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Precise spatial information of crop distribution is vital for government and research organizations to monitor agriculture activities like crop health monitoring, crop yield prediction, and food security. Mapping of crop area is challenging in smallholder farming like India, where crop parcels are smaller than two hectares. With an extension of artificial intelligence, an artificial neural network has ability to learn the spectral feature of multispectral satellite images and map them to a land cover class. However, mixed pixel is a challenging problem in pixel wise classification of coarse resolution satellite images. The linear mixture model is successfully utilized to unmix the signals of a mixed classes. The success of linear mixture model is depending on the selection of endmembers of a mixed class. Therefore, this paper presents an adaptive approach for automatic selection of endmembers of a mixed pixel in linear mixture model using spectral and spatial information. The proposed approach is capable of extracting the fraction area cover of each class by using a constrained least-squares error solution. The GPS field surveys, and drone images are employed to create reference data for the accuracy assessment of proposed algorithm. The experimentation results indicate that the solution of the proposed approach outperformed recent baseline methods in terms of efficiency and accuracy of pixelwise estimated area and overall estimated area of various land cover classes.

Many studies in recent years have been devoted to estimating the per-pixel proportions of three broad classes of materials (e.g., photosynthetic vegetation, non-photosynthetic vegetation and bare soil) using data from multispectral sensors. Oftentimes, the estimated proportions are used to monitor environmental change in both urban and non-urban environments. Many of these papers use proportion estimation methods based on the linear mixture model. Very few of these papers assess the accuracy of their estimators. This paper shows how to produce confidence intervals (CIs) and joint confidence regions (JCRs) for the proportions associated with various linear mixture models. There are two main models, both of which assume that the coefficients in the model are non-negative. The first model assumes that the coefficients sum to 1. The second does not, but uses rescaling of the estimated coefficients to produce estimated proportions. Three variants of these two models are also analysed. JCRs are shown to be particularly informative, because they are typically better at localising the information than CIs are. The methodology is illustrated using examples from Landsat Thematic Mapper data at 1169 locations across Australia, each of which has associated field observations. There is also a discussion about the extent to which the methodology can be extended to hyperspectral data. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role in solving this problem. In this article, we present a comprehensive survey of the NMF-based methods proposed for hyperspectral unmixing. Taking the NMF model as a baseline, we show how to improve NMF by utilizing the main properties of HSIs (e.g., spectral, spatial, and structural information). We categorize three important development directions, including constrained NMF, structured NMF, and generalized NMF. Furthermore, several experiments are conducted to illustrate the effectiveness of associated algorithms. Finally, we conclude this article with possible future directions with the purposes of providing guidelines and inspiration to promote the development of hyperspectral unmixing.

Since remote sensing images offer unique access to the distribution of land cover on earth, many countries are investing in this technique to monitor urban sprawl. For this purpose, the most widely used methodology is spectral unmixing which, after identifying the spectra of the mixed-pixel constituents, determines their fractional abundances in the pixel. However, the literature highlights shortcomings in spatial validation due to the lack of detailed ground truth knowledge and proposes five key requirements for accurate reference fractional abundance maps: they should cover most of the area, their spatial resolution should be higher than that of the results, they should be validated using other ground truth data, the full range of abundances should be validated, and errors in co-localization and spatial resampling should be minimized. However, most proposed reference maps met two or three requirements and none met all five. In situ and remote data acquired in Venice were exploited to meet all five requirements. Moreover, to obtain more information about the validation procedure, not only reference spectra, synthetic image, and fractional abundance models (FAMs) that met all the requirements, but also other data, that no previous work exploited, were employed: reference fractional abundance maps that met four out of five requirements, and fractional abundance maps retrieved from the synthetic image. Briefly summarizing the main results obtained from MIVIS data, the average of spectral accuracies in root mean square error was equal to 0.025; using FAMs, the average of spatial accuracies in mean absolute error (MAEk-Totals) was equal to 1.32 and more than 78% of these values were related to sensor characteristics; using reference fractional abundance maps, the average MAEk-Totals value increased to 1.97 because errors in co-localization and spatial-resampling affected about 29% of these values. In conclusion, meeting all requirements and the exploitation of different reference data increase the spatial accuracy, upgrade the validation procedure, and improve the knowledge of accuracy. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing including endmember extraction and abundance estimation has been investigated successively in recent years due to increasingly hyperspectral processing requirements. As one type of decision after solution paradigm, the multiobjective endmember estimation (MoEE) method is able to obtain a set of Pareto optimal solutions, thus providing a wealth of information to determine the most representative endmembers. In addition, multiobjective optimization methods also have the characteristics of flexible modeling, excellent global convergence, commendable adaptability, and so on. However, the evolutionary algorithms designed for this kind of method generally use little spatial–spectral information of the hyperspectral image. In this article, we delve into the memetic strategy by exploiting the topological structure of hyperspectral data in the high-dimensional space to establish a vertex-directed MoEE method, termed VD-MoEE. According to the frequently used linear mixture model, endmembers of hyperspectral images are generally distributed at the vertices of the hyperspectral data manifold. Therefore, we design a vertex-directed local search operator to guide the search direction of the individuals in evolutionary algorithms. Experimental results on synthetic and real datasets demonstrated that the proposed VD-MOEE is able to achieve appealing performance in terms of solution selection and accuracy in comparison with several classic and state-of-the-art endmember estimation methods. [ABSTRACT FROM AUTHOR]

Many studies in recent years have been devoted to estimating the per-pixel proportions of three broad classes of materials (e.g., photosynthetic vegetation, non-photosynthetic vegetation and bare soil) using data from multispectral sensors. Oftentimes, the estimated proportions are used to monitor environmental change in both urban and non-urban environments. Many of these papers use proportion estimation methods based on the linear mixture model. Very few of these papers assess the accuracy of their estimators. This paper shows how to produce confidence intervals (CIs) and joint confidence regions (JCRs) for the proportions associated with various linear mixture models. There are two main models, both of which assume that the coefficients in the model are non-negative. The first model assumes that the coefficients sum to 1. The second does not, but uses rescaling of the estimated coefficients to produce estimated proportions. Three variants of these two models are also analysed. JCRs are shown to be particularly informative, because they are typically better at localising the information than CIs are. The methodology is illustrated using examples from Landsat Thematic Mapper data at 1169 locations across Australia, each of which has associated field observations. There is also a discussion about the extent to which the methodology can be extended to hyperspectral data.

