Fast unsupervised technique for extraction of endmembers spectra from hyperspectral data

One of the most challenging task underlying many hyperspectral imagery applications is the linear unmixing. The key to linear unmixing is to find the set of reference substances, also called endmembers, that are representative of a given scene. This paper presents the vertex component analysis (VCA) a new method to unmix linear mixtures of hyperspectral sources. The algorithm is unsupervised and exploits a simple geometric fact: endmembers are vertices of a simplex. The algorithm complexity, measured in floating points operations, is O (n), where n is the sample size. The effectiveness of the proposed scheme is illustrated using simulated data.

Estimation of signal subspace on hyperspectral data

Dimensionality reduction plays a crucial role in many hyperspectral data processing and analysis algorithms. This paper proposes a new mean squared error based approach to determine the signal subspace in hyperspectral imagery. The method first estimates the signal and noise correlations matrices, then it selects the subset of eigenvalues that best represents the signal subspace in the least square sense. The effectiveness of the proposed method is illustrated using simulated and real hyperspectral images.

Unsupervised hyperspectral signal subspace identification

Hyperspectral imaging sensors provide image data containing both spectral and spatial information from the Earth surface. The huge data volumes produced by these sensors put stringent requirements on communications, storage, and processing. This paper presents a method, termed hyperspectral signal subspace identification by minimum error (HySime), that infer the signal subspace and determines its dimensionality without any prior knowledge. The identification of this subspace enables a correct dimensionality reduction yielding gains in algorithm performance and complexity and in data storage. HySime method is unsupervised and fully-automatic, i.e., it does not depend on any tuning parameters. The effectiveness of the proposed method is illustrated using simulated data based on U.S.G.S. laboratory spectra and real hyperspectral data collected by the AVIRIS sensor over Cuprite, Nevada.

Parallel hyperspectral coded aperture for compressive sensing on GPUs

The application of compressive sensing (CS) to hyperspectral images is an active area of research over the past few years, both in terms of the hardware and the signal processing algorithms. However, CS algorithms can be computationally very expensive due to the extremely large volumes of data collected by imaging spectrometers, a fact that compromises their use in applications under real-time constraints. This paper proposes four efficient implementations of hyperspectral coded aperture (HYCA) for CS, two of them termed P-HYCA and P-HYCA-FAST and two additional implementations for its constrained version (CHYCA), termed P-CHYCA and P-CHYCA-FAST on commodity graphics processing units (GPUs). HYCA algorithm exploits the high correlation existing among the spectral bands of the hyperspectral data sets and the generally low number of endmembers needed to explain the data, which largely reduces the number of measurements necessary to correctly reconstruct the original data. The proposed P-HYCA and P-CHYCA implementations have been developed using the compute unified device architecture (CUDA) and the cuFFT library. Moreover, this library has been replaced by a fast iterative method in the P-HYCA-FAST and P-CHYCA-FAST implementations that leads to very significant speedup factors in order to achieve real-time requirements. The proposed algorithms are evaluated not only in terms of reconstruction error for different compressions ratios but also in terms of computational performance using two different GPU architectures by NVIDIA: 1) GeForce GTX 590; and 2) GeForce GTX TITAN. Experiments are conducted using both simulated and real data revealing considerable acceleration factors and obtaining good results in the task of compressing remotely sensed hyperspectral data sets.

Separação de dados hiperespectrais baseada na análise de vértices de um simplex

Os sensores hiperespectrais que estão a ser desenvolvidos para aplicações em detecção remota, produzem uma elevada quantidade de dados. Tal quantidade de dados obriga a que as ferramentas de análise e processamento sejam eficientes e tenham baixa complexidade computacional. Uma tarefa importante na detecção remota é a determinação das substâncias presentes numa imagem hiperespectral e quais as suas concentrações. Neste contexto, Vertex component analysis (VCA), é um método não-supervisionado recentemente proposto que é eficiente e tem a complexidade computacional mais baixa de todos os métodos conhecidos. Este método baseia-se no facto de os vértices do simplex corresponderem às assinaturas dos elementos presentes nos dados. O VCA projecta os dados em direcções ortogonais ao subespaço gerado pelas assinaturas das substâncias já encontradas, correspondendo o extremo desta projecção à assinatura da nova substância encontrada. Nesta comunicação apresentam-se várias optimizações ao VCA nomeadamente: 1) a introdução de um método de inferência do sub-espaço de sinal que permite para além de reduzir a dimensionalidade dos dados, também permite estimar o número de substâncias presentes. 2) projeção dos dados é executada em várias direcções para garantir maior robustez em situações de baixa relação sinal-ruído. As potencialidades desta técnica são ilustradas num conjunto de experiências com dados simulados e reais, estes últimos adquiridos pela plataforma AVIRIS.

