. Besides, spectral similarity can be well maintained in local homogeneous regions. Second, the polynomial postnonlinear model is employed to represent observed pixels and explain nonlinear components. Regularized by a Fisher transformation operator and abundances’ spatial smoothness, data reconstruction errors in the original spectral space and the transformed space are weighed to derive the unmixing problem. Finally, this problem is solved by a dimensional division-based particle swarm optimization algorithm to produce accurate unmixing results. Extensive experiments on synthetic and real hyperspectral remote sensing data demonstrate the superiority of the proposed method in comparison with state-of-the-art approaches.

Spectral–Spatial Reweighted Robust Nonlinear Unmixing for Hyperspectral Images Based on an Extended Multilinear Mixing Model

Recently, nonlinear unmixing algorithms have attracted special attention in hyperspectral image (HSI) processing. However, the inherent wavelength-dependent nonlinear intensity and noise effects in real HSIs are often overlooked, and the spatial information of HSIs has not been fully utilized in current studies. In this paper, we propose a spectral-spatial reweighted robust nonlinear unmixing algorithm to solve the above problems. First, a robust unmixing method is built on an extended multilinear mixing model (EMLM), which employs the vectorized nonlinear parameters to describe the nonlinear intensity varying along with spectral bands, and adopts the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> norm-based loss function to suppress the influence of noise. Second, to fully exploit the spectral-spatial information of HSIs, the nonlinear unmixing problem is reformulated with two regularizers. Specifically, a reweighted collaborative sparse regularizer is used to make the pixels in a superpixel-based neighborhood share the same subset of endmembers and have similar abundances because the neighboring pixels are usually composed of several materials in similar proportions, and a reweighted spectral total variation regularizer is utilized to improve the spectral-spatial smoothness of the vectorized nonlinear parameters by considering the local-region similarities of the nonlinear mixing effects. Finally, the constrained optimization problem is solved by the alternating direction method of multipliers (ADMM). Experimental results on simulated, semi-simulated, and real hyperspectral datasets demonstrate that the proposed method outperforms several state-of-the-art nonlinear unmixing methods.

Nonlinear Unmixing for Hyperspectral Images via Kernel-Transformed Bilinear Mixing Models

Due to the presence of multiple scatterings, linear unmixing methods may not perform well in practical applications, and thus nonlinear unmixing has become an urgent problem to be solved. Usually, the mixing process in the observed scenarios is physically based, and many well-designed models have been proposed to interpret it. Recently, kernel-based nonlinear unmixing methods have been popularly studied to achieve a model-free and flexible representation of the nonlinearity. However, the existing kernel-based methods are mainly data-driven, which could make them fail to match the real physical mixing mechanism and result in the occurrence of overfitting. In this article, a kernel-based bilinear unmixing (KBU) method was proposed to transform the classic bilinear mixing models into their equivalent kernel forms that are more general and effective in expressing second-order scatterings. Two specific types of kernel transformations were designed, and the alternating direction method of multipliers (ADMM) was used to solve the kernel-transformed model-based optimization problem for unmixing. Moreover, the spatial prior was exploited to further improve the unmixing accuracy, and here we employ the total variation (TV) regularization as a paradigm. Experiments on synthetic data sets, physics-based simulated data sets, and real data were conducted to evaluate the algorithms. It is validated that our methods have better performance in abundance estimation and nonlinear reconstruction compared with other nonlinear unmixing methods.