Since remote sensing images offer unique access to the distribution of land cover on earth, many countries are investing in this technique to monitor urban sprawl. For this purpose, the most widely used methodology is spectral unmixing which, after identifying the spectra of the mixed-pixel constituents, determines their fractional abundances in the pixel. However, the literature highlights shortcomings in spatial validation due to the lack of detailed ground truth knowledge and proposes five key requirements for accurate reference fractional abundance maps: they should cover most of the area, their spatial resolution should be higher than that of the results, they should be validated using other ground truth data, the full range of abundances should be validated, and errors in co-localization and spatial resampling should be minimized. However, most proposed reference maps met two or three requirements and none met all five. In situ and remote data acquired in Venice were exploited to meet all five requirements. Moreover, to obtain more information about the validation procedure, not only reference spectra, synthetic image, and fractional abundance models (FAMs) that met all the requirements, but also other data, that no previous work exploited, were employed: reference fractional abundance maps that met four out of five requirements, and fractional abundance maps retrieved from the synthetic image. Briefly summarizing the main results obtained from MIVIS data, the average of spectral accuracies in root mean square error was equal to 0.025; using FAMs, the average of spatial accuracies in mean absolute error (MAEk-Totals) was equal to 1.32 and more than 78% of these values were related to sensor characteristics; using reference fractional abundance maps, the average MAEk-Totals value increased to 1.97 because errors in co-localization and spatial-resampling affected about 29% of these values. In conclusion, meeting all requirements and the exploitation of different reference data increase the spatial accuracy, upgrade the validation procedure, and improve the knowledge of accuracy.

The detection of strategically important geospatial objects in remote sensing images is one of the important tasks for interpreting satellite images. Identification and mapping of objects such as tank, airplane, roads, buildings, etc. from remotely sensed images has gained much research and exploration in both defense and civilian applications. Detection and identification of buildings become more challenging when analyzed in forest neighborhood environment. The presence of dense trees in the surroundings increases the complexity and the rates of both false positives and false negatives. In the current study, an integration of image pan-sharpening (Gram-Schmidt) and sub-pixel image classification (Linear Mixture Model) algorithm is used for identification and mapping of building objects in two high resolution remote sensing satellite imagery (IKONOS and Worldview-2). Building objects having large, medium and small geometric size are selected from both the satellite imagery in strategically challenged forest neighborhood. The capability of pan-sharpening and sub-pixel classification techniques are jointly used for detection of building objects. The accuracy of target detection has been evaluated qualitatively (visual interpretation) and quantitatively (statistical analysis). Results on selected datasets show that the proposed combination of pan-sharpening and sub-pixel classification offers higher correctness in identification of building than other contemporary techniques. Although, significant improvement is noticed in results obtained for both the satellite imagery. Irrespective of having lower spatial resolution, after pan-sharpening, IKONOS datasets are found to be slightly more accurate in building identification in comparison to Worldview-2 datasets. [ABSTRACT FROM AUTHOR]

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There have been a significant number of recent papers about hyperspectral imaging, which propose various methods for estimating the number of materials/endmembers in hyperspectral images. This is sometimes called the “intrinsic” dimension (ID) of the image. Estimation of the error variance in each spectral band is a critical first step in ID estimation. The estimated error variances can then be used to preprocess (e.g., whiten) the data, prior to ID estimation. A range of variance estimation methods have been advocated in the literature. We investigate the impact of five variance estimation methods (three using spatial information and two using spectral information) on five ID estimation methods, with the aid of four different, but semirealistic, sets of simulated hyperspectral images. Our findings are as follows: first, for all four sets, the two spectral variance estimation methods significantly outperform the three spatial methods; second, when used with the spectral variance estimation methods, two of the ID estimation methods (called random matrix theory and NWHFC) consistently outperform the other three ID estimation methods; third, the better spectral variance estimation method sometimes gives negative variance estimates; fourth, we introduce a simple correction that guarantees positivity; and fifth, we give a fast algorithm for its computation. [ABSTRACT FROM AUTHOR]

Many methods have been proposed in the literature for estimating the number of materials/endmembers in a hyperspectral image. This is sometimes called the “intrinsic” dimension (ID) of the image. A number of recent papers have proposed ID estimation methods based on various aspects of random matrix theory (RMT), under the assumption that the errors are uncorrelated, but with possibly unequal variances. A recent paper, which reviewed a number of the better known methods (including one RMT-based method), has shown that they are all biased, especially when the true ID is greater than about 20 or 30, even when the error structure is known. I introduce two RMT-based estimators ( R M T G , which is new, and R M T K N , which is a modification of an existing estimator), which are approximately unbiased when the error variances are known. However, they are biased when the error variance is unknown and needs to be estimated. This bias increases as ID increases. I show how this bias can be reduced. The results use semi-realistic simulations based on three real hyperspectral scenes. Despite this, when applied to the real scenes, R M T G and R M T K N are larger than expected. Possible reasons for this are discussed, including the presence of errors which are either deterministic, spectrally and/or spatially correlated, or signal-dependent. Possible future research into ID estimation in the presence of such errors is outlined.