System-on-chip field-programmable gate array design for onboard real-time hyperspectral unmixing

Hyperspectral instruments have been incorporated in satellite missions, providing large amounts of data of high spectral resolution of the Earth surface. This data can be used in remote sensing applications that often require a real-time or near-real-time response. To avoid delays between hyperspectral image acquisition and its interpretation, the last usually done on a ground station, onboard systems have emerged to process data, reducing the volume of information to transfer from the satellite to the ground station. For this purpose, compact reconfigurable hardware modules, such as field-programmable gate arrays (FPGAs), are widely used. This paper proposes an FPGA-based architecture for hyperspectral unmixing. This method based on the vertex component analysis (VCA) and it works without a dimensionality reduction preprocessing step. The architecture has been designed for a low-cost Xilinx Zynq board with a Zynq-7020 system-on-chip FPGA-based on the Artix-7 FPGA programmable logic and tested using real hyperspectral data. Experimental results indicate that the proposed implementation can achieve real-time processing, while maintaining the methods accuracy, which indicate the potential of the proposed platform to implement high-performance, low-cost embedded systems, opening perspectives for onboard hyperspectral image processing.

Embedded system for individual recognition based on ECG biometrics

Biometric recognition is emerging has an alternative solution for applications where the privacy of the information is crucial. This paper presents an embedded biometric recognition system based on the Electrocardiographic signals (ECG) for individual identification and authentication. The proposed system implements a real-time state-of-the-art recognition algorithm, which extracts information from the frequency domain. The system is based on a ARM Cortex 4. Preliminary results show that embedded platforms are a promising path for the implementation of ECG-based applications in real-world scenario.

Vertex component analysis GPU-based implementation for hyperspectral unmixing

Endmember extraction (EE) is a fundamental and crucial task in hyperspectral unmixing. Among other methods vertex component analysis ( VCA) has become a very popular and useful tool to unmix hyperspectral data. VCA is a geometrical based method that extracts endmember signatures from large hyperspectral datasets without the use of any a priori knowledge about the constituent spectra. Many Hyperspectral imagery applications require a response in real time or near-real time. Thus, to met this requirement this paper proposes a parallel implementation of VCA developed for graphics processing units. The impact on the complexity and on the accuracy of the proposed parallel implementation of VCA is examined using both simulated and real hyperspectral datasets.

Parallel hyperspectral unmixing method via split augmented lagrangian on GPU

One of the main problems of hyperspectral data analysis is the presence of mixed pixels due to the low spatial resolution of such images. Linear spectral unmixing aims at inferring pure spectral signatures and their fractions at each pixel of the scene. The huge data volumes acquired by hyperspectral sensors put stringent requirements on processing and unmixing methods. This letter proposes an efficient implementation of the method called simplex identification via split augmented Lagrangian (SISAL) which exploits the graphics processing unit (GPU) architecture at low level using Compute Unified Device Architecture. SISAL aims to identify the endmembers of a scene, i.e., is able to unmix hyperspectral data sets in which the pure pixel assumption is violated. The proposed implementation is performed in a pixel-by-pixel fashion using coalesced accesses to memory and exploiting shared memory to store temporary data. Furthermore, the kernels have been optimized to minimize the threads divergence, therefore achieving high GPU occupancy. The experimental results obtained for the simulated and real hyperspectral data sets reveal speedups up to 49 times, which demonstrates that the GPU implementation can significantly accelerate the method's execution over big data sets while maintaining the methods accuracy.

Parallel method for sparse semisupervised hyperspectral unmixing

Parallel hyperspectral unmixing problem is considered in this paper. A semisupervised approach is developed under the linear mixture model, where the abundance's physical constraints are taken into account. The proposed approach relies on the increasing availability of spectral libraries of materials measured on the ground instead of resorting to endmember extraction methods. Since Libraries are potentially very large and hyperspectral datasets are of high dimensionality a parallel implementation in a pixel-by-pixel fashion is derived to properly exploits the graphics processing units (GPU) architecture at low level, thus taking full advantage of the computational power of GPUs. Experimental results obtained for real hyperspectral datasets reveal significant speedup factors, up to 164 times, with regards to optimized serial implementation.

