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.

Does independent component analysis play a role in unmixing hyperspectral data?

Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2)sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signal-to-noise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.

Patrocínio: influência na atitude relativamente à marca e intenção de compra: caso Nike e selecção portuguesa de futebol

Devido à enorme importância que tem sido atribuída ao desporto nas últimas décadas, os marketers abraçam agora totalmente o facto de uma campanha integrada de patrocínio desportivo poder atingir um imensurável número de benefícios. Na verdade, apesar das empresas se comprometerem hoje com muitas outras áreas como a cultura, caridade e domínios humanitários, o desporto continua a ser o campo mais requisitado no que ao patrocínio se refere. Para muitas organizações o patrocínio desportivo é, de facto, o elemento-chave de uma comunicação integrada de marketing. Devido então a todo este enfase dado ao desporto, decidimos verificar se a relação de patrocínio entre a marca Nike e a Selecção Portuguesa de Futebol (SPF) influencia a atitude relativamente à marca e a intenção de compra dos seus produtos, o que constitui o objectivo desta investigação. Assim, tendo como ponto de partida a questão: exercerá a relação de patrocínio entre a Nike e a SPF alguma influência na atitude relativamente à marca e sua intenção de compra? E, por meio de uma revisão da literatura referente a este tema, desenvolvemos um modelo conceptual, o qual é baseado no criado por Martensen et al (2007) e integra quatro principais conceitos: envolvimento, atitudes, intenção de compra e congruência entre a marca e o evento. O presente estudo emprega um design exploratório envolvendo uma colecta de dados quantitativos, através da aplicação de um questionário online. De modo a confirmarmos o modelo proposto, duas técnicas estatísticas foram utilizadas: análise factorial e análise de equações estruturais (AEE). As conclusões desta investigação podem fornecer directivas para a compreensão de como uma relação de patrocínio pode criar ou melhorar a atitude relativamente a uma marca e sua intenção de compra. Como principal resultado, podemos destacar a existência de uma influência positiva da relação de patrocínio na atitude relativamente à marca.

Vertex component analysis: a fast algorithm to unmix hyperspectral data

Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

Programação em artes performativas para idosos nos serviços educativos das redes culturais

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Artística, na especialização de Teatro na Educação

As competências dos técnicos de radiologia: um contributo para a sua identificação e definição

Mestrado em Intervenção Sócio-Organizacional em Saúde - Ramo de especialização: Políticas de Administração e Gestão de Serviços de Saúde

A divulgação da responsabilidade social empresarial nas empresas do PSI Geral da Euronext Lisboa (2012-2013): relatórios de sustentabilidade vs. divulgação online

Mestrado em Contabilidade

Da condição da génese do erro em enfermagem à segurança do cliente em serviços de urgência

Mestrado em Intervenção Sócio-Organizacional na Saúde - Área de especialização: Políticas de Administração e Gestão de Serviços de Saúde

Non-enzymatic assay for glucose by using immobilized whole-cells of E. coli containing glucose binding protein fused to fluorescent proteins

Glucose monitoring in vivo is a crucial issue for gaining new understanding of diabetes. Glucose binding protein (GBP) fused to two fluorescent indicator proteins (FLIP) was used in the present study such as FLIP-glu- 3.2 mM. Recombinant Escherichia coli whole-cells containing genetically encoded nanosensors as well as cell-free extracts were immobilized either on inner epidermis of onion bulb scale or on 96-well microtiter plates in the presence of glutaraldehyde. Glucose monitoring was carried out by Förster Resonance Energy Transfer (FRET) analysis due the cyano and yellow fluorescent proteins (ECFP and EYFP) immobilized in both these supports. The recovery of these immobilized FLIP nanosensors compared with the free whole-cells and cell-free extract was in the range of 50–90%. Moreover, the data revealed that these FLIP nanosensors can be immobilized in such solid supports with retention of their biological activity. Glucose assay was devised by FRET analysis by using these nanosensors in real samples which detected glucose in the linear range of 0–24 mM with a limit of detection of 0.11 mM glucose. On the other hand, storage and operational stability studies revealed that they are very stable and can be re-used several times (i.e. at least 20 times) without any significant loss of FRET signal. To author's knowledge, this is the first report on the use of such immobilization supports for whole-cells and cell-free extract containing FLIP nanosensor for glucose assay. On the other hand, this is a novel and cheap high throughput method for glucose assay.

Hyperspectral unmixing algorithm via dependent component analysis

This paper introduces a new method to blindly unmix hyperspectral data, termed dependent component analysis (DECA). This method decomposes a hyperspectral images into a collection of reflectance (or radiance) spectra of the materials present in the scene (endmember signatures) and the corresponding abundance fractions at each pixel. DECA assumes that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. These abudances are modeled as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum. The mixing matrix is inferred by a generalized expectation-maximization (GEM) type algorithm. This method overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical based approaches. 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.