Normalized difference vegetation index (NDVI) of highly dense vegetation (NDVI v ) and bare soil (NDVI s ), identified as the key parameters for Fractional Vegetation Cover (FVC) estimation, are usually obtained with empirical statistical methods However, it is often difficult to obtain reasonable values of NDVI v and NDVI s at a coarse resolution (e.g., 1 km), or in arid, semiarid, and evergreen areas. The uncertainty of estimated NDVI s and NDVI v can cause substantial errors in FVC estimations when a simple linear mixture model is used. To address this problem, this paper proposes a physically based method. The leaf area index (LAI) and directional NDVI are introduced in a gap fraction model and a linear mixture model for FVC estimation to calculate NDVI v and NDVI s . The model incorporates the Moderate Resolution Imaging Spectroradiometer (MODIS) Bidirectional Reflectance Distribution Function (BRDF) model parameters product (MCD43B1) and LAI product, which are convenient to acquire. Two types of evaluation experiments are designed 1) with data simulated by a canopy radiative transfer model and 2) with satellite observations. The root-mean-square deviation (RMSD) for simulated data is less than 0.117, depending on the type of noise added on the data. In the real data experiment, the RMSD for cropland is 0.127, for grassland is 0.075, and for forest is 0.107. The experimental areas respectively lack fully vegetated and non-vegetated pixels at 1 km resolution. Consequently, a relatively large uncertainty is found while using the statistical methods and the RMSD ranges from 0.110 to 0.363 based on the real data. The proposed method is convenient to produce NDVI v and NDVI s maps for FVC estimation on regional and global scales. [ABSTRACT FROM AUTHOR]

Changes in the spatial distributions of vegetation across the globe are routinely monitored by satellite remote sensing, in which the reflectance spectra over land surface areas are measured with spatial and temporal resolutions that depend on the satellite instrumentation. The use of multiple synchronized satellite sensors permits long-term monitoring with high spatial and temporal resolutions. However, differences in the spatial resolution of images collected by different sensors can introduce systematic biases, called scaling effects, into the biophysical retrievals. This study investigates the mechanism by which the scaling effects distort normalized difference vegetation index (NDVI). This study focused on the monotonicity of the area-averaged NDVI as a function of the spatial resolution. A monotonic relationship was proved analytically by using the resolution transform model proposed in this study in combination with a two-endmember linear mixture model. The monotonicity allowed the inherent uncertainties introduced by the scaling effects (error bounds) to be explicitly determined by averaging the retrievals at the extrema of theresolutions. Error bounds could not be estimated, on the other hand, for non-monotonic relationships. Numerical simulations were conducted to demonstrate the monotonicity of the averaged NDVI along spatial resolution. This study provides a theoretical basis for the scaling effects and develops techniques for rectifying the scaling effects in biophysical retrievals to facilitate cross-sensor calibration for the long-term monitoring of vegetation dynamics.

The fraction of vegetation cover (FVC) is often estimated by unmixing a linear mixture model (LMM) to assess the horizontal spread of vegetation within a pixel based on a remotely sensed reflectance spectrum. The LMM-based algorithm produces results that can vary to a certain degree, depending on the model assumptions. For example, the robustness of the results depends on the presence of errors in the measured reflectance spectra. The objective of this study was to derive a factor that could be used to assess the robustness of LMM-based algorithms under a two-endmember assumption. The factor was derived from the analytical relationship between FVC values determined according to several previously described algorithms. The factor depended on the target spectra, endmember spectra, and choice of the spectral vegetation index. Numerical simulations were conducted to demonstrate the dependence and usefulness of the technique in terms of robustness against the measurement noise.

Remotely sensed reflectance spectra may be biased by several intervening factors, and the biases are propagated into estimations of the fraction of vegetation cover (FVC) by algorithms based on a linear mixture model (LMM). The errors propagated in FVCs depend on the retrieval algorithm used, due to differences in the assumptions of the model as well as constraints employed in the algorithm. These differences should be fully understood prior to algorithm selection for practical applications. Although numerous studies have investigated the relationships between errors propagated by different algorithms, these relationships have not been fully understood from a deterministic perspective. This study introduces a technique for deriving the analytical underpinnings of error propagation in FVC based on several LMM-based algorithms. The derivation assumes that measurement noise is band-correlated additive noise. The bias errors propagated in FVC depended on the endmember spectra assumed in the algorithm, the target spectrum, and the coefficients of the spectral vegetation index, which were employed as constraints, as well as magnitude of the input error. It was found that the relationships among the propagated errors assume asymmetric elliptical forms with coefficients that are determined by the input variables. These results suggest that the relationships depend heavily on the choice of endmember spectra as well as the spectrum of the target pixel and the vegetation index employed as a constraint. The present findings should assist in the selection of an optimum algorithm based on prior knowledge of the target field.

High-resolution hyperspectral images are in great demand but hard to acquire due to several existing fundamental and technical limitations. A practical way around this is to fuse multiple multiband images of the same scene with complementary spatial and spectral resolutions. We propose an algorithm for fusing an arbitrary number of coregistered multiband, i.e., panchromatic, multispectral, or hyperspectral, images through estimating the endmember and their abundances in the fused image. To this end, we use the forward observation and linear mixture models and formulate an appropriate maximum-likelihood estimation problem. Then, we regularize the problem via a vector total-variation penalty and the non-negativity/sum-to-one constraints on the endmember abundances and solve it using the alternating direction method of multipliers. The regularization facilitates exploiting the prior knowledge that natural images are mostly composed of piecewise smooth regions with limited abrupt changes, i.e., edges, as well as coping with potential ill-posedness of the fusion problem. Experiments with multiband images constructed from real-world hyperspectral images reveal the superior performance of the proposed algorithm in comparison with the state-of-the-art algorithms, which need to be used in tandem to fuse more than two multiband images.

