Number Of Endmembers Research Articles

Robust hyperspectral unmixing using weighted group sparsity and minimum volume regularization

ABSTRACT Hyperspectral unmixing (HU) has been a vital technique in hyperspectral image processing. Over the past years, many algorithms have been developed based on the nonnegative matrix factorization (NMF) framework. However, the conventional methods based on the NMF need prior information of the number of endmembers, which is usually estimated by a separate procedure. Therefore, the precision of estimating the number of endmembers will impact the subsequent unmixing effect. Thus, collaborating between the two processes is desired to avoid the propagation of errors. This paper proposes a new NMF-based method, which can estimate the number of endmembers and extract the endmembers and the abundance maps. Firstly, we introduce the weighted group sparsity regularization to adaptively eliminate the abundances corresponding to the redundant endmembers, while the abundances of the true endmembers are preserved. Then the number of endmembers can be determined by the reconstruction error function and the l 2 -norm of the abundance vectors. Secondly, since the simplex determined by the endmembers has the minimum volume among all simplexes that circumscribe the data points, we impose the total variational regularization to force the endmembers to be close to each other to minimize the simplex volume. And because the total variational regularization avoids the use of noisy pixels, it can decrease the influence of noise and improve the robustness of the solution. For the proposed model, we design an effective algorithm to solve it. Also, the experimental results based on the synthetic data and real data demonstrate that the proposed method can identify the endmembers number well and achieve robust unmixing results.

Exploring the Potential of PRISMA Satellite Hyperspectral Image for Estimating Soil Organic Carbon in Marvdasht Region, Southern Iran

Soil organic carbon (SOC) is a crucial factor for soil fertility, directly impacting agricultural yields and ensuring food security. In recent years, remote sensing (RS) technology has been highly recommended as an efficient tool for producing SOC maps. The PRISMA hyperspectral satellite was used in this research to predict the SOC map in Fars province, located in southern Iran. The main purpose of this research is to investigate the capabilities of the PRISMA satellite in estimating SOC and examine hyperspectral processing techniques for improving SOC estimation accuracy. To this end, denoising methods and a feature generation strategy have been used. For denoising, three distinct algorithms were employed over the PRISMA image, including Savitzky–Golay + first-order derivative (SG + FOD), VisuShrink, and total variation (TV), and their impact on SOC estimation was compared in four different methods: Method One (reflectance bands without denoising, shown as M#1), Method Two (denoised with SG + FOD, shown as M#2), Method Three (denoised with VisuShrink, shown as M#3), and Method Four (denoised with TV, shown as M#4). Based on the results, the best denoising algorithm was TV (Method Four or M#4), which increased the estimation accuracy by about 27% (from 40% to 67%). After TV, the VisuShrink and SG + FOD algorithms improved the accuracy by about 23% and 18%, respectively. In addition to denoising, a new feature generation strategy was proposed to enhance accuracy further. This strategy comprised two main steps: first, estimating the number of endmembers using the Harsanyi–Farrand–Chang (HFC) algorithm, and second, employing Principal Component Analysis (PCA) and Independent Component Analysis (ICA) transformations to generate high-level features based on the estimated number of endmembers from the HFC algorithm. The feature generation strategy was unfolded in three scenarios to compare the ability of PCA and ICA transformation features: Scenario One (without adding any extra features, shown as S#1), Scenario Two (incorporating PCA features, shown as S#2), and Scenario Three (incorporating ICA features, shown as S#3). Each of these three scenarios was repeated for each denoising method (M#1–4). After feature generation, high-level features were added to the outputs of Methods One, Three, and Four. Subsequently, three machine learning algorithms (LightGBM, GBRT, RF) were employed for SOC modeling. The results showcased the highest accuracy when features obtained from PCA transformation were added to the results from the TV algorithm (Method Four—Scenario Two or M#4–S#2), yielding an R2 of 81.74%. Overall, denoising and feature generation methods significantly enhanced SOC estimation accuracy, escalating it from approximately 40% (M#1–S#1) to 82% (M#4–S#2). This underscores the remarkable potential of hyperspectral sensors in SOC studies.

