Iterative method to decompose hyperspectral mixed pixel using barycentric coordinate

Efficient denoising of hyperspectral imagery (HSI) relies on an representational model that is capable of capturing the spatial and spectral correlation in HSI. Recently, an intrinsic representation (IR) approach based on the linear spectral mixture model (LSMM) was proposed for unsupervised feature extraction. The IR model constitutes a sound representational model due to its ability to account for the physical data generation process of HSI, the spatial correlation effect, and the noise variance heterogeneity effect. In this paper, we explore the potential of IR for the denoising of HSI. A noisy pixel in HSI is expressed as a nonnegative linear combination of several endmembers, plus some Gaussian noise with heterogeneous noise variances. In order to perform denoising, the IR approach is used to adaptively estimate both the endmembers and the nonnegative coefficients (i.e., the abundances), which are finally used to reconstruct the clean image. The experiments on both simulated and real hyperspectral images demonstrate that the IR approach not only can resist the influence of noise, but also can preserve the image details.

This article proposes a symmetric sparse representation (SSR) method to extract pure endmembers from hyperspectral imagery (HSI). The SSR combines the features of the linear unmixing model and the sparse subspace clustering model of endmembers, and it assumes that the desired endmembers and all the HSI pixel points can be sparsely represented by each other. It formulates the endmember extraction problem into a famous program of archetypal analysis, and accordingly, extracting pure endmembers can be transformed as finding the archetypes in the minimal convex hull containing all the HSI pixel points. The vector quantization scheme is adopted to help in carefully choosing the initial pure endmembers, and the archetypal analysis program is solved using the simple projected gradient algorithm. Seven state-of-the-art methods are implemented to make comparisons with the SSR on both synthetic and real hyperspectral images. Experimental results show that the SSR outperforms all the seven methods in spectral angle distance and root-mean-square error, and it can be a good alternative choice for extracting pure endmembers from HSI data.

Independent component analysis (ICA) has shown much success in blind source separation and channel equalization. Its applications to remotely sensed images are investigated in recent years. Linear spectral mixture analysis (LSMA) has been widely used for subpixel detection and mixed pixel classification in remote sensing image processing and already studied in Chapters 3, 8–10, . It models the spectral signature of an image pixel vector as a linear mixture of spectral signatures of targets present in the image data and the target abundance fractions are assumed to be unknown, but nonrandom constants. This chapter combines these two approaches to one, called ICA-based linear spectral random mixture analysis (LSRMA), which describes an image pixel vector as a random process resulting from a random composition of multiple spectral signatures of distinct targets in the image data. It differs from LSMA in that the abundance fractions of the target signatures in LSRMA are considered to be unknown random independent signal sources. Two major advantages can be benefited from LSRMA. First, LSRMA does not require any prior knowledge of the targets used in the linear mixture model. Second and most importantly, LSRMA models each of target signatures as an independent random signal source so that the spectral variability of target signatures can be captured more effectively in a stochastic manner. The only required knowledge for LSRMA is the number of signal sources, p assumed to be present in the image data. This number is estimated by Neyman-Pearson detection theory-based eigen-thresholding methods to be investigated in Chapter 17.

ABSTRACTAn experimental linear mixture modelling using ground spectroradiometric measurements in the Kola Peninsula, Russia has been carried out to create a basis for mapping vegetation and non-vegetation components in the tundra-taiga ecotone using satellite imagery. We concentrated on the ground level experiment with the goal to use it further for the classification of multispectral satellite imagery through spectral unmixing. This experiment was performed on the most detailed level of remote sensing research which is free from atmospheric effects and easy to understand. We have measured typical ecotone components, including Cetraria nivalis, Betula tortuosa, Empetrum nigrum, Betula nana, Picea abies and rocks (nepheline syenite). The result of the experiment shows that the spectral mixture is indeed formed linearly but different components have different influence. Typical spectral thresholds for each component were found which are significant for vegetation mapping. Spectral unmixing of ground level data was performed and accuracy was estimated. The results add new information on typical spectral thresholds which can potentially be applied for multispectral satellite imagery when upscaling from high resolution to coarser resolution.

Spectral unmixing is an important task in remotely sensed hyperspectral data exploitation. The linear mixture model has been widely used to unmix hyperspectral images by identifying a set of pure spectral signatures, called endmembers, and estimating their respective abundances in each pixel of the scene. Several algorithms have been proposed in the recent literature to automatically identify endmembers, even if the original hyperspectral scene does not contain any pure signatures. A popular strategy for endmember identification in highly mixed hyperspectral scenes has been the minimum volume simplex analysis (MVSA), known to be a computationally very expensive algorithm. This algorithm calculates the minimum volume enclosing simplex, as opposed to other algorithms that perform maximum simplex volume analysis (MSVA). The high computational complexity of MVSA, together with its very high memory requirements, has limited its adoption in the hyperspectral imaging community. In this paper, we develop several optimizations to the MVSA algorithm. The main computational task of MVSA is the solution of a quadratic optimization problem with equality and inequality constraints, with the inequality constraints being in the order of the number of pixels multiplied by the number of endmembers. As a result, storing and computing the inequality constraint matrix is highly inefficient. The first optimization presented in this paper uses algebra operations in order to reduce the memory requirements of the algorithm. In the second optimization, we use graphics processing units (GPUs) to effectively solve (in parallel) the quadratic optimization problem involved in the computation of MVSA. In the third optimization, we extend the single GPU implementation to a multi-GPU one, developing a hybrid strategy that distributes the computation while taking advantage of GPU accelerators at each node. The presented optimizations are tested in different analysis scenarios (using both synthetic and real hyperspectral data) and shown to provide state-of-the-art results from the viewpoint of unmixing accuracy and computational performance. The speedup achieved using the full GPU cluster compared to the CPU implementation in tenfold in a real hyperspectral image.

Many spectral unmixing approaches ranging from geometry, algebra to statistics have been proposed, in which nonnegative matrix factorization (NMF)-based ones form an important family. The original NMF-based unmixing algorithm loses the spectral and spatial information between mixed pixels when stacking the spectral responses of the pixels into an observed matrix. Therefore, various constrained NMF methods are developed to impose spectral structure, spatial structure, and spectral-spatial joint structure into NMF to enforce the estimated endmembers and abundances preserve these structures. Compared with matrix format, the third-order tensor is more natural to represent a hyperspectral data cube as a whole, by which the intrinsic structure of hyperspectral imagery can be losslessly retained. Extended from NMF-based methods, a matrix-vector nonnegative tensor factorization (NTF) model is proposed in this paper for spectral unmixing. Different from widely used tensor factorization models, such as canonical polyadic decomposition CPD) and Tucker decomposition, the proposed method is derived from block term decomposition, which is a combination of CPD and Tucker decomposition. This leads to a more flexible frame to model various application-dependent problems. The matrix-vector NTF decomposes a third-order tensor into the sum of several component tensors, with each component tensor being the outer product of a vector (endmember) and a matrix (corresponding abundances). From a formal perspective, this tensor decomposition is consistent with linear spectral mixture model. From an informative perspective, the structures within spatial domain, within spectral domain, and cross spectral-spatial domain are retreated interdependently. Experiments demonstrate that the proposed method has outperformed several state-of-the-art NMF-based unmixing methods.

Hyperspectral imaging is concerned with the measurement, analysis, and interpretation of spectra acquired from a given scene (or specific object) at a short, medium or long distance by an airbone or satellite sensor. Over the last few years, hyperspectral image data sets have been collected for a great amount of locations over the world, using a variety of instruments for Earth observation. Despite the increasing importance of hyperspectral images in remote sensing applications, there is no common repository of hyperspectral data intended to distribute and share hyperspectral data sets in the community. Quite opposite, the hyperspectral data sets which are available for public use are spread among different storage locations and present significant heterogeneity regarding the storage format, associated meta-data (if any), or ground-truth availability. As a result, the development of a standardized hyperspectral data repository is a highly desired goal in the remote sensing community. In this paper, we take a necessary first step towards the development of a digital repository for remotely sensed hyperspectral data. The proposed system allows uploading new hyperspectral data sets along with meta-data, ground-truth and analysis results, with the ultimate goal of sharing publicly available hyperspectral images within the remote sensing community. The database has been designed in order to allow storing relevant information for the hyperspectral data available through the system, including basic image characteristics (width, height, number of bands, format) and more advanced meta-data (ground-truth information, publications in which the data has been used). The current implementation consists of a front-end to ease the management of images through a web interface, thus containing both synthetic and real hyperspectral images from two highly representative instruments, such as NASAs Airborne Visible Infra-Red Imaging Spectrometer (AVIRIS) over the Cuprite Mining District in Nevada. Most importantly, the developed system includes a spectral unmixing-based content based image retrieval (CBIR) functionality which allows searching for images on the spectral unmixing information (spectrally pure components or endmembers and their associated abundances in the scene). This information is stored as meta-data associated to each hyperspectral image instance, and then used to search and retrieve images based on information content. This paper presents the design of the system and a preliminary validation of the unmixing-based retrieval functionality using both synthetic and real hyperspectral images stored in the database.