This paper presents the automatic analysis of surface thermograms in response to a long-pulsed thermography inspection to classify buried defects in composite materials. Time-dependent thermal contrasts, captured from the sample surface by an infrared thermal camera, are linearly unmixed at the pixel scale to produce results independent of the in-plane defect shapes in the training dataset. The extended blind end-member and abundance extraction (EBEAE) method unmix the thermograms to compute feature vectors carrying information about the internal structure of the composite. The estimated abundances fed an optimized support vector machine (SVM) classifier, which learns a model from the data and labels the defects accordingly to their depths. The inspection of a calibrated glass fiber reinforced polymer proves the ability of EBEAE and SVM in defect classification with an average balanced accuracy of 96.18% in testing. This methodology clearly improves the current state of the art, even without the need for inspections with different source excitations. Furthermore, the estimated end-members automatically model the thermal response of the surface, providing crucial feedback for experimental optimization. • Surface thermograms from long-pulse IR thermography unmixed to classify buried defects. • High accuracy and sensitivity even with a small dataset, without multiple source excitations. • Results independence of the in-plane shapes of the defects, thanks to pixel-scale processing. • Interpretability of end-members as crucial feedback for experimental optimization. [ABSTRACT FROM AUTHOR]

Seagrass beds comprise a unique marine ecosystem that acts as a biofilter in marine environments and serves as a spawning ground and nursery for various species of fish. Long-term monitoring of seagrass beds is critical to understanding the dynamic relationships between the ecosystems and the stresses from natural systems and society. This study investigated temporal changes of seagrass beds in Cam Ranh Bay (CRB), Vietnam using multi-temporal Landsat data from 1996 to 2015. The data were processed through 5 main steps including: (1) image preprocessing to convert Landsat data to the top of atmosphere reflectance (TOA) and to correct atmospheric effects, (2) water column correction to eliminate effects on remotely sensed data of aquatic environments, (3) image classification using a linear mixed model, (4) accuracy assessment using the ground reference data, and (5) change detection of seagrass beds. The classification results compared with the ground reference data indicated that the overall accuracies and Kappa coefficients were higher than 91.7% and 0.8, respectively, in all cases. From 1996 to 2015, the total area of seagrass beds had declined by approximately 25% (66 ha), mainly attributed to coastal development and infrastructure construction. [ABSTRACT FROM AUTHOR]

Many papers in the hyperspectral literature use simulations (based on a linear mixture model) to test algorithms, which either estimate the “intrinsic” dimensionality (ID) of the data or endmembers. Usually, these simulations use “real-world” endmembers, proportions distributed according to a uniform or Dirichlet distribution on the endmember simplex, and Gaussian errors which are “spectrally” and “spatially” uncorrelated. When the error standard deviations (SDs) in different bands are assumed to be unequal, they are usually estimated using Roger's method. The simulated and real-world data in these papers are so different that one cannot be confident that the various advocated methods work well with real-world data. We propose a general methodology which produces more realistic simulations, providing us with greater insights into the strengths and weaknesses of various advocated methods. With the aid of the well-known Indian Pines and Cuprite scenes, we compare several specific options within the proposed methodological framework. We also compare the performance of five well-known ID estimators using both real and simulated datasets and demonstrate that Roger's SD estimates are positively biased. A proof that Roger's estimates are always positively biased is given. [ABSTRACT FROM PUBLISHER]

Researchers in remote sensing have attempted to increase the accuracy of land cover information extracted from remotely sensed imagery. Factors that influence the supervised and unsupervised classification accuracy are the presence of atmospheric effect and mixed pixel information. A linear mixture simulated model experiment is generated to simulate real world data with known end member spectral sets and class cover proportions (CCP). The CCP were initially generated by a random number generator and normalized to make the sum of the class proportions equal to 1.0 using MATLAB program. Random noise was intentionally added to pixel values using different combinations of noise levels to simulate a real world data set. The atmospheric scattering error is computed for each pixel value for three generated images with SPOT data. Accuracy can either be classified or misclassified. Results portrayed great improvement in classified accuracy, for example, in image 1, misclassified pixels due to atmospheric noise is 41 %. Subsequent to the degradation of atmospheric effect, the misclassified pixels were reduced to 4 %. We can conclude that accuracy of classification can be improved by degradation of atmospheric noise.

In this paper, we perform multi-sensor multi-resolution data fusion of Landsat-5 TM bands (at 30 m spatial resolution) and multispectral bands of World View-2 (WV-2 at 2 m spatial resolution) through linear spectral unmixing model. The advantages of fusing Landsat and WV-2 data are two fold: first, spatial resolution of the Landsat bands increases to WV-2 resolution. Second, integration of data from two sensors allows two additional SWIR bands from Landsat data to the fused product which have advantages such as improved atmospheric transparency and material identification, for example, urban features, construction materials, moisture contents of soil and vegetation, etc. In 150 separate experiments, WV-2 data were clustered in to 5, 10, 15, 20 and 25 spectral classes and data fusion were performed with 3x3, 5x5, 7x7, 9x9 and 11x11 kernel sizes for each Landsat band. The optimal fused bands were selected based on Pearson product-moment correlation coefficient, RMSE (root mean square error) and ERGAS index and were subsequently used for vegetation, urban area and dark objects (deep water, shadows) classification using Random Forest classifier for a test site near Golden Gate Bridge, San Francisco, California, USA. Accuracy assessment of the classified images through error matrix before and after fusion showed that the overall accuracy and Kappa for fused data classification (93.74%, 0.91) was much higher than Landsat data classification (72.71%, 0.70) and WV-2 data classification (74.99%, 0.71). This approach increased the spatial resolution of Landsat data to WV-2 spatial resolution while retaining the original Landsat spectral bands with significant improvement in classification. [ABSTRACT FROM AUTHOR]

Independent component analysis (ICA) has been recently applied into hyperspectral unmixing as a result of its low computation time and its ability to perform without prior information. However, when applying ICA for hyperspectral unmixing, the independence assumption in the ICA model conflicts with the abundance sum-to-one constraint and the abundance nonnegative constraint in the linear mixture model, which affects the hyperspectral unmixing accuracy. In this paper, we consider an abundance matrix composed of Np-dimensional variables, and we propose a new hyperspectral unmixing approach with an abundance characteristic-based ICA model. Two characteristics of the abundance variables are explored, and the model is constructed by these characteristics. A corresponding gradient descent algorithm is also proposed to solve the proposed objective function. Both the synthetic and real experimental results demonstrate that the proposed method performs better than the other state-of-the-art methods in abundance and endmember extraction. [ABSTRACT FROM PUBLISHER]

