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.

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.

Vertex component analysis: a geometric-based approach to unmix hyperspectral data

Hyperspectral remote sensing exploits the electromagnetic scattering patterns of the different materials at specific wavelengths [2, 3]. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum extending from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands [4, 5]. The number and variety of potential civilian and military applications of hyperspectral remote sensing is enormous [6, 7]. Very often, the resolution cell corresponding to a single pixel in an image contains several substances (endmembers) [4]. In this situation, the scattered energy is a mixing of the endmember spectra. A challenging task underlying many hyperspectral imagery applications is then decomposing a mixed pixel into a collection of reflectance spectra, called endmember signatures, and the corresponding abundance fractions [8–10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. Linear mixing model holds approximately when the mixing scale is macroscopic [13] and there is negligible interaction among distinct endmembers [3, 14]. If, however, the mixing scale is microscopic (or intimate mixtures) [15, 16] and the incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [17], the linear model is no longer accurate. Linear spectral unmixing has been intensively researched in the last years [9, 10, 12, 18–21]. It considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions. Under this model, and assuming that the number of substances and their reflectance spectra are known, hyperspectral unmixing is a linear problem for which many solutions have been proposed (e.g., maximum likelihood estimation [8], spectral signature matching [22], spectral angle mapper [23], subspace projection methods [24,25], and constrained least squares [26]). In most cases, the number of substances and their reflectances are not known and, then, hyperspectral unmixing falls into the class of blind source separation problems [27]. Independent component analysis (ICA) has recently been proposed as a tool to blindly unmix hyperspectral data [28–31]. ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images as shown in Refs. [21, 32]. In fact, ICA finds the endmember signatures by multiplying the spectral vectors with an unmixing matrix, which minimizes the mutual information among sources. If sources are independent, ICA provides the correct unmixing, since the minimum of the mutual information is obtained only when sources are independent. This is no longer true for dependent abundance fractions. Nevertheless, some endmembers may be approximately unmixed. These aspects are addressed in Ref. [33]. Under the linear mixing model, the observations from a scene are in a simplex whose vertices correspond to the endmembers. Several approaches [34–36] have exploited this geometric feature of hyperspectral mixtures [35]. Minimum volume transform (MVT) algorithm [36] determines the simplex of minimum volume containing the data. The method presented in Ref. [37] is also of MVT type but, by introducing the notion of bundles, it takes into account the endmember variability usually present in hyperspectral mixtures. The MVT type approaches are complex from the computational point of view. Usually, these algorithms find in the first place the convex hull defined by the observed data and then fit a minimum volume simplex to it. For example, the gift wrapping algorithm [38] computes the convex hull of n data points in a d-dimensional space with a computational complexity of O(nbd=2cþ1), where bxc is the highest integer lower or equal than x and n is the number of samples. The complexity of the method presented in Ref. [37] is even higher, since the temperature of the simulated annealing algorithm used shall follow a log( ) law [39] to assure convergence (in probability) to the desired solution. Aiming at a lower computational complexity, some algorithms such as the pixel purity index (PPI) [35] and the N-FINDR [40] still find the minimum volume simplex containing the data cloud, but they assume the presence of at least one pure pixel of each endmember in the data. 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. PPI algorithm uses the minimum noise fraction (MNF) [41] as a preprocessing step to reduce dimensionality and to improve the signal-to-noise ratio (SNR). The algorithm then projects every spectral vector onto skewers (large number of random vectors) [35, 42,43]. The points corresponding to extremes, for each skewer direction, are stored. A cumulative account records the number of times each pixel (i.e., a given spectral vector) is found to be an extreme. The pixels with the highest scores are the purest ones. N-FINDR algorithm [40] is based on the fact that in p spectral dimensions, the p-volume defined by a simplex formed by the purest pixels is larger than any other volume defined by any other combination of pixels. This algorithm finds the set of pixels defining the largest volume by inflating a simplex inside the data. ORA SIS [44, 45] is a hyperspectral framework developed by the U.S. Naval Research Laboratory consisting of several algorithms organized in six modules: exemplar selector, adaptative learner, demixer, knowledge base or spectral library, and spatial postrocessor. The first step consists in flat-fielding the spectra. Next, the exemplar selection module is used to select spectral vectors that best represent the smaller convex cone containing the data. The other pixels are rejected when the spectral angle distance (SAD) is less than a given thresh old. The procedure finds the basis for a subspace of a lower dimension using a modified Gram–Schmidt orthogonalizati on. The selected vectors are then projected onto this subspace and a simplex is found by an MV T pro cess. ORA SIS is oriented to real-time target detection from uncrewed air vehicles using hyperspectral data [46]. In this chapter we develop a new algorithm to unmix linear mixtures of endmember spectra. First, the algorithm determines the number of endmembers and the signal subspace using a newly developed concept [47, 48]. Second, the algorithm extracts the most pure pixels present in the data. Unlike other methods, this algorithm is completely automatic and unsupervised. To estimate the number of endmembers and the signal subspace in hyperspectral linear mixtures, the proposed scheme begins by estimating sign al and noise correlation matrices. The latter is based on multiple regression theory. The signal subspace is then identified by selectin g the set of signal eigenvalue s that best represents the data, in the least-square sense [48,49 ], we note, however, that VCA works with projected and with unprojected data. The extraction of the end members exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. As PPI and N-FIND R algorithms, VCA also assumes the presence of pure pixels in the data. The algorithm iteratively projects data on to a direction orthogonal to the subspace spanned by the endmembers already determined. The new end member signature corresponds to the extreme of the projection. The algorithm iterates until all end members are exhausted. VCA performs much better than PPI and better than or comparable to N-FI NDR; yet it has a computational complexity between on e and two orders of magnitude lower than N-FINDR. The chapter is structure d as follows. Section 19.2 describes the fundamentals of the proposed method. Section 19.3 and Section 19.4 evaluate the proposed algorithm using simulated and real data, respectively. Section 19.5 presents some concluding remarks.