Linear spectral mixture analysis (LSMA) is a widely used technique in remote sensing to estimate abundance fractions of materials present in an image pixel. In order for an LSMA-based estimator to produce accurate amounts of material abundance, it generally requires two constraints imposed on the linear mixture model used in LSMA, which are the abundance sum-to-one constraint and the abundance nonnegativity constraint. The first constraint requires the sum of the abundance fractions of materials present in an image pixel to be one and the second imposes a constraint that these abundance fractions be nonnegative. While the first constraint is easy to deal with, the second constraint is difficult to implement since it results in a set of inequalities and can only be solved by numerical methods. Consequently, most LSMA-based methods are unconstrained and produce solutions that do not necessarily reflect the true abundance fractions of materials. In this case, they can only be used for the purposes of material detection, discrimination, and classification, but not for material quantification. The authors present a fully constrained least squares (FCLS) linear spectral mixture analysis method for material quantification. Since no closed form can be derived for this method, an efficient algorithm is developed to yield optimal solutions. In order to further apply the designed algorithm to unknown image scenes, an unsupervised least squares error (LSE)-based method is also proposed to extend the FCLS method in an unsupervised manner.

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Endmember extraction plays an important role in spectral unmixing. Traditional endmember extraction algorithms, such as EEAs, only use spectral information to get the endmember, but ignore the spatial characteristic of the remote sensing image. Because of this, the algorithms are susceptible to the noise and anomaly image, which reduces the accuracy of endmember extraction. Focusing on this problem, a new EEA (OSP-LSC) combining subspace projection and local spatial information is proposed. Based on the theory of convex simplex, the algorithm sequentially extracts the endmembers by combining the subspace projection and simplex volume analysis. During the extracting process, the local spectral similarity constraint is used to improve the robustness to the noise and anomaly pixel, which also avoids to the huge computational cost caused by global spatial information. Furthermore, the simplex volume calculation is free of dimensionality which may cause the possible loss of original information, The experimental results on synthetic and real hyperspectral image show that the experimental results on synthetic and real hyperspectral image show that the proposed algorithm can improve the accuracy of the endmember extraction, and is more robust to the noise and anomaly pixels compared to the spectral based EEAs.

Independent Component Analysis (ICA) is a blind source separation method which is exploited for various applications in signal processing. In hyperspectral imagery, ICA is commonly employed for detection and segmentation purposes. But it is often thought to be unable to quantify abundances. In this paper, we propose an ICA-based method to estimate the anomaly abundances from the independent components. The first experiments on synthetic and real world hyperspectral images are very promising referring to the estimation accuracy and robustness.

Although accurate training and initialization information is difficult to acquire, unsupervised hyperspectral subpixel mapping (SPM) without relying on this predefined information is an insufficiently addressed research issue. This letter presents a novel Bayesian approach for unsupervised SPM of hyperspectral imagery (HSI) based on the Markov random field (MRF) and a band-weighted discrete spectral mixture model (BDSMM), with the following key characteristics. First, this is an unsupervised approach that allows adjustment of abundance and endmember information adaptively for less relying on algorithm initialization. Second, this approach consists of the BDSMM for accommodating the noise heterogeneity and the hidden label field of subpixels in HSI. The BDSMM also integrates SPM into the spectral mixture analysis and allows enhanced SPM by fully exploring the endmember-abundance patterns in HSI. Third, the MRF and BDSMM are integrated into a Bayesian framework to use both the spatial and spectral information efficiently, and an expectation-maximization (EM) approach is designed to solve the model by iteratively estimating the endmembers and the label field. Experiments on both simulated and real HSI demonstrate that the proposed algorithm can yield better performance than traditional methods.