The recently developed theory of compressive sensing (CS) exhibits enormous potentials in signal recovery. In this paper, we investigate its application on spectral unmixing, which appears in hyperspectral data analysis and is usually based on a linear mixture model (LMM) that assumes that a mixed pixel is a linear combination of a set of pure spectral signatures (called endmembers) weighted by their corresponding abundances. Unlike the classical LMM that is a compact representation, we first extend it to a sparse representation (SR) by using a redundant and known endmember set instead of the complete one. Then, the SR model is multiplied by a random Gaussian measurement matrix, so spectral unmixing is casted in the framework of CS. Finally, the ℓ1-minimization algorithms are used to recover the nonnegative abundances by solving the SR model and our proposed model named CS+SR, respectively. Experimental results on both simulated and real hyperspectral data demonstrate that the CS+SR model, formed by multiplying a random Gaussian matrix on the SR model, can improve, at least in the sense of probability, the ability of the ℓ1-minimization algorithms for recovering the nonnegative sparse abundances. [ABSTRACT FROM PUBLISHER]

Sparsity-based unmixing algorithms, exploiting the sparseness property of the abundances, have recently been proposed with promising performances. However, these algorithms are developed for the linear mixture model (LMM), which cannot effectively handle the nonlinear effects. In this paper, we extend the current sparse regression methods for the LMM to bilinear mixture models (BMMs), where the BMMs introduce additional bilinear terms in the LMM in order to model second-order photon scattering effects. To solve the abundance estimation problem for the BMMs, we propose to perform a sparsity-based abundance estimation by using two dictionaries: a linear dictionary containing all the pure endmembers and a bilinear dictionary consisting of all the possible second-order endmember interaction components. Then, the abundance values can be estimated from the sparse codes associated with the linear dictionary. Moreover, to exploit the spatial data structure where the adjacent pixels are usually homogeneous and are often mixtures of the same materials, we first employ the joint-sparsity (row-sparsity) model to enforce structured sparsity on the abundance coefficients. However, the joint-sparsity model is often a strict assumption, which might cause some aliasing artifacts for the pixels that lie on the boundaries of different materials. To deal with this problem, the low-rank-representation model, which seeks the lowest rank representation of the data, is further introduced to better capture the spatial data structure. Our simulation results demonstrate that the proposed algorithms provide much enhanced performance compared with state-of-the-art algorithms. [ABSTRACT FROM PUBLISHER]

In the field of endmember extraction, most methods involve calculating the volume of simplex in high-dimensional space. Two different simplex volume formulas are used in these methods. One requires dimensionality reduction (DR); therefore, it may result in loss of the information of targets classes with a low priori probability, such as that used in N-FINDR. The other one, which is based on Gram determinant, avoids DR but is time consuming. In this letter, we explain a recursion rule of the calculation for the second simplex volume. Based on that rule, this letter presents a fast endmember extraction algorithm named as Fast Gram Determinant based Algorithm (FGDA). The theoretical analysis and experiments on both simulated and real hyperspectral data demonstrate that, compared to other volume-based methods, FGDA can greatly reduce the computational complexity of endmember extraction. [ABSTRACT FROM PUBLISHER]

Abstract: Variable Endmember Constrained Least Square (VECLS) technique is proposed to account endmember variability in the linear mixture model by incorporating the variance for each class, the signals of which varies from pixel to pixel due to change in urban land cover (LC) structures. VECLS is first tested with a computer simulated three class endmember considering four bands having small, medium and large variability with three different spatial resolutions. The technique is next validated with real datasets of IKONOS, Landsat ETM+ and MODIS. The results show that correlation between actual and estimated proportion is higher by an average of 0.25 for the artificial datasets compared to a situation where variability is not considered. With IKONOS, Landsat ETM+ and MODIS data, the average correlation increased by 0.15 for 2 and 3 classes and by 0.19 for 4 classes, when compared to single endmember per class. [Copyright &y& Elsevier]

We propose and analyze a new model for hyperspectral images (HSIs) based on the assumption that the whole signal is composed of a linear combination of few sources, each of which has a specific spectral signature, and that the spatial abundance maps of these sources are themselves piecewise smooth and therefore efficiently encoded via typical sparse models. We derive new sampling schemes exploiting this assumption and give theoretical lower bounds on the number of measurements required to reconstruct HSI data and recover their source model parameters. This allows us to segment HSIs into their source abundance maps directly from compressed measurements. We also propose efficient optimization algorithms and perform extensive experimentation on synthetic and real datasets, which reveals that our approach can be used to encode HSI with far less measurements and computational effort than traditional compressive sensing methods. [ABSTRACT FROM AUTHOR]

Non-negative matrix factorization (NMF) has been introduced into the field of hyperspectral unmixing in the last ten years. To relieve the non-convex problem of NMF, different constraints are imposed on NMF. In this paper, a new constraint, termed the endmember dissimilarity constraint (EDC), is proposed. The proposed constraint can measure the difference between the signatures as well as constrain the signatures to be smooth. A set of smooth spectra contained in the dataset space with the largest differences can be obtained, as far as is possible, which can be seen as endmembers. The experimental performances of our method and other state-of-the-art constrained NMF algorithms were obtained and analyzed, proving that the proposed method outperforms other NMF unmixing methods. [ABSTRACT FROM PUBLISHER]

Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process and under- or overestimation of this number may lead to incorrect unmixing in unsupervised methods. In this paper, we discuss a new method for determining the intrinsic dimension using recent advances in random matrix theory. This method is entirely unsupervised, free from any user-determined parameters and allows spectrally correlated noise in the data. Robustness tests are run on synthetic data, to determine how the results were affected by noise levels, noise variability, noise approximation, and spectral characteristics of the endmembers. Success rates are determined for many different synthetic images, and the method is tested on two pairs of real images, namely a Cuprite scene taken from Airborne Visible InfraRed Imaging Spectrometer (AVIRIS) and SpecTIR sensors, and a Lunar Lakes scene taken from AVIRIS and Hyperion, with good results. [ABSTRACT FROM PUBLISHER]

In the linear unmixing of hyperspectral images, the observation pixels form a simplex whose vertices correspond to the endmembers, hence finding the endmembers is equivalent to extracting these vertices. A common technique for determining vertices is to analyze the simplex volume, but it usually has a high computational complexity, resulting from the exhaustive searching of volume in the large hyperspectral data. This problem limits the practicability and real-time application. In this paper, we utilize triangular factorization (TF) to calculate the volume, deducing a method named simplex volume analysis based on TF (SVATF). It requires just one comparison through the data to succeed in finding the global optimal solution for all the endmembers, thus improving the searching efficiency. Dimensionality reduction transformation is not necessary, which is another advantage of this method. Moreover, since TF is a broad conception including different methods, SVATF is a framework including various implementations. Based on TF, we also propose a fast learning algorithm named abundance quantification based on TF to estimate the abundances, which further saves the computation by utilizing the intermediate values involved in SVATF. The abundance estimation method can rectify possible errors in the given endmembers by utilizing two important constraints (abundance nonnegative constraint and abundance sum-to-one constraint) of the linear mixture model, so it is useful for the imagery without pure pixels. Experimental results on synthetic and real hyperspectral data demonstrate that the proposed methods can obtain accurate results with much lower computational complexity, with respect to other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Abstract: This study proposes a new approach to change detection in remote sensing multi-temporal image data. Rather than allocating pixels to one of two disjoint classes (change, no-change) which is the approach most commonly found in the literature, we propose in this study to define change in terms of degrees of membership to the class change. The methodology aims to model images depicting the natural environment more realistically, taking into account that changes tend to occur in a continuum rather than being sharply distinguished. To this end, a sub-pixel approach is implemented to help detect degrees of change in every pixel. Three experiments employing the proposed approach using synthetic and real image data are reported and their results discussed. [Copyright &y& Elsevier]

Abstract: Information on rice growing areas is important for policymakers to devise agricultural plans. This research explores the monitoring of rice cropping intensity in the upper Mekong Delta, Vietnam (from 2001 to 2007) using time-series MODIS NDVI 250-m data. Data processing includes three steps: (1) noise is filtered from the time-series NDVI data using empirical mode decomposition (EMD); (2) endmembers are extracted from the filtered time-series data and trained in a linear mixture model (LMM) for classification of rice cropping systems; and (3) classification results are verified by comparing them with the ground-truth and statistical data. The results indicate that EMD is a good filter for noise removal from the time-series data. The classification results confirm the validity of LMM, giving an overall accuracy of 90.1% and a Kappa coefficient of 0.7. The lowest producer and user accuracies were associated with single crop rain-fed rice class due to the mixed pixel problems. A strong yearly correlation at the district level was revealed in the MODIS-derived areas (R 2 ⩾0.9). Investigation of interannual changes in rice cropping intensity from 2001 to 2007 showed a remarkable conversion from double to triple crop irrigated rice from 2001 to 2003, especially in the Thoai Son and Phu Tan districts. A big conversion from triple crop rice back to double crop rice cultivation was also observed in Phu Tan from 2005 to 2006. These changes were verified by visual interpretation of Landsat images and examination of NDVI profiles. [Copyright &y& Elsevier]

Changes in the spatial distributions of vegetation across the globe are routinely monitored by satellite remote sensing, in which the reflectance spectra over land surface areas are measured with spatial and temporal resolutions that depend on the satellite instrumentation. The use of multiple synchronized satellite sensors permits long-term monitoring with high spatial and temporal resolutions. However, differences in the spatial resolution of images collected by different sensors can introduce systematic biases, called scaling effects, into the biophysical retrievals. This study investigates the mechanism by which the scaling effects distort normalized difference vegetation index (NDVI). This study focused on the monotonicity of the area-averaged NDVI as a function of the spatial resolution. A monotonic relationship was proved analytically by using the resolution transform model proposed in this study in combination with a two-endmember linear mixture model. The monotonicity allowed the inherent uncertainties introduced by the scaling effects (error bounds) to be explicitly determined by averaging the retrievals at the extrema of the resolutions. Error bounds could not be estimated, on the other hand, for non-monotonic relationships. Numerical simulations were conducted to demonstrate the monotonicity of the averaged NDVI along spatial resolution. This study provides a theoretical basis for the scaling effects and develops techniques for rectifying the scaling effects in biophysical retrievals to facilitate cross-sensor calibration for the long-term monitoring of vegetation dynamics. [ABSTRACT FROM AUTHOR]

The fraction of vegetation cover (FVC) is often estimated by unmixing a linear mixture model (LMM) to assess the horizontal spread of vegetation within a pixel based on a remotely sensed reflectance spectrum. The LMM-based algorithm produces results that can vary to a certain degree, depending on the model assumptions. For example, the robustness of the results depends on the presence of errors in the measured reflectance spectra. The objective of this study was to derive a factor that could be used to assess the robustness of LMM-based algorithms under a two-endmember assumption. The factor was derived from the analytical relationship between FVC values determined according to several previously described algorithms. The factor depended on the target spectra, endmember spectra, and choice of the spectral vegetation index. Numerical simulations were conducted to demonstrate the dependence and usefulness of the technique in terms of robustness against the measurement noise. [ABSTRACT FROM AUTHOR]