Evolutionary Competition Multitasking Optimization with Online Resource Allocation for Endmemeber Extraction of Hyperspectral Images

Hyperspectral remote sensing images typically have mixed rather than pure pixels. Endmember extraction aims to find a group of endmembers to represent the original image. In fact, the amount of endmembers is not easily determined in the existing endmember extraction studies.It requires several separate and laborious runs in order to produce results for endmember extraction with varying numbers of endmembers. There is also a correlation between the individual runs, which should be taken into account to accelerate algorithm convergence and improve accuracy. In this paper, an evolutionary competition multitasking optimization method (CMTEE) is proposed to achieve endmember extraction. In the proposed method, endmember extraction problems with different numbers of endmembers are considered as a group of optimization tasks. Specially, these tasks are assumed to be competitive. Then, online resource allocation is employed to assign suitable computational resources to the considered tasks. Experiments on simulated and real hyperspectral datasets demonstrated the effectiveness of the proposed evolutionary competition multitasking optimization method for endmember extraction.

Efficient Blind Hyperspectral Unmixing Framework Based on CUR Decomposition (CUR-HU)

Hyperspectral imaging captures detailed spectral data for remote sensing. However, due to the limited spatial resolution of hyperspectral sensors, each pixel of a hyperspectral image (HSI) may contain information from multiple materials. Although the hyperspectral unmixing (HU) process involves estimating endmembers, identifying pure spectral components, and estimating pixel abundances, existing algorithms mostly focus on just one or two tasks. Blind source separation (BSS) based on nonnegative matrix factorization (NMF) algorithms identify endmembers and their abundances at each pixel of HSI simultaneously. Although they perform well, the factorization results are unstable, require high computational costs, and are difficult to interpret from the original HSI. CUR matrix decomposition selects specific columns and rows from a dataset to represent it as a product of three small submatrices, resulting in interpretable low-rank factorization. In this paper, we propose a new blind HU framework based on CUR factorization called CUR-HU that performs the entire HU process by exploiting the low-rank structure of given HSIs. CUR-HU incorporates several techniques to perform the HU process with a performance comparable to state-of-the-art methods but with higher computational efficiency. We adopt a deterministic sampling method to select the most informative pixels and spectrum components in HSIs. We use an incremental QR decomposition method to reduce computation complexity and estimate the number of endmembers. Various experiments on synthetic and real HSIs are conducted to evaluate the performance of CUR-HU. CUR-HU performs comparably to state-of-the-art methods for estimating the number of endmembers and abundance maps, but it outperforms other methods for estimating the endmembers and the computational efficiency. It has a 9.4 to 249.5 times speedup over different methods for different real HSIs.

A novel linear spectral unmixing-based method for tree decline monitoring by fusing UAV-RGB and optical space-borne data

ABSTRACT Remote sensing-assisted monitoring of forest health entails methods that can provide up-to-date and accurate information on decline and mortality of individual trees, while maintaining time and cost efficiency. However, the trade-off of applying consumer-grade UAV-RGB data as the most affordable and accessible data source at the catchment level is constrained by its poor spectral information content. We developed a method based on the fusion of UAV-RGB data with space-borne Sentinel-2 Multispectral Instrument (MSI) at the level of tree crowns, with the specific target of supporting studies on semi-arid tree decline. We applied linear spectral unmixing (Spectral Unmixing-Based data Fusion method, LSUBF) by considering a limited number of endmembers and calculating the abundances (fractional covers) from the UAV data, and evaluated the results by high-resolution MSI space-borne data including SPOT-6 (1.5 m spatial resolution) and PlanetScope (3 m spatial resolution). This method suggested an increase in the coefficient of determination of the applied generalized additive model for decline severity estimation at tree crown level from 0.61 to 0.69, while it was improved from 0.70 to 0.91 when fitting a non-parametric random forest model. The results of sensitivity analysis demonstrated that the additional spectral information obtained from the proposed method results in higher accuracy in estimating decline severity. We suggest this method as a cost-effective alternative to monitor periodical tree decline, in particular across semi-arid ecosystems.

Source apportionment of polychlorinated biphenyls (PCBs) using different receptor models: A case study on sediment from the Portland Harbor Superfund Site (PHSS), Oregon, USA

Multivariate modelling techniques are used by a wide variety of investigations in environmental chemistry. It is surprisingly rare for studies to show a detailed understanding of uncertainties created by modelling or how uncertainties in chemical analysis impact model outputs. It is common to use untrained multivariate models for receptor modelling. These models produce a slightly different output each time they are run. The fact that a single model can provide different results is rarely acknowledged. In this manuscript, we attempt to address this by investigating differences that can be generated using four different receptor models (NMF, ALS, PMF & PVA) to perform source apportionment of polychlorinated biphenyls (PCBs) in surface sediments from Portland Harbor. Results showed that models generally had a strong agreement and identified the same main signatures that represented commercial PCB mixtures, however, subtle differences were identified by; different models, same models but with a different number of end members (EM), and the same model with the same number of end members. As well as identifying different Aroclor-like signatures, the relative proportion of these sources also varied. Depending on which method is selected it may have a significant impact on conclusions of a scientific report or litigation case and ultimately, allocation on who is responsible for paying for remediation. Therefore, care must be taken to understand these uncertainties to select a method that produces consistent results with end members that can be chemically explained. We also investigated a novel approach to use our multivariate models to identify inadvertent sources of PCBs. By using a residual plot produced from one of our models (NMF) we were able to suggest the presence of approximately 30 different potentially inadvertently produced PCBs which account for 6.6 % of the total PCBs in Portland Harbor sediments.

Spectral mixture analysis of AVIRIS-NG data for grouping plant functional types

In a recent scenario, the prediction of environmental changes through plant functional types can aid in simplification of ecosystem processes. The present study attempts to identify and map plant functional types (PFTs) in the AVIRIS-NG campaign site, namely Shoolpaneshwar Wildlife Sanctuary (site id 67), using AVIRIS-NG data combined with spectral mixture analysis that accounts for endmember variability. Due to the occurrence of heterogeneous vegetation in the selected AVIRIS-NG site, the measured spectral signal for every pixel of surface reflectance data will be the outcome of fractions in which various plant functional types and the soil background exist. The interest of the present research lies in these fractions; hence spectral mixture analysis was applied. Ground truthing was carried out simultaneous to AVIRIS-NG flight pass. Six plant functional traits, namely Diameter at breast height (DBH), Height, biomass, leaf chlorophyll content (CC), Fraction of Photosynthetic Active Radiation (FPAR), and Leaf Area Index (LAI), were measured for twenty-three tree species found in the study site which were further used for plant functional grouping by applying k-means clustering algorithm. Trait-based cluster analysis classified the tree species into four plant functional types. Endmember selection from AVIRIS-NG image for these plant functional types was done using a manual field observation-based approach, which was used as input in spectral mixture analysis. The final product of the analysis is a set of fractional abundance images for each plant functional type. Considerable accuracy was obtained on validating the fractional abundance image by in situ data. The study highlighted the potential of a spectral mixture analysis classifier in identifying and mapping different plant functional types using AVIRIS-NG data when performed using an appropriate number of end members.

Estimation of sub-endmembers using spatial-spectral approach for hyperspectral images

In Blind Hyperspectral Unmixing, the accuracy of the estimated number of endmembers affects the succeeding steps of extraction of endmember signatures and acquiring their fractional abundances. The characteristics of endmember signature depend on the nature of the material on the ground and share similar characteristics for variants of the same material. In this paper, we introduce a new concept of sub-endmembers to identify similar materials that are variants of a global endmember. Identifying the sub-endmembers will provide a meaningful interpretation of the endmember variability along with increased unmixing accuracy. This paper proposes a new algorithm exploiting both the spatial and spectral information present in hyperspectral data. The hyperspectral data are segmented into homogenous regions (superpixels) based on the Simple Linear Iterative Clustering (SLIC) algorithm, and the mean spectral of each region is accounted for in finding the global endmembers. The difference of eigenvalues-based thresholding method is used to find the number of global and sub-endmembers. The method has been tested on synthetic and real hyperspectral data and has successfully estimated the number of global endmembers as well as sub-endmembers. The method is also compared with other state-of-the-art methods, and better performances are obtained at a reasonably lower computational complexity.

A Comparative Analysis of Methods of Endmember Selection for Use in Subpixel Classification: A Convex Hull Approach.

Mixed pixels in aerial and satellite images are common, especially near the boundaries of two or more discrete classes; that is, they tend to occur at the transitional region between two classes. Ideally, to decipher the mixed pixel, a soft classification is performed compared to a hard- or a per-pixel classification. Soft or subpixel classification is carried out where the fractional cover of the LULC contained within a pixel is derived. Endmembers are extracted for three VNIR bands of ASTER data for two image datasets using three approaches, namely, principal component analysis (PCA), pixel purity index (PPI), and convex hull-Graham scan (CHGS). On comparing the DN values of the identified endmembers, it is observed that the CHGS method provides the most appropriate end members than the PCA-derived and PPI-derived end members. This is based on deriving the endmembers from two different image conditions. Convex hull implemented using the Graham scan algorithm delineates the pure pixel and pinpoints the exact number of endmembers. These accurate end members would result in accurate proportions of the land cover for better modeling of the terrain.

An assessment of background removal approaches for improved estimation of rice leaf nitrogen concentration with unmanned aerial vehicle multispectral imagery at various observation times

Background effect is a crucial limitation for the monitoring of leaf nitrogen concentration (LNC) in crops with unmanned aerial vehicle (UAV) multispectral imagery. Some background removal approaches have been developed for improve the estimation of LNC, but their performances are not compared in one study and it is unclear whether they are sensitive to the observation time of UAV imagery. This study evaluated three background removal approaches, i.e., the soil-adjusted vegetation index (SAVI) approach, the green pixel vegetation index approach (GPVI) and abundance adjusted vegetation index (AAVI), for estimating rice LNC from UAV-based multispectral imagery at individual and across growth stages as well as different observation times of the day. The red edge chlorophyll index (CIre) was chosen as the common basis for the last two approaches. In particular, the AAVI approach was refined with a higher number of endmembers and automated endmember extraction, and further evaluated for assessing the effect of separating sunlit components from shaded components of the canopy. Our results demonstrated that the vegetation indices (VIs) for off-noon observation times showed better relationships with LNC than those for noon at individual and across growth stages. Compared to both SAVI and CIre-green, the AACIre for all pixels (AACIre-all) exhibited the weakest sensitivity to observation time and yielded the best relationships for single-stage (jointing: r2=0.70, booting: r2=0.76, heading: r2=0.70) and across-stage (r2=0.66) models. Among the AAVIs derived from three categories of pixels, the AACIre-sunlit (R2 =0.90, RMSE=0.17%, Bias=0.03%) outperformed AACIre-all (R2 =0.85, RMSE=0.23%, Bias=0.08%) and then AACIre-shaded (R2 =0.38, RMSE=0.49%, Bias=0.40%) remarkably for the estimation accuracy of LNC. This study suggests that the refined AAVI approach has great value in reducing the background effect for more accurate monitoring of growth parameters and could be extended to other crops and regions for improved precision crop management and field-based high-throughput phenotyping.

Fusion of airborne hyperspectral and LiDAR canopy-height data for estimating fractional cover of tall woody plants, herbaceous vegetation, and other soil cover types in a semi-arid savanna ecosystem

ABSTRACT Vegetation in semi-arid regions is often a spatially heterogeneous mix of bare soil, herbaceous vegetation, and woody plants. Detecting the fractional cover of woody plants versus herbaceous vegetation, in addition to non-photosynthetically active cover types such as biological soil crusts, dry grasses, and bare ground, is crucial for understanding spatial patterns and temporal changes in semi-arid savanna ecosystems. With and without the inclusion of LiDAR-derived canopy height information, we tested different configurations of unsupervised linear unmixing classification of hyperspectral data to estimate fractional cover of tall woody plants, herbaceous vegetation, and other non-photosynthetically active cover types. To perform this analysis, we used 1 m resolution hyperspectral and LiDAR data collected by the NEON airborne observation platform at the Santa Rita Experimental Range in Arizona. Our results show that both hyperspectral and canopy height information are needed in the linear unmixing algorithm to correctly identify tall woody plants versus herbaceous vegetation. However, including height data is not always sufficient to be able to separate the two vegetation types: selecting the optimum number of endmembers is also crucial for separating these two types of photosynthetically active vegetation. In comparison to our reference dataset, fractional cover accuracy was highest for the woody plant class based on two accuracy assessment methods, although the fractional cover of dense woody plant is likely underestimated because linear unmixing also detects sub-canopy elements. The accuracy of the herbaceous vegetation class was lower than the other classes, likely because of the presence of both active and senesced grasses. Our study presents the first use of both hyperspectral and canopy height information to separately detect fractional cover of woody plants versus herbaceous vegetation in addition to other bare soil cover types that should be useful for fractional cover classification in other semi-arid savanna ecosystems where hyperspectral and LiDAR data are available.

Hyperspectral image non-linear unmixing using joint extrinsic and intrinsic priors with L1/2-norms to non-negative matrix factorisation

Hyperspectral unmixing (HU) is one of the most active emerging areas in image processing that estimates the hyperspectral image’s endmember and abundance. HU enhances the quality of both spectral and spatial dimensions of the image by modifying the endmember and abundance parameters of the hyperspectral images. There are several HU algorithms available in the literature based on the linear mixing model (LMM) that deals with the microscopic contents of the pixels in the images. Non-negative matrix factorisation (NMF) is the prominent method widely used in LMMs that simultaneously estimates both the endmembers and abundances parameters along with some residual factors of the image to improve the quality of unmixing. In addition to this, the quality of the image is enhanced by incorporating some constraints to both endmember and abundance matrices with the NMF method. However, all the existing methods apply any of these constraints to the endmember and abundance matrices by considering the linearity features of the images. In this paper, we propose an unmixing model called joint extrinsic and intrinsic priors with L1/2 norms to non-negative matrix factorisation (JEIp L1/2-NMF) that applies multiple constraints simultaneously to both endmember and abundance matrices of the hyperspectral image to enhance its quality. Three main external and internal constraints such as minimum volume, sparsity and total variation are applied to both the endmembers and abundance parameters of the image. In addition, a L1/2-norms is imposed to extract good quality spectral data. Therefore, the proposed method enhances spatial as well as spectral data and considers the non-linearity of the pixels in the image by adding a residual term to the model. Performance of our proposed model is measured by using different quality measuring indexes on four benchmark public datasets and found that the proposed method shows outstanding performance compared to all the conventional baseline methods. Further, we also evaluated the performance of our method by varying the number of endmembers empirically and concluded that less than five endmembers provides high-quality spectral and spatial data during the unmixing process.

Endmember Estimation From Hyperspectral Images Using Geometric Distances

Endmember estimation consists of two tasks, that is, determining the number of pure spectral constituents (endmembers) and extracting their spectral signatures. We present a new geometric distance-based method for endmember estimation from hyperspectral images (HSIs), which does not need to know the number of endmembers in advance. Our strategy optimizes the widely used maximum distance analysis (MDA) method from two viewpoints. First, the traditional MDA method performs endmember estimation by computing the maximum distances between any pixel and one specific pixel, line, plane, or affine hull (AH) composed by the endmembers that have been formerly extracted. Instead, our new strategy only requires computing the maximum distance between any pixel and one specific AH. This operation provides a simpler way than MDA to estimate endmembers. Second, our strategy exploits a new distance computation between any pixel and an AH and just needs the normal vector (compared to the traditional MDA method, which uses the normal vector and offset). The new distance computation in our method is much more efficient than that in the traditional MDA method.

Spatial-Aware Hyperspectral Nonlinear Unmixing Autoencoder With Endmember Number Estimation

In this article, we develop a novel fully unsupervised autoencoder-based scheme for nonlinear hyperspectral pixel unmixing. A unique approach is derived where high noise and unresponsive pixels are accounted for, by a unique averaging approach based on spatially aware filters built using radial basis function (RBF) kernels. A novel technique is implemented via calculating rank-equivalent kernel covariance matrices in order to estimate the unknown number of endmembers contributing to the data. Utilization of spatial information is done via RBF-based weighted averaging, which is then followed by endmember estimation via K-means clustering. The RBF distances from the cluster centers are determined to measure the position of the mixed pixels in relation to the centers, which is utilized as a preliminary estimation of the abundances. The proposed framework is robust in the presence of unresponsive pixels, while highly versatile working with different nonlinear unmixing models. Extensive numerical tests establish the superiority of the novel approach with respect to state-of-the-art methods.