Reweighted Kernel-Based Nonlinear Hyperspectral Unmixing With Regional ℓ₁-Norm Regularization

Improving the performance of nonlinear unmixing has become an active topic among the remote sensing applications. Usually, the noise levels of hyperspectral images (HSIs) vary with different bands. However, this fact is generally ignored and may, to some extent, result in a degradation of the unmixing results. Nonetheless, valuable spatial information that provides a great potential for improving the performance has seldom been considered in the current nonlinear unmixing. In this letter, we propose a novel kernel-based nonlinear unmixing model in which the band-wise noise characterization and the spatial relationships of HSIs are incorporated to solve the above problems. Firstly, the noise levels of different bands are estimated based on the results of superpixel segmentation, and then they are used to characterize the roles of different bands in the unmixing process. To exploit the spatial relationships in the superpixels, a regional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\ell }_{1} {-\text {norm}}$ </tex-math></inline-formula> regularization is proposed and incorporated into the unmixing model. Experimental results on both synthetic and real hyperspectral datasets demonstrate the superiority of the proposed model compared to the state-of-the-art nonlinear unmixing methods.

Supervised Nonlinear Hyperspectral Unmixing With Automatic Shadow Compensation Using Multiswarm Particle Swarm Optimization

The presence of shadows has always been a troublesome problem in image processing and can also affect spectral unmixing with hyperspectral remote sensing images. Traditional unmixing algorithms regard shadows as a special type of ground cover, so they can only estimate real materials&#x2019; sunlit abundances, and materials with low reflectance may be wrongly recognized as shadows. Without regarding shadows as ground cover, we propose a supervised nonlinear unmixing method to accurately estimate real materials&#x2019; total abundances inside and outside shadow areas. First, sunlit and shadowed constituents in every pixel of an image are modeled explicitly and integrated by a tractable bilinear mixing mechanism. Second, based on the constructed model, the strong sparsity of shadow spatial distribution and the spatial correlation among neighboring material abundances are exploited to produce a constrained optimization problem for nonlinear unmixing. Third, an existing unmixing framework based on particle swarm optimization is extended to calculate unknown variables of the optimization problem. Three alternatingly updated swarms using improved dimensional division strategies are designed to accordingly address the unmixing subproblems with respect to variables to be estimated during the solution search. This process has the potential to be generalized to solve complex nonlinear unmixing optimization problems. Finally, model-based simulated data, virtual citrus orchard data, and real hyperspectral remote sensing images are used in experiments to evaluate the proposed method and compare it with traditional and state-of-the-art nonlinear unmixing algorithms. Experimental results verify that the proposed method can achieve acceptable unmixing performance when managing nonlinear mixing effects and shadows.

UAV Remote Sensing Estimation of Rice Yield Based on Adaptive Spectral Endmembers and Bilinear Mixing Model

The accurate estimation of rice yield using remote sensing (RS) technology is crucially important for agricultural decision-making. The rice yield estimation model based on the vegetation index (VI) is commonly used when working with RS methods, however, it is affected by irrelevant organs and background especially at heading stage. The spectral mixture analysis (SMA) can quantitatively obtain the abundance information and mitigate the impacts. Furthermore, according to the spectral variability and information complexity caused by the rice cropping system and canopy characteristics of reflection and scattering, in this study, the multi-endmember extraction by the pure pixel index (PPI) and the nonlinear unmixing method based on the bandwise generalized bilinear mixing model (NU-BGBM) were applied for SMA, and the VIE (VIs recalculated from endmember spectra) was integrated with abundance data to establish the yield estimation model at heading stage. In two paddy fields of different cultivation settings, multispectral images were collected by an unmanned aerial vehicle (UAV) at booting and heading stage. The correlation of several widely-used VIs and rice yield was tested and weaker at heading stage. In order to improve the yield estimation accuracy of rice at heading stage, the VIE and foreground abundances from SMA were combined to develop a linear yield estimation model. The results showed that VIE incorporated with abundances exhibited a better estimation ability than VI alone or the product of VI and abundances. In addition, when the structural difference of plants was obvious, the addition of the product of VIF (VIs recalculated from bilinear endmember spectra) and the corresponding bilinear abundances to the original product of VIE and abundances, enhanced model reliability. VIs using the near-infrared bands improved more significantly with the estimation error below 8.1%. This study verified the validation of the targeted SMA strategy while estimating crop yield by remotely sensed VI, especially for objects with obvious different spectra and complex structures.