Fast unsupervised extraction of endmembers spectra from hyperspectral data

Linear unmixing decomposes an hyperspectral image into a collection of re ectance spectra, called endmember signatures, and a set corresponding abundance fractions from the respective spatial coverage. This paper introduces vertex component analysis, an unsupervised algorithm to unmix linear mixtures of hyperpsectral data. VCA exploits the fact that endmembers occupy vertices of a simplex, and assumes the presence of pure pixels in data. VCA performance is illustrated using simulated and real data. VCA competes with state-of-the-art methods with much lower computational complexity.

Downstream processing development of enveloped viruses for clinical applications: innovative tools for rational process optimization

Dissertation presented to obtain a Ph.D. degree in Engineering and Technology Sciences, Biotechnology at the Instituto de Tecnologia Química e Biológica, Universidade Nova de Lisboa

Personal learning environments: integration of Web 2.0 applications and content management systems

This paper presents an ongoing project that implements a platform for creating personal learning environments controlled by students, integrating Web 2.0 applications and content management systems, enabling the safe use of content created in Web 2.0 applications, allowing its publication in the infrastructure controlled by the HEI. Using this platform, students can develop their personal learning environment (PLE) integrated with the Learning Management System (LMS) of the HEI, enabling the management of their learning and, simultaneously, creating their e-portfolio with digital content developed for Course Units (CU). All this can be maintained after the student completes his academic studies, since the platform will remain accessible to students even after they leave the HEI and lose access to its infrastructure. The platform will enable the safe use of content created in Web 2.0 applications, allowing its protected publication in the infrastructure controlled by HEI, thus contributing to the adaptation of the L&T paradigm to the Bologna process.

Teaching and learning with social software in higher education: content management systems integrated with Web-based applications as a key factor for success

The change of paradigm imposed by the Bologna process, in which the student will be responsible for their own learning, and the presence of a new generation of students with higher technological skills, represent a huge challenge for higher education institutions. The use of new Web Social concepts in teaching process, supported by applications commonly called Web 2.0, with which these new students feel at ease, can bring benefits in terms of motivation and the frequency and quality of students' involvement in academic activities. An e-learning platform with web-based applications as a complement can significantly contribute to the development of different skills in higher education students, covering areas which are usually in deficit.

Upper Ontology for Multi-Agent Energy Systems’ Applications

Energy systems worldwide are complex and challenging environments. Multi-agent based simulation platforms are increasing at a high rate, as they show to be a good option to study many issues related to these systems, as well as the involved players at act in this domain. In this scope the authors research group has developed three multi-agent systems: MASCEM, which simulates the electricity markets; ALBidS that works as a decision support system for market players; and MASGriP, which simulates the internal operations of smart grids. To take better advantage of these systems, their integration is mandatory. For this reason, is proposed the development of an upper-ontology which allows an easier cooperation and adequate communication between them. Additionally, the concepts and rules defined by this ontology can be expanded and complemented by the needs of other simulation and real systems in the same areas as the mentioned systems. Each system’s particular ontology must be extended from this top-level ontology.