Anomaly detection is one of the practical applications in hyperspectral imagery (HSI) over the last two decades. In this paper, we propose a combined similarity criterion anomaly detector (CSCAD) method for HSI anomaly detection. The proposed method approximates the background using the surrounding neighbor pixels. Then, the residual error is obtained by subtracting the approximated background from the original data. Similarity criterion between the central and the adjacent pixels is applied simultaneously to detect anomalies more precisely. Finally, the criterion number is calculated for each pair of the central-adjacent pixels in the dual window, and then anomalies are detected. The main contribution of the paper is removing the noise and outlier, employing an efficient method that conducts us to more accurate detection performance. Contamination of the noise and outlier is reduced by the residual error and similarity criterion values. So, applying the criterion numbers is an accurate method for removing the outliers and noise without any need to use an additive stage that was introduced in our previous work. We implement the proposed method on three real hyperspectral images. CSCAD outputs are depicted by receiver operating characteristic curves, area under curve values, and intuitive images. Comparing the results of the proposed method with eight popular and the state-of-the-art methods proves that the CSCAD is an accurate and effective method to detect anomalies.

Hyperspectral image provides a way to analyze component and the fraction by spectral unmixing. The classical method is Least Squares algorithm. But it is defined without any constraint on the abundance. The Fully constrained Least Squares (FCLS) algorithm allows resulted abundances satisfying sum-to-one and non-negative, which is practical. It has been widely used till now because it may work quickly with a small unmxing error. But when the number of endmembers is large, it gets much slow. And unmxing error is high if the endmembers are not found out completely. As for improving the speed of the algorithm, there have been many research works. But fewer algorithms are developed for increasing accurateness. Here in this paper, a primal-dual interior-point method is tested for the fully constraint unmixing with the linear unmixing model being modified slightly. A dual problem is established firstly, and then the process of the algorithm is designed to decrease distance between original problem and the dual problem based on result of FCLS. In order to promise high unmxing accurateness, the unmxing error of resulted abundances is added into the optimizing goal. Several algorithms of fully constraint abundance estimation are tested on both simulation and real hyperspectral images. The experimental results show that the prompted algorithm may find the optimal abundance for existing endmembers even though the endmember set is not complete. Accurateness of unmxing is increased, especially on the real image.

Hyperspectral images acquired by remote sensing systems are generally degraded by noise and can be sometimes more severely degraded by blur. When no knowledge is available about the degradations present on the original image, blind restoration methods can only be considered. By blind, we mean absolutely no knowledge neither of the blur point spread function (PSF) nor the original latent channel and the noise level. In this study, we address the blind restoration of the degraded channels component-wise, according to a sequential scheme. For each degraded channel, the sequential scheme estimates the blur point spread function (PSF) in a first stage and deconvolves the degraded channel in a second and final stage by means of using the PSF previously estimated. We propose a new component-wise blind method for estimating effectively and accurately the blur point spread function. This method follows recent approaches suggesting the detection, selection and use of sufficiently salient edges in the current processed channel for supporting the regularized blur PSF estimation. Several modifications are beneficially introduced in our work. A new selection of salient edges through thresholding adequately the cumulative distribution of their corresponding gradient magnitudes is introduced. Besides, quasi-automatic and spatially adaptive tuning of the involved regularization parameters is considered. To prove applicability and higher efficiency of the proposed method, we compare it against the method it originates from and four representative edge-sparsifying regularized methods of the literature already assessed in a previous work. Our attention is mainly paid to the objective analysis (via l1-norm) of the blur PSF error estimation accuracy. The tests are performed on a synthetic hyperspectral image. This synthetic hyperspectral image has been built from various samples from classified areas of a real-life hyperspectral image, in order to benefit from realistic spatial distribution of reference spectral signatures to recover after synthetic degradation. The synthetic hyperspectral image has been successively degraded with eight real blurs taken from the literature, each of a different support size. Conclusions, practical recommendations and perspectives are drawn from the results experimentally obtained.