An improved continuous medium technique for structural frame analysis

This paper presents an improved constitutive equation of frame in the context of continuous medium technique. This improved constitutive equation, which is a consistent formulation of column global bending, is applicable to a complete class of frameworks including the ideal shear frame panel, for which the beams are assumed to be rigid, and the associated column system, for which the rigidity of beams is negligible. Global buckling and second-order effects of the frame structure are discussed. The main results can be extended to other types of lateral stiffening elements as built-up columns. A worked example is presented in order to compare the main results with those obtained by the classic matrix method. Copyright (C) 2007 John Wiley & Sons, Ltd.

Modelling grain boundary migration during geometric dynamic recrystallization

High-angle grain boundary migration is predicted during geometric dynamic recrystallization (GDRX) by two types of mathematical models. Both models consider the driving pressure due to curvature and a sinusoidal driving pressure owing to subgrain walls connected to the grain boundary. One model is based on the finite difference solution of a kinetic equation, and the other, on a numerical technique in which the boundary is subdivided into linear segments. The models show that an initially flat boundary becomes serrated, with the peak and valley migrating into both adjacent grains, as observed during GDRX. When the sinusoidal driving pressure amplitude is smaller than 2 pi, the boundary stops migrating, reaching an equilibrium shape. Otherwise, when the amplitude is larger than 2 pi, equilibrium is never reached and the boundary migrates indefinitely, which would cause the protrusions of two serrated parallel boundaries to impinge on each other, creating smaller equiaxed grains.

A Geometric Approach for Turbo Decoding of Reed-Solomon Codes in QAM Modulation Schemes

This work studies the turbo decoding of Reed-Solomon codes in QAM modulation schemes for additive white Gaussian noise channels (AWGN) by using a geometric approach. Considering the relations between the Galois field elements of the Reed-Solomon code and the symbols combined with their geometric dispositions in the QAM constellation, a turbo decoding algorithm, based on the work of Chase and Pyndiah, is developed. Simulation results show that the performance achieved is similar to the one obtained with the pragmatic approach with binary decomposition and analysis.

Application of hydrophobic resin adhesives to acid-etched dentin with an alternative wet bonding technique

Hydrophilic dentin adhesives are prone to water sorption that adversely affects the durability of resin-dentin bonds. This study examined the feasibility of bonding to dentin with hydrophobic resins via the adaptation of electron microscopy tissue processing techniques. Hydrophobic primers were prepared by diluting 2,2-bis[4(2-hydroxy-3-methacryloyloxy-propyloxy)-phenyl] propane/triethyleneglycol dimethacrylate resins with known ethanol concentrations. They were applied to acid-etched moist dentin using an ethanol wet bonding technique that involved: (1) stepwise replacement of water with a series of increasing ethanol concentrations to prevent the demineralized collagen matrix from collapsing; (2) stepwise replacement of the ethanol with different concentrations of hydrophobic primers and subsequently with neat hydrophobic resin. Using the ethanol wet bonding technique, the experimental primer versions with 40, 50, and 75% resin exhibited tensile strengths which were not significantly different from commercially available hydrophilic three-step adhesives that were bonded with water wet bonding technique. The concept of ethanol wet bonding may be explained in terms of solubility parameter theory. This technique is sensitive to water contamination, as depicted by the lower tensile strength results from partial dehydration protocols. The technique has to be further improved by incorporating elements of dentin permeability reduction to avoid water from dentinal tubules contaminating water-free resin blends during bonding. (c) 2007 Wiley Periodicals, Inc. J Biomed Mater Res 84A: 19-29, 2008.

Surface modification of metals by calcium carbonate thin films on a layer-by-layer polyelectrolyte matrix

A multilayer organic film containing poly(acrylic acid) and chitosan was fabricated on a metallic support by means of the layer-by-layer technique. This film was used as a template for calcium carbonate crystallization and presents two possible binding sites where the nucleation may be initiated, either calcium ions acting as counterions of the polyelectrolyte or those trapped in the template gel network formed by the polyelectrolyte chains. Calcium carbonate formation was carried out by carbon dioxide diffusion, where CO, was generated from ammonium carbonate decomposition. The CaCO3 nanocrystals obtained, formed a dense, homogeneous, and continuous film. Vaterite and calcite CaCO3 crystalline forms were detected. (c) 2007 Elsevier B.V All rights reserved.