Parallel hyperspectral unmixing method on GPU

Many Hyperspectral imagery applications require a response in real time or near-real time. To meet this requirement this paper proposes a parallel unmixing method developed for graphics processing units (GPU). This method is based on the vertex component analysis (VCA), which is a geometrical based method highly parallelizable. VCA is a very fast and accurate method that extracts endmember signatures from large hyperspectral datasets without the use of any a priori knowledge about the constituent spectra. Experimental results obtained for simulated and real hyperspectral datasets reveal considerable acceleration factors, up to 24 times.

Hyperspectral signal subspace estimation

Given an hyperspectral image, the determination of the number of endmembers and the subspace where they live without any prior knowledge is crucial to the success of hyperspectral image analysis. This paper introduces a new minimum mean squared error based approach to infer the signal subspace in hyperspectral imagery. The method, termed hyperspectral signal identification by minimum error (HySime), is eigendecomposition based and it does not depend on any tuning parameters. It first estimates the signal and noise correlation matrices and then selects the subset of eigenvalues that best represents the signal subspace in the least squared error sense. The effectiveness of the proposed method is illustrated using simulated data based on U.S.G.S. laboratory spectra and real hyperspectral data collected by the AVIRIS sensor over Cuprite, Nevada.

Unmixing hyperspectral data: independent and dependent component analysis

The development of high spatial resolution airborne and spaceborne sensors has improved the capability of ground-based data collection in the fields of agriculture, geography, geology, mineral identification, detection [2, 3], and classification [4–8]. The signal read by the sensor from a given spatial element of resolution and at a given spectral band is a mixing of components originated by the constituent substances, termed endmembers, located at that element of resolution. This chapter addresses hyperspectral unmixing, which is the decomposition of the pixel spectra into a collection of constituent spectra, or spectral signatures, and their corresponding fractional abundances indicating the proportion of each endmember present in the pixel [9, 10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. The linear mixing model holds when the mixing scale is macroscopic [13]. The nonlinear model holds when the mixing scale is microscopic (i.e., intimate mixtures) [14, 15]. The linear model assumes negligible interaction among distinct endmembers [16, 17]. The nonlinear model assumes that incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [18]. Under the linear mixing model and assuming that the number of endmembers and their spectral signatures are known, hyperspectral unmixing is a linear problem, which can be addressed, for example, under the maximum likelihood setup [19], the constrained least-squares approach [20], the spectral signature matching [21], the spectral angle mapper [22], and the subspace projection methods [20, 23, 24]. Orthogonal subspace projection [23] reduces the data dimensionality, suppresses undesired spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel onto a subspace that is orthogonal to the undesired signatures. As shown in Settle [19], the orthogonal subspace projection technique is equivalent to the maximum likelihood estimator. This projection technique was extended by three unconstrained least-squares approaches [24] (signature space orthogonal projection, oblique subspace projection, target signature space orthogonal projection). Other works using maximum a posteriori probability (MAP) framework [25] and projection pursuit [26, 27] have also been applied to hyperspectral data. In most cases the number of endmembers and their signatures are not known. Independent component analysis (ICA) is an unsupervised source separation process that has been applied with success to blind source separation, to feature extraction, and to unsupervised recognition [28, 29]. ICA consists in finding a linear decomposition of observed data yielding statistically independent components. Given that hyperspectral data are, in given circumstances, linear mixtures, ICA comes to mind as a possible tool to unmix this class of data. In fact, the application of ICA to hyperspectral data has been proposed in reference 30, where endmember signatures are treated as sources and the mixing matrix is composed by the abundance fractions, and in references 9, 25, and 31–38, where sources are the abundance fractions of each endmember. In the first approach, we face two problems: (1) The number of samples are limited to the number of channels and (2) the process of pixel selection, playing the role of mixed sources, is not straightforward. In the second approach, ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of the abundance fractions is constant, implying dependence among abundances. This dependence compromises ICA applicability to hyperspectral images. In addition, hyperspectral data are immersed in noise, which degrades the ICA performance. IFA [39] was introduced as a method for recovering independent hidden sources from their observed noisy mixtures. IFA implements two steps. First, source densities and noise covariance are estimated from the observed data by maximum likelihood. Second, sources are reconstructed by an optimal nonlinear estimator. Although IFA is a well-suited technique to unmix independent sources under noisy observations, the dependence among abundance fractions in hyperspectral imagery compromises, as in the ICA case, the IFA performance. Considering the linear mixing model, hyperspectral observations are in a simplex whose vertices correspond to the endmembers. Several approaches [40–43] have exploited this geometric feature of hyperspectral mixtures [42]. Minimum volume transform (MVT) algorithm [43] determines the simplex of minimum volume containing the data. The MVT-type approaches are complex from the computational point of view. Usually, these algorithms first find the convex hull defined by the observed data and then fit a minimum volume simplex to it. Aiming at a lower computational complexity, some algorithms such as the vertex component analysis (VCA) [44], the pixel purity index (PPI) [42], and the N-FINDR [45] still find the minimum volume simplex containing the data cloud, but they assume the presence in the data of at least one pure pixel of each endmember. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. Hyperspectral sensors collects spatial images over many narrow contiguous bands, yielding large amounts of data. For this reason, very often, the processing of hyperspectral data, included unmixing, is preceded by a dimensionality reduction step to reduce computational complexity and to improve the signal-to-noise ratio (SNR). Principal component analysis (PCA) [46], maximum noise fraction (MNF) [47], and singular value decomposition (SVD) [48] are three well-known projection techniques widely used in remote sensing in general and in unmixing in particular. The newly introduced method [49] exploits the structure of hyperspectral mixtures, namely the fact that spectral vectors are nonnegative. The computational complexity associated with these techniques is an obstacle to real-time implementations. To overcome this problem, band selection [50] and non-statistical [51] algorithms have been introduced. This chapter addresses hyperspectral data source dependence and its impact on ICA and IFA performances. The study consider simulated and real data and is based on mutual information minimization. Hyperspectral observations are described by a generative model. This model takes into account the degradation mechanisms normally found in hyperspectral applications—namely, signature variability [52–54], abundance constraints, topography modulation, and system noise. The computation of mutual information is based on fitting mixtures of Gaussians (MOG) to data. The MOG parameters (number of components, means, covariances, and weights) are inferred using the minimum description length (MDL) based algorithm [55]. We study the behavior of the mutual information as a function of the unmixing matrix. The conclusion is that the unmixing matrix minimizing the mutual information might be very far from the true one. Nevertheless, some abundance fractions might be well separated, mainly in the presence of strong signature variability, a large number of endmembers, and high SNR. We end this chapter by sketching a new methodology to blindly unmix hyperspectral data, where abundance fractions are modeled as a mixture of Dirichlet sources. This model enforces positivity and constant sum sources (full additivity) constraints. The mixing matrix is inferred by an expectation-maximization (EM)-type algorithm. This approach is in the vein of references 39 and 56, replacing independent sources represented by MOG with mixture of Dirichlet sources. Compared with the geometric-based approaches, the advantage of this model is that there is no need to have pure pixels in the observations. The chapter is organized as follows. Section 6.2 presents a spectral radiance model and formulates the spectral unmixing as a linear problem accounting for abundance constraints, signature variability, topography modulation, and system noise. Section 6.3 presents a brief resume of ICA and IFA algorithms. Section 6.4 illustrates the performance of IFA and of some well-known ICA algorithms with experimental data. Section 6.5 studies the ICA and IFA limitations in unmixing hyperspectral data. Section 6.6 presents results of ICA based on real data. Section 6.7 describes the new blind unmixing scheme and some illustrative examples. Section 6.8 concludes with some remarks.

Hyperspectral imagery framework for unmixing and dimensionality estimation

In hyperspectral imagery a pixel typically consists mixture of spectral signatures of reference substances, also called endmembers. Linear spectral mixture analysis, or linear unmixing, aims at estimating the number of endmembers, their spectral signatures, and their abundance fractions. This paper proposes a framework for hyperpsectral unmixing. A blind method (SISAL) is used for the estimation of the unknown endmember signature and their abundance fractions. This method solve a non-convex problem by a sequence of augmented Lagrangian optimizations, where the positivity constraints, forcing the spectral vectors to belong to the convex hull of the endmember signatures, are replaced by soft constraints. The proposed framework simultaneously estimates the number of endmembers present in the hyperspectral image by an algorithm based on the minimum description length (MDL) principle. Experimental results on both synthetic and real hyperspectral data demonstrate the effectiveness of the proposed algorithm.

A toolbox for hyperspectral image analysis

This paper introduces a new toolbox for hyperspectral imagery, developed under the MATLAB environment. This toolbox provides easy access to different supervised and unsupervised classification methods. This new application is also versatile and fully dynamic since the user can embody their own methods, that can be reused and shared. This toolbox, while extends the potentiality of MATLAB environment, it also provides a user-friendly platform to assess the results of different methodologies. In this paper it is also presented, under the new application, a study of several different supervised and unsupervised classification methods on real hyperspectral data.