Remotely sensed reflectance spectra may be biased by several intervening factors, and the biases are propagated into estimations of the fraction of vegetation cover (FVC) by algorithms based on a linear mixture model (LMM). The errors propagated in FVCs depend on the retrieval algorithm used, due to differences in the assumptions of the model as well as constraints employed in the algorithm. These differences should be fully understood prior to algorithm selection for practical applications. Although numerous studies have investigated the relationships between errors propagated by different algorithms, these relationships have not been fully understood from a deterministic perspective. This study introduces a technique for deriving the analytical underpinnings of error propagation in FVC based on several LMM-based algorithms. The derivation assumes that measurement noise is band-correlated additive noise. The bias errors propagated in FVC depended on the endmember spectra assumed in the algorithm, the target spectrum, and the coefficients of the spectral vegetation index, which were employed as constraints, as well as magnitude of the input error. It was found that the relationships among the propagated errors assume asymmetric elliptical forms with coefficients that are determined by the input variables. These results suggest that the relationships depend heavily on the choice of endmember spectra as well as the spectrum of the target pixel and the vegetation index employed as a constraint. The present findings should assist in the selection of an optimum algorithm based on prior knowledge of the target field. [ABSTRACT FROM AUTHOR]

In land change science studies, a cover type is defined by land surface attributes, specifically including the types of vegetation, topography and human structures, which makes it difficult to characterize land cover as discrete classes. One of the challenges in characterizing a land-cover type is to distinguish variability within the class from actual land-cover transformation. The spread of plant invasions in tropical systems is affected by seasonal variations and disturbances such as agricultural activities and fires, making it difficult to determine the spread through thematic classifications. In this paper, we estimate the changes in spatial extent and seasonal variation of bracken fern invasion in Southern Yucatán from 1989 to 2005 by using a linear mixture model (LMM), a widely used method in the classification of remotely sensed data. The results show an increase in areas affected by bracken from 40 km2 in 1989 to almost 80 km2 in 2000. Lower estimates of the invasion resulted from data acquired at the end of the dry season (March–May), when bracken mixes with secondary vegetation or is removed by fires. The accuracy of the maps is estimated through the use of sketch maps of farmer's parcels and field data collected from 2000 to 2001. Understanding the spatial distribution and annual variability of bracken fern cover in the region is critical to determining the relation between disturbances such as fire and forest recovery. Using LMM may enhance this understanding by giving a more accurate picture of the extent and distribution of bracken fern invasion. Abstract in Spanish is available at [ABSTRACT FROM AUTHOR]

Abstract: Global time series of low resolution images are available with high repeat frequency and at low cost, but their analysis is hampered by the presence of mixed pixels and the difficulty in locating detailed spatial features. This study examined the potential of sub-pixel classification for regional crop area estimation using time series of monthly NDVI-composites of the 1km resolution sensor SPOT-VEGETATION. Belgium was selected as test zone, because of the availability of ample reference data in the form of a vectorial GIS with the boundaries and cover type of the large majority of agricultural fields. Two different methods were investigated: the linear mixture model and neural networks. Both result in area fraction images (AFIs), which contain for each 1km pixel the estimated area proportions occupied by the different cover types (crops or other land use). Both algorithms were trained with part of the reference data and validated with the remainder. Validation was repeated at three different levels: the 1km pixel, the municipality and the agro-statistical district. In general, the neural network outperformed the linear mixture model. For the major classes (winter wheat, maize, forest) the obtained acreage estimates showed good agreement with the true values, especially when aggregated to the level of the municipality (R 2 ≈85%) or district (R 2 ≈95%). The method seems attractive for wide-scale, regional area estimation in data-poor countries. [Copyright &y& Elsevier]

Abstract: Tethered balloon remote sensing platforms can be used to study radiometric issues in terrestrial ecosystems by effectively bridging the spatial gap between measurements made on the ground and those acquired via airplane or satellite. In this study, the Short Wave Aerostat-Mounted Imager (SWAMI) tethered balloon-mounted platform was utilized to evaluate linear and nonlinear spectral mixture analysis (SMA) for a grassland-conifer forest ecotone during the summer of 2003. Hyperspectral measurement of a 74-m diameter ground instantaneous field of view (GIFOV) attained by the SWAMI was studied. Hyperspectral spectra of four common endmembers, bare soil, grass, tree, and shadow, were collected in situ, and images captured via video camera were interpreted into accurate areal ground cover fractions for evaluating the mixture models. The comparison between the SWAMI spectrum and the spectrum derived by combining in situ spectral data with video-derived areal fractions indicated that nonlinear effects occurred in the near infrared (NIR) region, while nonlinear influences were minimal in the visible region. The evaluation of hyperspectral and multispectral mixture models indicated that nonlinear mixture model-derived areal fractions were sensitive to the model input data, while the linear mixture model performed more stably. Areal fractions of bare soil were overestimated in all models due to the increased radiance of bare soil resulting from side scattering of NIR radiation by adjacent grass and trees. Unmixing errors occurred mainly due to multiple scattering as well as close endmember spectral correlation. In addition, though an apparent endmember assemblage could be derived using linear approaches to yield low residual error, the tree and shade endmember fractions calculated using this technique were erroneous and therefore separate treatment of endmembers subject to high amounts of multiple scattering (i.e. shadows and trees) must be done with caution. Including the short wave infrared (SWIR) region in the hyperspectral and multispectral endmember data significantly reduced the Pearson correlation coefficient values among endmember spectra. Therefore, combination of visible, NIR, and SWIR information is likely to further improve the utility of SMA in understanding ecosystem structure and function and may help narrow uncertainties when utilizing remotely sensed data to extrapolate trace glas flux measurements from the canopy scale to the landscape scale. [Copyright &y& Elsevier]

A mixture experiment involves combining two or more components in various proportions and collecting data on one or more responses. A linear mixture model may adequately represent the relationship between a response and mixture component proportions and be useful in screening the mixture components. The Scheffé and Cox parameterizations of the linear mixture model are commonly used for analyzing mixture experiment data. With the Scheffé parameterization, the fitted coefficient for a component is the predicted response at that pure component (i.e. single-component mixture). With the Cox parameterization, the fitted coefficient for a mixture component is the predicted difference in response at that pure component and at a pre-specified reference composition. This article presents a new component-slope parameterization, in which the fitted coefficient for a mixture component is the predicted slope of the linear response surface along the direction determined by that pure component and at a pre-specified reference composition. The component-slope, Scheffé, and Cox parameterizations of the linear mixture model are compared and their advantages and disadvantages are discussed. [ABSTRACT FROM AUTHOR]