Expression of smooth muscle and extracellular matrix proteins in relation to airway function in asthma

Background: Smooth muscle content is increased within the airway wall in patients with asthma and is likely to play a role in airway hyperresponsiveness. However, smooth muscle cells express several contractile and structural proteins, and each of these proteins may influence airway function distinctly. Objective: We examined the expression of contractile and structural proteins of smooth muscle cells, as well as extracellular matrix proteins, in bronchial biopsies of patients with asthma, and related these to lung function, airway hyperresponsiveness, and responses to deep inspiration. Methods: Thirteen patients with asthma (mild persistent, atopic, nonsmoking) participated in this cross-sectional study. FEV1 % predicted, PC20 methacholine, and resistance of the respiratory system by the forced oscillation technique during tidal breathing and deep breath were measured. Within 1 week, a bronchoscopy was performed to obtain 6 bronchial biopsies that were immunuhistochemically stained for alpha-SM-actin, desmin, myosin light chain kinase (MLCK), myosin, calponin, vimentin, elastin, type III collagen, and fibronectin. The level of expression was determined by automated densitometry. Results: PC20 methacholine was inversely related to the expression of alpha-smooth muscle actin (r = -0.62), desmin (r = -0.56), and elastin (r = -0.78). In addition, FEV1% predicted was positively related and deep inspiration-induced bronchodilation inversely related to desmin (r = -0.60), MLCK (r = -0.60), and calponin (r = -0.54) expression. Conclusion: Airway hyperresponsiveness, FEV1% predicted, and airway responses to deep inspiration are associated with selective expression of airway smooth muscle proteins and components of the extracellular matrix.

Expression of Extracellular Matrix Proteins in Human Dental Pulp Stem Cells Depends on the Donor Tooth Conditions

Introduction: Stem cells are characterized by the ability to renew themselves through mitotic cell division and differentiating into a diverse range of specialized cell types. An important source of adult stem cells is the dental pulp. In dentistry, regenerative strategies are of importance because of hard dental tissue damage especially as result of caries lesions, trauma, or iatrogenic procedures. The regeneration of dental tissues relies on the ability of stem cells to produce extracellular (ECM) proteins encountered in the dental pulp tissue. Thus, the aim of this study was to analyze the expression and distribution of proteins encountered in dental pulp ECM (type I collagen, fibronectin, and tenascin) in stem cells. Methods: Human immature dental pulp stem cells (hIDPSCs) from deciduous (DL-1 and DL-4 cell lines) and permanent (DL-2) teeth were used. The distribution of ECM proteins was observed using the immunofluorescence technique. The gene expression profile was evaluated using reverse transcription polymerase chain reaction (RT-PCR) analysis. Results: Positive reactions for all ECM proteins were observed independently of the hIDPSCs analyzed. Type I collagen appeared less evident in DL-2 than in other hIDPSCs. Fibronectin and tenascin were less clear in DL-4. The RT-PCR reactions showed that type I collagen was lesser expressed in the DL-2 cells, whereas fibronectin and tenascin were similarly expressed in all hIDPSCs. Conclusions: The distribution and expression of ECM proteins differ among the hIDPSCs. These differences seemed to be related to the donor tooth conditions (deciduous or permanent, retained or erupted, and degree of root reabsorption). (J Endod 2010;36:826-831)

Expression analysis of matrix metalloproteinase-9 in epithelialized and nonepithelialized apical periodontitis lesions

Objective. The objective of this study was to determine the expression of matrix metalloproteinase-9 (MMP-9) in apical periodontitis lesions. Study design. Nineteen epithelialized and 18 nonepithelialized apical periodontitis lesions were collected after periapical surgery. After histological processing, serial sectioning, H&E staining, and microscopic analysis, 10 epithelialized and 10 nonepithelialized lesions were selected for immunohistochemical analysis for MMP-9 and CD 68. At least one third of each specimen collected was frozen at -70 degrees C for further mRNA isolation and reverse transcription into cDNA for real-time-PCR procedures. Geometric averaging of multiple housekeeping genes normalized MMP-9 mRNA expression level. Results. Polymorphonuclear neutrophils, macrophages and lymphocytes presented MMP-9 positive immunostaining in both types of lesions. When present, epithelial cells were also stained. The number and the ratio of MMP-9(+)/total cells were greater in nonepithelialized than epithelialized lesions (P = .0001) presenting a positive correlation to CD68(+)/total cells (P = .045). Both types of lesions presented increased MMP-9 expression (P < .0001) when compared to healthy periapical ligaments. However, no significant differences were observed for MMP-9 mRNA expression between ephithelized and nonephithelized lesions. Conclusion. The present data suggest the participation of several inflammatory cells, mainly CD68(+) cells, in the MMP-9 expression in apical periodontitis lesions. MMP-9 could be actively enrolled in the extracellular matrix degradation in apical periodontitis lesions. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2009; 107: 127-132)

Expression of matrix metalloproteinases-2 and-9 and RECK during alveolar bone regeneration in rat

MMPs are endopeptidases that play a pivotal role in ECM turnover. RECK is a single membrane-anchored MMP-regulator. Here, we evaluated the temporal and spatial expression of MMP-2, MMP-9, and RECK during alveolar bone regeneration. The maxillary central incisor of Wistar rats was extracted and the animals were killed at 1, 3, 7, 10, 14, 21, 28, and 42 days post-operatively (n = 3/period). The hemimaxillae were collected, demineralized and embedded in paraffin. Immunohistochemical analysis was performed by the immunoperoxidase technique with polyclonal antibodies. On day 1, polymorphonuclear cells in the blood clot presented mild immunolabeling for MMPs. During bone remodeling, osteoblasts facing new bone showed positive staining for gelatinases and RECK in all experimental periods. MMPs were also found in the connective tissue and endothelial cells. Our results show for the first time that inactive and/or active forms of MMP-2, MMP-9 and RECK are differentially expressed by osteogenic and connective cells during several events of alveolar bone regeneration. This may be important for the replacement of the blood clot by connective tissue, and in the formation, maturation and remodeling of new bone.

Matrix metalloproteinase-2 and-9 involvement in canine tumors

Matrix metalloproteinases (MMPs) are a family of enzymes implicated in the degradation and remodeling of extracellular matrix and in vascularization. They are also involved in pathologic processes such as tumor invasion and metastasis in experimental cancer models and in human malignancies. We used gelatin zymography and inummohistochemistry to determine whether MMP-2 and MMP-9 are present in canine tumors and normal tissues and whether MMP production correlates with clinicopathologic parameters of prognostic importance. High levels of pro-MMP-9, pro-MMP-2, and active MMP-2 were detected in most canine tumors. Significantly higher MMP levels were measured in canine tumors than in nontumors, malignancies had higher MMP levels than benign tumors, and sarcomas had higher active MMP-2 than carcinomas. Cartilaginous tumors produced higher MMP levels than did nonsarcomatous malignancies, benign tumors, and normal tissues, and significantly greater MMP-2 than osteosarcomas and fibrosarcomas. Pro-MMP-9 production correlated with the histologic grade of osteosarcomas. The 62-kd form of active MMP-2 was detected only in high-grade, p53-positive, metastatic malignancies. Zymography proved to be a sensitive and quantitative technique for the assessment of MMP presence but has the limitation of requiring fresh tissue; inummohistochemistry is qualitative and comparatively insensitive but could be of value in archival studies. MMP presence was shown in a range of canine tumors, and their link to tumor type and grade was demonstrated for the first time. This study will allow a substantially improved evaluation of veterinary cancer patients and provides baseline information necessary for the design of clinical trials targeting MMPs.

A model updating technique based on FRFs for damped structures

Model updating methods often neglect that in fact all physical structures are damped. Such simplification relies on the structural modelling approach, although it compromises the accuracy of the predictions of the structural dynamic behaviour. In the present work, the authors address the problem of finite element (FE) model updating based on measured frequency response functions (FRFs), considering damping. The proposed procedure is based upon the complex experimental data, which contains information related to the damped FE model parameters and presents the advantage of requiring no prior knowledge about the damping matrix structure or its content, only demanding the definition of the damping type. Numerical simulations are performed in order to establish the applicability of the proposed damped FE model updating technique and its results are discussed in terms of the correlation between the simulated experimental complex FRFs and the ones obtained from the updated FE model.

Implementação e validação de um método de avaliação do perfil de ácidos gordos e do teor de gordura em alimentos por cromatografia gasosa

Nos dias de hoje é necessário criar hábitos de vida mais saudáveis que contribuam para o bem-estar da população. Adoptar medidas e práticas de modo regular e disciplinado, pode diminuir o risco do aparecimento de determinadas doenças, como a obesidade, as doenças cardiovasculares, a hipertensão, a diabetes, alguns tipos de cancro e tantas outras. É também importante salientar que, uma alimentação cuidada dá saúde e aumenta a esperança média de vida. Em Portugal, nos últimos anos, os costumes alimentares da população têm vindo a alterar-se significativamente. As refeições caseiras confeccionadas com produtos frescos dão lugar à designada “cultura do fast food”. Em contrapartida, os consumidores são cada vez mais exigentes, estando em permanente alerta no que se refere ao estado dos alimentos. A rotulagem de um produto, para além da função publicitária, tem vindo a ser objecto de legislação específica de forma a fornecer informação simples e clara, correspondente à composição, qualidade, quantidade, validade ou outras características do produto. Estas informações devem ser acessíveis a qualquer tipo de público, com mais ou menos formação e de qualquer estrato social. A qualidade e segurança dos produtos deve basear-se na garantia de que todos os ingredientes, materiais de embalagem e processos produtivos são adequados à produção de produtos seguros, saudáveis e saborosos. A Silliker Portugal, S.A. é uma empresa independente de prestação de serviços para o sector agro-alimentar, líder mundial na prestação de serviços para a melhoria da qualidade e segurança alimentar. A Silliker dedica-se a ajudar as empresas a encontrar soluções para os desafios actuais do sector, oferecendo uma ampla gama de serviços, onde se inclui o serviço de análises microbiológicas, químicas e sensorial; consultadoria em segurança alimentar e desenvolvimento; auditorias; rotulagem e legislação. A actualização permanente de procedimentos na procura de uma melhoria contínua é um dos objectivos da empresa. Para responder a um dos desafios colocados à Silliker, surgiu este trabalho, que consistiu no desenvolvimento de um novo método para determinação de ácidos gordos e da gordura total em diferentes tipos de alimentos e comparação dos resultados, com os obtidos com o método analítico até então adoptado. Se a gordura é um elemento de grande importância na alimentação, devido às suas propriedades nutricionais e organoléticas, recentemente, os investigadores têm focado a sua atenção nos mais diversos ácidos gordos (saturados, monoinsaturados e polinsaturados), em particular nos ácidos gordos essenciais e nos isómeros do ácido linoleico conjugado (CLA), uma mistura de isómeros posicionais e geométricos do ácido linoleico com actividade biológica importante. A técnica usada nas determinações foi a cromatografia gasosa com ionização de chama, GC-FID, tendo as amostras sido previamente tratadas e extraídas de acordo com o tipo de matriz. A metodologia analítica desenvolvida permitiu a correcta avaliação do perfil em ácidos gordos, tendo-se para isso usado uma mistura de 37 ésteres metílicos, em que o ácido gordo C13:0 foi usado como padrão interno. A identificação baseou-se nos tempos de retenção de cada ácido gordo da mistura e para a quantificação usaram-se os factores de resposta. A validação do método implementado foi baseada nos resultados obtidos no estudo de três matrizes relativas a materiais certificados pela BIPEA (Bureau Interprofessionnel des Etudes Analytiques), para o que foram efectuadas doze réplicas de cada matriz. Para cada réplica efectuada foi calculado o teor de matéria gorda, sendo posteriormente o resultado comparado com o emitido pela entidade certificada. Após análise de cada constituinte foi também possível calcular o teor em ácidos gordos saturados, monoinsaturados e polinsaturados. A determinação do perfil em ácidos gordos dos materiais certificados foi aceitável atendendo aos valores obtidos, os quais se encontravam no intervalo de valores admissíveis indicados nos relatórios. A quantificação da matéria gorda no que se refere à matriz de “Paté à Tartinier” apresentou um z-score de 4,3, o que de acordo com as exigências internas da Silliker, não é válido. Para as outras duas matrizes (“Mélange Nutritif” e “Plat cuisiné à base de viande”) os valores de z-score foram, respectivamente, 0,7 e -1,0, o que permite concluir a validade do método. Para que o método possa vir a ser adoptado como método alternativo é necessário um estudo mais alargado relativamente a amostras com diferentes composições. O método foi aplicado na análise de amostras de fiambre, leite gordo, queijo, ovo com ómega 3, amendoim e óleo de girassol, e os resultados foram comparados com os obtidos pelo método até então adoptado.

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.

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.