Environmental/Regatta Buoy: Telemetry and Configuration

A monitorização ambiental é essencial para a tomada de decisões tanto na ciência como na indústria. Em particular, uma vez que a água é essencial à vida e a superfície da Terra é composta principalmente por água, a monitorização do clima e dos parâmetros relacionados com a água em ecossistemas sensíveis, tais como oceanos, lagoas, rios e lagos, é de extrema importância. Um dos métodos mais comuns para monitorar a água é implantar bóias. O presente trabalho está integrado num projeto mais amplo, com o objetivo de projectar e desenvolver uma bóia autónoma para a investigação científica com dois modos de funcionamento: (i) monitorização ambiental ; e (ii) baliza ativa de regata. Assim, a bóia tem duas aplicações principais: a coleta e armazenamento de dados e a assistência a regatas de veleiros autónomos. O projeto arrancou há dois anos com um grupo de quatro estudantes internacionais. Eles projetaram e construíram a estrutura física, compraram e montaram o sistema de ancoragem da bóia e escolherem a maioria dos componentes electrónicos para o sistema geral de controlo e medição. Este ano, durante o primeiro semestre, dois estudantes belgas - Jeroen Vervenne e Hendrick Verschelde – trabalharam nos subsistemas de recolha e armazenamento de dados (unidade de controlo escrava) e de telemetria e configuração (unidade de controlo mestre) assim como definiram o protocolo de comunicação da aplicação. O trabalho desta tese continua o desenvolvimento do subsistema de telemetria e configuração. Este subsistema _e responsável pela configuração do modo de funcionamento e dos sensores assim como pela comunicação com a estacão de base (controlo ambiental), barcos (baliza ativa de regata) e com o subsistema de recolha e armazenamento de dados. O desenvolvimento do subsistema de recolha e armazenamento de dados, que coleta e armazena num cartão SD os dados dos sensores selecionados, prossegue com outro estudante belga - Mathias van Flieberge. O objetivo desta tese é, por um lado, implementar o subsistema de telemetria e de configuração na unidade de controle mestre e, por outro lado, refinar e implementar, conjuntamente com Mathias van Flieberge, o protocolo de nível de aplicação projetado. Em particular, a unidade de controlo mestre deve processar e atribuir prioridades às mensagens recebidas da estacão base, solicitar dados à unidade de controlo escrava e difundir mensagens com informação de posição e condições de vento e água no modo de regata. Enquanto que a comunicação entre a unidade de controlo mestre e a estacão base e a unidade de controlo mestre e os barcos é sem fios, a unidade de controlo mestre e a unidade de controlo escrava comunicam através de uma ligação série. A bóia tem atualmente duas limitações: (i) a carga máxima é de 40 kg; e (ii) apenas pode ser utilizada em rios ou próximo da costa dada à limitação de distância imposta pela técnica de comunicação sem fios escolhida.

Artificial Intelligence in geospatial analysis: applications of self-organizing maps in the context of geographic information science.

A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Information Systems.

Environmental/Regatta Buoy: Sensing System

Um dos principais objetivos da ciência é perceber a natureza, i.e., descobrir e explicar o funcionamento do mundo que nos rodeia. Para tal, os cientistas precisam de coligir dados e monitorar o meio ambiente. Em particular, considerando que cerca de 70% da Terra é coberta por água, a coleta de parâmetros de caracterização da água de grandes superfícies é uma prioridade. A monitorização das condições da água é feita principalmente através de bóias. No entanto, as bóias disponíveis no mercado não satisfazem as necessidades existentes. Esta é uma das principais razões que levaram o Laboratório de Sistemas Autónomos (LSA) do Instituto Superior de Engenharia do Porto a lançarem um projeto para o desenvolvimento de uma bóia reconfigurável e com dois modos de funcionamento: monitorização ambiental e baliza ativa de regata. O segundo modo é destinado a regatas de veleiros autónomos. O projeto começou há um ano com um projeto do European Project Project [1] (EPS), realizado por quatro estudantes internacionais, destinado à construção da estrutura da bóia e à selecção dos componentes mais adequados para o sistema de medição e controlo. A arquitetura que foi definida para este sistema é do tipo mestre-escravo e é composta por uma unidade de controlo mestre para a telemetria e configuração e uma unidade de controlo escrava para a medição e armazenamento de dados. O desenvolvimento do projeto continuou com dois estudantes belgas que trabalharam na comunicação e no armazenamento de dados. Este projeto, que prossegue com o desenvolvimento da medição e do armazenamento de dados do lado da unidade de controlo escrava, tem os seguintes objetivos: (i ) implementar o protocolo de comunicação na unidade de controlo escrava; (ii ) coligir e armazenar os dados dos sensores no cartão SD em tempo real; (iii ) fornecer dados em tempo útil; e (iv) recuperar dados do cartão SD em tempo diferido. As contribuições anteriores foram estudadas e foi feito um levantamento dos projetos congéneres existentes. O desenvolvimento do projeto atual começou com o protocolo de comunicação. Este protocolo, que foi projetado pelos alunos anteriores, foi um bom ponto de partida. No entanto, o protocolo foi atualizado e melhorado com novas funcionalidades. Esta última componente foi um trabalho conjunto com Laurens Allart, que esteve a trabalhar no subsistema de telemetria e de configuração durante este semestre. O protocolo foi implementado do lado da unidade de controlo escrava através de uma estrutura de múltiplas actividades paralelas (multithreaded). Esta estrutura recebe as mensagens da unidade mestre, executa as ações solicitadas e envia de volta o resultado. A bóia é um dispositivo reconfigurável multimodo que pode ser expandido com novos modos de operação no futuro. Infelizmente, sofre de algumas limitações: suporta uma carga máxima de 40 kg e tem uma área de implantação limitada pela distância máxima à estacão base.

Every normal logic program has a 2-valued semantics: theory, extensions, applications, implementations

Trabalho apresentado no âmbito do Doutoramento em Informática, como requisito parcial para obtenção do grau de Doutor em Informática

Oxo-molybdenum(VI) complexes containing chiral ligands: catalytic applications in selective epoxidations

Dissertation presented to obtain the Ph.D. degree in Chemistry

A combined LNA-oscillator-mixer for biomedical applications

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores