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.

Qualified intervention/qualifying formation

An education promoting scientific literacy (SL) that prepares the citizens to a responsible citizenship has persisted as an argument across discussions on curricula design. The ubiquity of science and technology on contemporary societies and the ideological requirement of informed democratic participation led to the identification of relevant categories that drive curriculum reforms towards a humanistic approach of school science. The category ‘Science as culture’ acquires in the current work a major importance: it enlightens the meaning of scientific literacy. Looking closely to the French term, culture scientifique et tecnologique, turns science simultaneously into a cultural object and product that can be both received and worked at different levels and within several approaches by the individuals and the communities. On the other hand, nonformal and informal education spaces gain greater importance. Together with the formal school environment these spaces allow for an enrichment and diversification of learning experiences. Examples of nonformal spaces where animators can develop their work may be science museums or botanical gardens; television and internet can be regarded as informal education spaces. Due to the above mentioned impossibility of setting apart the individual or community-based experiences from Science and Technology (S&T), the work in nonformal and informal spaces sets an additional challenge to the preparation of socio-cultural animators. Socio-scientific issues take, at times, heavily relevance within the communities. Pollution, high tension lines, spreading of diseases, food contamination or natural resources conservation are among the socio-scientific issues that often call upon arguments and emotions. In the context of qualifying programmes on socio-cultural animation (social education and community development) within European Higher Education Area (EHEA) the present study describes the Portuguese framework. The comparison of programmes within Portugal aims to contribute to the discussion on the curriculum design for a socio-cultural animator degree (1st cycle of Bologna process). In particular, this study intends to assess how the formation given complies with enabling animators to work, within multiple scenarios, with communities in situations of socio-scientific relevance. A set of themes, issues and both current and potential fields of action, not described or insufficiently described in literature, is identified and analysed in the perspective of a qualified intervention of animators. One of these examples is thoroughly discussed. Finally, suggestions are made about curriculum reforms in order, if possible, to strongly link the desired qualified intervention with a qualifying formation.

Trajectórias de profissionalidade e ciclo de vida profissional: um contributo para o conhecimento dos professores de educação especial

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ciências da Educação - Especialidade Educação Especial

Implementação em hardware reconfigurável de método de separação de dados hiperespetrais

Relatório do Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Electrónica e Telecomunicações

Óbidos, literary village: innovation in the creative industries?

The village of Óbidos was recognized in 2015 as a creative city in the area of literature, becoming a member of the UNESCO Creative Cities Network. The attribution of the title depends on the fulfillment of a number of criteria the regions have to integrate. In addition to Óbidos, UNESCO attributed the same title in the same year to other European cities, including Barcelona, Nottingham, Ljubljana, Tartu and Lviv. This article intends to co nduct a case study to the cultural and artistic offer, as well as the cultural and literary legacy that different cities provide to be able to inquire the innovation of the proposals. The study aims to assess how much Óbidos, compared to other cities with the same title, is creative. Knowing that the concept of creative city (Landry and Bianchini, 1995) results from the emergence of new technologies and a new type of economy based on creativity and innovation and that creativity implies removing economic or social value of the creative work or talent, the study aims to determine to what extent the processes generated gave rise to new ideas (creativity) and what processes led to its implementation (innovation). Being innovation in the creative industries asso ciated with product, process, positioning, paradigmatic and social innovation (Storsul and Krumsvik, 2013), it is concluded that, in Óbidos, the entrepreneurship initiatives are more focused on tourists who occasionally visit the village and the business o pportunities that are generated there. New innovative and creative spaces were created, promoting literature and adding value and quality to urban space. This urban intervention resulted in the attraction of individuals who streamlined new habits of being and acting in the village