Abstract: The implementations of both the supervised and unsupervised fuzzy c-means classification algorithms require a priori selection of the fuzzy exponent parameter. This parameter is a weighting exponent and it determines the degree of fuzziness of the membership grades. The determination of an optimal value for this parameter in a fuzzy classification process is problematic and remains an open problem. This paper presents a new and efficient procedure for determining a local optimal value for the fuzzy exponent in the implementation of fuzzy classification technique. Numerical results using simulated image and real data sets are used to illustrate the simplicity and effectiveness of the proposed method. [Copyright &y& Elsevier]

Intensive and mixed land cover areas, the complexity of vegetation stand structure, abundant vegetation species, and the smooth transition between different vegetation covers are critical problems facing the classification process of satellite images when using traditional approaches such as the maximum likelihood classifier. Most of the time, classification distinguishes only between cultivated/non-cultivated. It has been difficult to accurately distinguish the different types of vegetation covers in areas that are within one pixel of satellite images. In this study, a linear mixture model (LMM) approach is applied to classify land covers in the eastern Nile delta of Egypt. Four endmembers (desert land, urban, cultivated land, water bodies) were identified based on the image itself and a constrained least-square solution was used to unmix the image. Same method was applied on other three endmembers representing the main vegetation covers in the study area. Relationship between fraction images and NDVI was determined and the fraction images were compared with ground truth data for validation. This study indicates that the LMM is a promising approach for distinguishing the different land cover types and to classify the different vegetation types using Landsat ETM+ data. [ABSTRACT FROM AUTHOR]

Many research projects require accurate delineation of different secondary succession (SS) stages over large regions/subregions of the Amazon basin. However, the complexity of vegetation stand structure, abundant vegetation species, and the smooth transition between different SS stages make vegetation classification difficult when using traditional approaches such as the maximum likelihood classifier (MLC). Most of the time, classification distinguishes only between forest/non-forest. It has been difficult to accurately distinguish stages of SS. In this paper, a linear mixture model (LMM) approach is applied to classify successional and mature forests using Thematic Mapper (TM) imagery in the Rondoˆnia region of the Brazilian Amazon. Three endmembers (i.e., shade, soil, and green vegetation or GV) were identified based on the image itself and a constrained least-squares solution was used to unmix the image. This study indicates that the LMM approach is a promising method for distinguishing successional and mature forests in the Amazon basin using TM data. It improved vegetation classification accuracy over that of the MLC. Initial, intermediate, and advanced successional and mature forests were classified with overall accuracy of 78.2% using a threshold method on the ratio of shade to GV fractions, a 7.4% increase over the MLC. The GV and shade fractions are sensitive to the change of vegetation stand structures and better capture biophysical structure information. [Copyright &y& Elsevier]

Not only does lagoon ecology represent a transitional zone between the sea and the continent but it also expresses the equilibrium belt between erosion and sedimentation processes. Within the framework of a coastal management scheme, a precise and timely mapping of morphological changes in this environment is important. This paper illustrates the possible contribution of multi-temporal satellite observations in the monitoring of the erosion/sedimentation processes of coastal zones, where landscape features are subjected to highly morphodynamical modifications. In particular, an improved mapping accuracy was obtained by the successive application of the Maximum Likelihood (MLH) classifier and the Linear Mixture Model (LMM) techniques to the satellite image classification procedure. In fact, by estimating the amount of shallow water and wetland within each satellite pixel, the LMM technique allows for an accurate mapping of the transitional zones in the lagoon environment, thus permitting an optimal separation between land and water. The study concerns the Venice lagoon (Italy) which has been sinking slowly since the beginning of this century. This has led to widespread loss of wetlands. In order to monitor the development of the land cover, four Landsat Thematic Mapper scenes were examined, during the period 1984 to 1993. The results obtained proved that the digital analysis method of multitemporal satellite imagery, applied over a selected test area, enables the evolution of an estuarine environment landscape, with its different sequences of erosion and periods of accretion, to be monitored. The significant influence of tidal stages is discussed in the data analysis. [ABSTRACT FROM AUTHOR]

Shadowing and illumination variations, caused by scene topography or non‐uniform lighting, are present in virtually all image data. Given its prevalence and nuisance value when making quantitative image measurements, the development of accurate shading compensation techniques is essential. The linear mixture model of image formation is broadly employed when dealing with hyperspectral data but makes no explicit provision for shading and this can lead to inaccurate analysis results. In this reported work, the effect of shading on a hyperspectral image is demonstrated, and new methods for mitigating the effect using a forced‐zero endmember and conical sub‐simplex projection are presented. It is shown that together they provide the most accurate and theoretically sound shadow‐corrected data. [ABSTRACT FROM AUTHOR]

Many methods have been proposed in the literature for estimating the number of materials/endmembers in a hyperspectral image. This is sometimes called the "intrinsic" dimension (ID) of the image. A number of recent papers have proposed ID estimation methods based on various aspects of random matrix theory (RMT), under the assumption that the errors are uncorrelated, but with possibly unequal variances. A recent paper, which reviewed a number of the better known methods (including one RMT-based method), has shown that they are all biased, especially when the true ID is greater than about 20 or 30, even when the error structure is known. I introduce two RMT-based estimators ( R M T G , which is new, and R M T K N , which is a modification of an existing estimator), which are approximately unbiased when the error variances are known. However, they are biased when the error variance is unknown and needs to be estimated. This bias increases as ID increases. I show how this bias can be reduced. The results use semi-realistic simulations based on three real hyperspectral scenes. Despite this, when applied to the real scenes, R M T G and R M T K N are larger than expected. Possible reasons for this are discussed, including the presence of errors which are either deterministic, spectrally and/or spatially correlated, or signal-dependent. Possible future research into ID estimation in the presence of such errors is outlined. [ABSTRACT FROM AUTHOR]