A Combined Unmixing Framework for Impervious Surface Mapping on Medium-Resolution Images with Visible Shadows

Spectral unmixing methods with medium-resolution remote sensing images have become the main approach to mapping urban impervious-surface information. However, as more tall buildings appear, numerous visible shadows exist in medium-resolution images; these have usually been ignored in previous research, but they seriously affect accuracy. To solve this problem, we propose a combined unmixing framework to extract impervious surface in nonshadow and shadow areas, using linear and nonlinear unmixing models, respectively. First shadow is separated from nonshadow. Then a nonlinear unmixing method is selected to map impervious surface in shadow, which is more suitable to the complex imaging environment in shadow, and a classic linear unmixing model in nonshadow. Through experimental tests, the proposed combined unmixing framework is shown to effectively reduce error in two study areas compared with classical unmixing methods.

LSTM-DNN Based Autoencoder Network for Nonlinear Hyperspectral Image Unmixing

Blind hyperspectral unmixing is an important technique in hyperspectral image analysis, aiming at estimating endmembers and their respective fractional abundances. Consider the limitations of using the linear model, nonlinear unmixing methods have been studied under different model assumptions. However, existing nonlinear unmixing algorithms do not fully exploit spectral and spatial correlation information. This paper proposes a nonsymmetric autoencoder network to overcome this issue. The proposed scheme benefits from the universal modeling ability of deep neural networks and enables to learn the nonlinear relation from the data. Particularly, the long short-term memory network (LSTM) structure is included to capture spectral correlation information, and a spatial regularization is introduced to improve the spatial continuity of results. An attention mechanism is also used to further enhance the unmixing performance. Experiments with synthetic and real data are conducted to illustrate the effectiveness of the proposed method.

Hyperspectral Images Unmixing Based on Abundance Constrained Multi-Layer KNMF

Due to the low spatial resolution of the sensors, the hyperspectral images contain mixed pixels. The purpose of hyperspectral unmixing is to decompose the mixed pixels into a series of endmembers and abundance fractions. In order to improve the performance of the nonlinear unmixing algorithm for hyperspectral images, a nonlinear unmixing method, i.e., abundance constrained multi-layer kernel non-negative matrix factorization (AC-MLKNMF), is presented. Firstly, MLKNMF is presented to iteratively decompose the mixed pixels into a multi-layer structure, and then AC-MLKNMF is presented based on MLKNMF by adding the sparseness constraint and total variation regularization to the abundance to characterize the sparseness and the piecewise smooth structure of the abundance maps according to the spatial distribution characteristics of the actual ground-objects. Experimental results on synthetic and real datasets show that the proposed AC-MLKNMF can improve the hyperspectral unmixing accuracy compared with single-layer KNMF, and it is also superior to multi-layer non-negative matrix factorization, KNMF without pure pixels, kernel sparse NMF, MLKNMF.

Hyperspectral Nonlinear Unmixing by Using Plug-and-Play Prior for Abundance Maps

Spectral unmixing (SU) aims at decomposing the mixed pixel into basic components, called endmembers with corresponding abundance fractions. Linear mixing model (LMM) and nonlinear mixing models (NLMMs) are two main classes to solve the SU. This paper proposes a new nonlinear unmixing method base on general bilinear model, which is one of the NLMMs. Since retrieving the endmembers’ abundances represents an ill-posed inverse problem, prior knowledge of abundances has been investigated by conceiving regularizations techniques (e.g., sparsity, total variation, group sparsity, and low rankness), so to enhance the ability to restrict the solution space and thus to achieve reliable estimates. All the regularizations mentioned above can be interpreted as denoising of abundance maps. In this paper, instead of investing effort in designing more powerful regularizations of abundances, we use plug-and-play prior technique, that is to use directly a state-of-the-art denoiser, which is conceived to exploit the spatial correlation of abundance maps and nonlinear interaction maps. The numerical results in simulated data and real hyperspectral dataset show that the proposed method can improve the estimation of abundances dramatically compared with state-of-the-art nonlinear unmixing methods.

Montmorillonite Estimation in Clay–Quartz–Calcite Samples from Laboratory SWIR Imaging Spectroscopy: A Comparative Study of Spectral Preprocessings and Unmixing Methods

Clay minerals play an important role in shrinking–swelling of soils and off–road vehicle mobility mainly due to the presence of smectites including montmorillonites. Since soils are composed of different minerals intimately mixed, an accurate estimation of its abundance is challenging. Imaging spectroscopy in the short wave infrared spectral region (SWIR) combined with unmixing methods is a good candidate to estimate clay mineral abundance. However, the performance of unmixing methods is mineral-dependent and may be enhanced by using appropriate spectral preprocessings. The objective of this paper is to carry out a comparative study in order to determine the best couple spectral preprocessing/unmixing method to quantify montmorillonite in intimate mixtures with clays, such as montmorillonite, kaolinite and illite, and no-clay minerals, such as calcite and quartz. To this end, a spectral database is built with laboratory hyperspectral imagery from 51 dry pure mineral samples and intimate mineral mixtures of controlled abundances. Six spectral preprocessings, standard normal variate (SNV), continuum removal (CR), continuous wavelet transform (CWT), Hapke model, first derivative (1st SGD) and pseudo–absorbance (Log(1/R)), are applied and compared with reflectance spectra. Two linear unmixing methods, fully constrained least square method (FCLS) and multiple endmember spectral mixture analysis (MESMA), and two non-linear unmixing methods, generalized bilinear method (GBM) and multi-linear model (MLM), are compared. Global results showed that the benefit of spectral preprocessings occurs when spectral absorption features of minerals overlap for SNV, CR, CWT and 1st SGD, whereas the use of reflectance spectra performs the best when no overlap is present. With one mineral having no spectral feature (quartz), montmorillonite abundance estimation is difficult and gives RMSE higher than 50%. For the other mixtures, performances of linear and non-linear unmixing methods are similar. Consequently, the recommended couple spectral preprocessing/unmixing method based on the trade-off between its simplicity and performance is 1st SGD/FCLS for clay binary and ternary mixtures (RMSE of 9.2% for montmorillonite–illite mixtures, 13.9% for montmorillonite–kaolinite mixtures and 10.8% for montmorillonite–illite–kaolinite mixtures) and reflectance/FCLS for binary mixtures with calcite (RMSE of 8.8% for montmorillonite–calcite mixtures). These performances open the way to improve the classification of expansive soils.

A Graph Regularized Multilinear Mixing Model for Nonlinear Hyperspectral Unmixing

Spectral unmixing of hyperspectral images is an important issue in the fields of remote sensing. Jointly exploring the spectral and spatial information embedded in the data is helpful to enhance the consistency between mixing/unmixing models and real scenarios. This paper proposes a graph regularized nonlinear unmixing method based on the recent multilinear mixing model (MLM). The MLM takes account of all orders of interactions between endmembers, and indicates the pixel-wise nonlinearity with a single probability parameter. By incorporating the Laplacian graph regularizers, the proposed method exploits the underlying manifold structure of the pixels’ spectra, in order to augment the estimations of both abundances and nonlinear probability parameters. Besides the spectrum-based regularizations, the sparsity of abundances is also incorporated for the proposed model. The resulting optimization problem is addressed by using the alternating direction method of multipliers (ADMM), yielding the so-called graph regularized MLM (G-MLM) algorithm. To implement the proposed method on large hypersepectral images in real world, we propose to utilize a superpixel construction approach before unmixing, and then apply G-MLM on each superpixel. The proposed methods achieve superior unmixing performances to state-of-the-art strategies in terms of both abundances and probability parameters, on both synthetic and real datasets.

Chemical fingerprinting of single glandular trichomes of Cannabis sativa by Coherent anti-Stokes Raman scattering (CARS) microscopy

BackgroundCannabis possesses a rich spectrum of phytochemicals i.e. cannabinoids, terpenes and phenolic compounds of industrial and medicinal interests. Most of these high-value plant products are synthesised in the disk cells and stored in the secretory cavity in glandular trichomes. Conventional trichome analysis was so far based on optical microscopy, electron microscopy or extraction based methods that are either limited to spatial or chemical information. Here we combine both information to obtain the spatial distribution of distinct secondary metabolites on a single-trichome level by applying Coherent anti-Stokes Raman scattering (CARS), a microspectroscopic technique, to trichomes derived from sepals of a drug- and a fibre-type.ResultsHyperspectral CARS imaging in combination with a nonlinear unmixing method allows to identify and localise Δ9-tetrahydrocannabinolic acid (THCA) in the secretory cavity of drug-type trichomes and cannabidiolic acid (CBDA)/myrcene in the secretory cavity of fibre-type trichomes, thus enabling an easy discrimination between high-THCA and high-CBDA producers. A unique spectral fingerprint is found in the disk cells of drug-type trichomes, which is most similar to cannabigerolic acid (CBGA) and is not found in fibre-type trichomes. Furthermore, we differentiate between different cell types by a combination of CARS with simultaneously acquired two-photon fluorescence (TPF) of chlorophyll a from chloroplasts and organic fluorescence mainly arising from cell walls enabling 3D visualisation of the essential oil distribution and cellular structures.ConclusionHere we demonstrate a label-free and non-destructive method to analyse the distribution of secondary metabolites and distinguish between different cell and chemo-types with high spatial resolution on a single trichome. The record of chemical fingerprints of single trichomes offers the possibility to optimise growth conditions as well as guarantee a direct process control for industrially cultivated medicinal Cannabis plants. Moreover, this method is not limited to Cannabis related issues but can be widely implemented for optimising and monitoring all kinds of natural or biotechnological production processes with simultaneous spatial and chemical information.

Band-Wise Nonlinear Unmixing for Hyperspectral Imagery Using an Extended Multilinear Mixing Model

Most nonlinear mixture models and unmixing methods in the literature assume implicitly that the degrees of multiple scatterings at each band are the same. However, it is commonly against the practical situation that spectral mixing is intrinsically wavelength dependent, and the nonlinear intensity varies along with bands. In this paper, a band-wise nonlinear unmixing algorithm is proposed to circumvent this drawback. Pixel dependent probability parameters of the recent multilinear mixing model that represent different orders of nonlinear contributions are vectorized. Therefore, each band can get a scalar probability parameter which explicitly corresponds to the nonlinear intensity at that band. Before solving the extended model, abundances’ sparsity and probability parameters’ smoothness are exploited to build two physical constraints. After incorporating them into the objective function as regularization terms, the issue of local minima can be well alleviated to produce better solutions. Finally, alternating direction method of multipliers is applied to solve the constrained optimization problem and implement the nonlinear spectral unmixing. Experiments are further carried out with current model-based simulated data, physical-based synthetic data of virtual vegetated areas, and real hyperspectral remote sensing images, to provide a more reasonable validation for the developed model and algorithm. In comparison with state-of-the-art nonlinear unmixing methods, this method performs better in explaining the band dependent nonlinear mixing effect for improving the unmixing accuracy.

Multiharmonic Postnonlinear Mixing Model for Hyperspectral Nonlinear Unmixing

In this letter, a new method for higher order nonlinear hyperspectral unmixing is introduced. The proposed scheme relies on the harmonic description of the endmembers contributions to characterize the interactions among the materials showing up in the given scenes. Moreover, it aims at directly estimating the probability of occurrence of each material in the images, so to provide an accurate quantification of the endmembers also in complex scenarios. Experimental results carried out on synthetic and real data sets show that the proposed method is able to obtain good unmixing performance when compared to other state-of-the-art architectures.

Hyperspectral Unmixing with Bandwise Generalized Bilinear Model

Generalized bilinear model (GBM) has received extensive attention in the field of hyperspectral nonlinear unmixing. Traditional GBM unmixing methods are usually assumed to be degraded only by additive white Gaussian noise (AWGN), and the intensity of AWGN in each band of hyperspectral image (HSI) is assumed to be the same. However, the real HSIs are usually degraded by mixture of various kinds of noise, which include Gaussian noise, impulse noise, dead pixels or lines, stripes, and so on. Besides, the intensity of AWGN is usually different for each band of HSI. To address the above mentioned issues, we propose a novel nonlinear unmixing method based on the bandwise generalized bilinear model (NU-BGBM), which can be adapted to the presence of complex mixed noise in real HSI. Besides, the alternative direction method of multipliers (ADMM) is adopted to solve the proposed NU-BGBM. Finally, extensive experiments are conducted to demonstrate the effectiveness of the proposed NU-BGBM compared with some other state-of-the-art unmixing methods.

Hybrid Unmixing Based on Adaptive Region Segmentation for Hyperspectral Imagery

Unmixing is an important issue of hyperspectral images. Most unmixing methods adopt linear mixing models for simplicity. However, multiple scattering usually occurs between vegetation and soil in a bilinear scene. Thus, nonlinear mixing problems which are difficult to be solved should be taken into consideration under this circumstance. In practice, both linear and nonlinear spectral mixtures exist in hyperspectral scenes. Considering the characteristics of different regions in images, we propose a hybrid unmixing algorithm for hyperspectral images based on region adaptive segmentation. Our method uses a standard K-means clustering algorithm to obtain different regions, including homogeneous regions and detailed regions. The model of the homogeneous regions is assumed to be linear, which will be pursued using the method of sparse-constrained nonnegative matrix factorization (NMF), and the mixing in the detailed regions is assumed to be based on a nonlinear model. We also propose a new nonlinear unmixing method, called graph-regularized semi-NMF, which considers the manifold structure of hyperspectral data as the unmixing method to deal with the detailed regions. Finally, by combining the two regions, we obtain the abundance of the whole hyperspectral image. The proposed method can not only achieve more precise abundance but also be good at keeping the edge information of the bilinear abundance. The experimental results on both synthetic and real data also show that the proposed method is effective for improving the unmixing accuracy of hyperspectral remote-sensing images.

Unsupervised Nonlinear Hyperspectral Unmixing Based on Bilinear Mixture Models via Geometric Projection and Constrained Nonnegative Matrix Factorization

Bilinear mixture model-based methods have recently shown promising capability in nonlinear spectral unmixing. However, relying on the endmembers extracted in advance, their unmixing accuracies decrease, especially when the data is highly mixed. In this paper, a strategy of geometric projection has been provided and combined with constrained nonnegative matrix factorization for unsupervised nonlinear spectral unmixing. According to the characteristics of bilinear mixture models, a set of facets are determined, each of which represents the partial nonlinearity neglecting one endmember. Then, pixels’ barycentric coordinates with respect to every endmember are calculated in several newly constructed simplices using a distance measure. In this way, pixels can be projected into their approximate linear mixture components, which reduces greatly the impact of collinearity. Different from relevant nonlinear unmixing methods in the literature, this procedure effectively facilitates a more accurate estimation of endmembers and abundances in constrained nonnegative matrix factorization. The updated endmembers are further used to reconstruct the facets and get pixels’ new projections. Finally, endmembers, abundances, and pixels’ projections are updated alternately until a satisfactory result is obtained. The superior performance of the proposed algorithm in nonlinear spectral unmixing has been validated through experiments with both synthetic and real hyperspectral data, where traditional and state-of-the-art algorithms are compared.