A New Endmember Extraction Method Based on Least Squares

Endmember extraction is frequently adopted to detect spectrally unique signatures of pure ground materials in hyperspectral imagery. These endmembers are the purest pixels in the HSI data cubes. Every pixel in a HSI data cube can be expressed as a linear combination of a finite number of endmembers. In this paper, we propose a novel method for endmember extraction by means of least squares. We perform minimum noise fraction to reduce the dimensionality of the data cube, initialize the endmembers by using automatic target generation process, compute the abundance map from the dimensionality reduced data cube and the initial endmembers, and calculate the final endmembers by using least squares. Our proposed method is comparable to and sometimes outperforms existing methods in term of spectral angle distance for all four testing data cubes for endmember extraction. In addition, our method is relatively fast as well because it only performs quite simple operations to find endmembers in the testing hyperspectral data cubes.

Multi-sensor data fusion of remotely-sensed images with sparse and logarithmic low-rank regularization for shadow removal and denoising

ABSTRACT Hyperspectral images have high spectral resolution but low spatial resolution, which results in a large number of mixed pixels. As an economical and effective means to improve image quality, the fusion of hyperspectral and multispectral data from different sensors can achieve the reconstruction of super-resolution images. As a representative of fusion method, coupled non-negative matrix factorization is an ill-posed problem, in which the number of endmembers was set to be no less than the groundtruth without requiring an accurate value. However, this often results in spectral shadows and spatial information redundancy, especially when the observed images are contaminated by noise. To address these problems above, this article incorporates sparse and low-rank regularization to reformulate a bi-convex fusion problem for the removal of shadows and noise, in which the logarithmic sum function is employed to suppress the small singular components of endmember and abundance matrices. Then, an efficient solver is designed to obtain the closed-form solutions via matrix-vector operators, in which the alternating direction method of multipliers is utilized to split the variables using equality constraints. The experimental results of real datasets demonstrate that the proposed fusion method can effectively enhance the quality of reconstructed super-resolution images especially in high-noise environments, which also verifies the validation of incorporated regularization.

Multi-fidelity evolutionary multitasking optimization for hyperspectral endmember extraction

Endmember extraction plays an indispensable role in hyperspectral image processing, which is also an important step to decompose the mixed pixels in spectral unmixing. Most of the existing methods based on the principle of convex geometry and intelligent optimization algorithms have achieved an excellent result, but they also suffer from the influence of outliers and expensive computation respectively. Furthermore, it is difficult to determine the number of endmembers in a hyperspectral image without any prior conditions. In order to alleviate these problems, we propose a multi-fidelity evolutionary multitasking optimization framework for hyperspectral endmember extraction in this article. In the proposed framework, multiple tasks to extract different numbers of endmembers are uniformly coded into a single population, aiming to process these similar tasks simultaneously with the implicit genetic transfer. Accordingly, our proposed algorithm is capable of extracting the best endmember set within a certain range of the number of endmembers without any prior knowledge. In addition, an ensemble surrogate model is firstly built to approximate the high-fidelity fitness with the low-fidelity fitness in endmember extraction, which greatly alleviates the time-consuming problem of individual evaluation. The experimental results on the simulated and the real hyperspectral data demonstrate the effectiveness of the proposed framework. The accuracy and the efficiency of endmember extraction are greatly improved compared with other classic endmember extraction methods.

Geodesic simplex based multiobjective endmember extraction for nonlinear hyperspectral mixtures

This paper presents a novel multiobjective endmember extraction approach for nonlinear hyperspectral mixtures by assuming that the distribution of mixtures conforms to a nonlinear manifold and the endmembers correspond to its extreme points. To identify the endmembers, the approach aims to seek a set of pixels which define a simplex with the maximum volume along the manifold. Meanwhile, several obstacles are properly settled to make it a good performance. First, calculating a simplex’s volume along the manifold needs to calculate the geodesic distance (i.e., the shortest path) between its vertices on the k-nearest neighbor (kNN) graph of the manifold data, but it is time-consuming to go through all the manifold points to search the desired simplex. Therefore, a boundary detection technique is proposed to restrict the identification of endmembers within the boundary points of the manifold to improve the time efficiency. Second, the volume of the geodesic distance based simplex is sensitive to the deviations in the geodesic distance caused by noise. To settle this issue, the multiple regression based noise estimation method is applied due to the high correlation among hundreds of spectral bands. Therefore, the spectral noise can be removed before the calculation of geodesic distance. Third, the number of endmembers is of crucial importance but hard to determine, so it is usually specified beforehand in most unmixing approaches. The proposed approach can instinctively obtain a set of simplices with the maximum volume corresponding to different numbers of endmembers, thus providing more insight for determining the optimal combination of endmembers. In addition, the proposed method is a population based optimization method which is less likely to get trapped into the local optimum. The experiments on synthetic as well as real data sets demonstrate the validity and superiority of the proposed method as compared with the methods of the same type.

Endmember Estimation with Maximum Distance Analysis

Endmember estimation plays a key role in hyperspectral image unmixing, often requiring an estimation of the number of endmembers and extracting endmembers. However, most of the existing extraction algorithms require prior knowledge regarding the number of endmembers, being a critical process during unmixing. To bridge this, a new maximum distance analysis (MDA) method is proposed that simultaneously estimates the number and spectral signatures of endmembers without any prior information on the experimental data containing pure pixel spectral signatures and no noise, being based on the assumption that endmembers form a simplex with the greatest volume over all pixel combinations. The simplex includes the farthest pixel point from the coordinate origin in the spectral space, which implies that: (1) the farthest pixel point from any other pixel point must be an endmember, (2) the farthest pixel point from any line must be an endmember, and (3) the farthest pixel point from any plane (or affine hull) must be an endmember. Under this scenario, the farthest pixel point from the coordinate origin is the first endmember, being used to create the aforementioned point, line, plane, and affine hull. The remaining endmembers are extracted by repetitively searching for the pixel points that satisfy the above three assumptions. In addition to behaving as an endmember estimation algorithm by itself, the MDA method can co-operate with existing endmember extraction techniques without the pure pixel assumption via generalizing them into more effective schemes. The conducted experiments validate the effectiveness and efficiency of our method on synthetic and real data.

Constrained Nonnegative Matrix Factorization for Blind Hyperspectral Unmixing Incorporating Endmember Independence

Hyperspectral unmixing (HU) has become an important technique in exploiting hyperspectral data since it decomposes a mixed pixel into a collection of endmembers weighted by fractional abundances. The endmembers of a hyperspectral image (HSI) are more likely to be generated by independent sources and be mixed in a macroscopic degree before arriving at the sensor element of the imaging spectrometer as mixed spectra. Over the past few decades, many attempts have focused on imposing auxiliary regularizes on the conventional nonnegative matrix factorization (NMF) framework in order to effectively unmix these mixed spectra. As a promising step toward finding an optimum regularizer to extract endmembers, this paper presents a novel blind HU algorithm, referred to as Kurtosis-based Smooth Nonnegative Matrix Factorization (KbSNMF) which incorporates a novel regularizer based on the statistical independence of the probability density functions of endmember spectra. Imposing this regularizer on the conventional NMF framework promotes the extraction of independent endmembers while further enhancing the parts-based representation of data. Experiments conducted on diverse synthetic HSI datasets (with numerous numbers of endmembers, spectral bands, pixels, and noise levels) and three standard real HSI datasets demonstrate the validity of the proposed KbSNMF algorithm compared to several stateof- the-art NMF-based HU baselines. The proposed algorithm exhibits superior performance especially in terms of extracting endmember spectra from hyperspectral data; therefore, it could uplift the performance of recent deep learning HU methods which utilize the endmember spectra as supervisory input data for abundance extraction.