Development of TNBS-induced colitis: animal model to test new pharmacological approaches

IBD is a gastro-intestinal disorder marked with chronic inflammation of intestinal epithelium, damaging mucosal tissue and manifests into several intestinal and extra-intestinal symptoms. Currently used medical therapy is able to induce and maintain the patient in remission, however no modifies or reverses the underlying pathogenic mechanism. The research of other medical approaches is crucial to the treatment of IBD and, for this, it´s important to use animal models to mimic the characteristics of disease in real life. The aim of the study is to develop an animal model of TNBS-induced colitis to test new pharmacological approaches. TNBS was instilled intracolonic single dose as described by Morris et al. It was administered 2,5% TNBS in 50% ethanol through a catheter carefully inserted into the colon. Mice were kept in a Tredelenburg position to avoid reflux. On day 4 and 7, the animals were sacrificed by cervical dislocation. The induction was confirmed based on clinical symptoms/signs, ALP determination and histopathological analysis. At day 4, TNBS group presented a decreased body weight and an alteration of intestinal motility characterized by diarrhea, severe edema of the anus and moderate morbidity, while in the two control groups weren’t identified any alteration on the clinical symptoms/signs with an increase of the body weight. TNBS group presented the highest concentrations of ALP comparing with control groups. The histopathology analysis revealed severe necrosis of the mucosa with widespread necrosis of the intestinal glands. Severe hemorrhagic and purulent exsudates were observed in the submucosa, muscular and serosa. TNBS group presented clinical symptoms/signs and histopathological features compatible with a correct induction of UC. The peak of manifestations became maximal at day 4 after induction. This study allows concluding that it’s possible to develop a TNBS induced colitis 4 days after instillation.

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.

Efeito fisiológico da cafeína em estudos neurológicos com base na ponderação em susceptibilidade ferromagnética (SWI)

Introdução – O presente estudo avaliou o efeito da cafeína no valor da razão contraste ruído (CNR) em imagens SWI. Objetivos – Avaliar o efeito da cafeína qualitativamente e quantificado pelo cálculo do valor CNR em imagens de magnitude e MIP para as estruturas: veia cerebral interna, seio sagital superior, tórcula e artéria cerebral média. Metodologia – A população do estudo incluiu 24 voluntários saudáveis que estiveram pelo menos 24h privados da ingestão de cafeína. Adquiriram-se imagens SWI antes e após a ingestão de 100ml de café. Os voluntários foram subdivididos em quatro grupos de seis indivíduos/grupo e avaliados separadamente após decorrido um intervalo de tempo diferente para cada grupo (15, 25, 30 ou 45min pós-cafeína). Utilizou-se um scanner Siemens Avanto 1,5 T com bobine standard de crânio e os parâmetros: T2* GRE 3D de alta resolução no plano axial, TR=49; TE=40; FA=15; FOV=187x230; matriz=221x320. O processamento de imagem foi efetuado no software OsiriX® e a análise estatística no GraphPadPrism®. Resultados e Discussão – As alterações de sinal e diferenças de contraste predominaram nas estruturas venosas e não foram significantes na substância branca, LCR e artéria cerebral média. Os valores CNR pré-cafeína diferiram significativamente do pós-cafeína nas imagens de magnitude e MIP na veia cerebral interna e nas imagens de magnitude do seio sagital superior e da tórcula (p<0,0001). Não se verificaram diferenças significativas entre os grupos avaliados nos diferentes tempos pós-cafeína. Conclusões – Especulamos que a cafeína possa vir a ser usada como agente de contraste nas imagens SWI barato, eficaz e de fácil administração.

Development and validation of a psychometric scale for assessing PA chest image quality: a pilot study

Purpose - To develop and validate a psychometric scale for assessing image quality perception for chest X-ray images. Methods - Bandura's theory was used to guide scale development. A review of the literature was undertaken to identify items/factors which could be used to evaluate image quality using a perceptual approach. A draft scale was then created (22 items) and presented to a focus group (student and qualified radiographers). Within the focus group the draft scale was discussed and modified. A series of seven postero-anterior chest images were generated using a phantom with a range of image qualities. Image quality perception was confirmed for the seven images using signal-to-noise ratio (SNR 17.2–36.5). Participants (student and qualified radiographers and radiology trainees) were then invited to independently score each of the seven images using the draft image quality perception scale. Cronbach alpha was used to test interval reliability. Results - Fifty three participants used the scale to grade image quality perception on each of the seven images. Aggregated mean scale score increased with increasing SNR from 42.1 to 87.7 (r = 0.98, P < 0.001). For each of the 22 individual scale items there was clear differentiation of low, mid and high quality images. A Cronbach alpha coefficient of >0.7 was obtained across each of the seven images. Conclusion - This study represents the first development of a chest image quality perception scale based on Bandura's theory. There was excellent correlation between the image quality perception scores derived using the scale and the SNR. Further research will involve a more detailed item and factor analysis.

Increasing source to image distance for AP pelvis imaging: impact on radiation dose and image quality

Aim - A quantative primary study to determine whether increasing source to image distance (SID), with and without the use of automatic exposure control (AEC) for antero-posterior (AP) pelvis imaging, reduces dose whilst still producing an image of diagnostic quality. Methods - Using a computed radiography (CR) system, an anthropomorphic pelvic phantom was positioned for an AP examination using the table bucky. SID was initially set at 110 cm, with tube potential set at a constant 75 kVp, with two outer chambers selected and a fine focal spot of 0.6 mm. SID was then varied from 90 cm to 140 cm with two exposures made at each 5 cm interval, one using the AEC and another with a constant 16 mAs derived from the initial exposure. Effective dose (E) and entrance surface dose (ESD) were calculated for each acquisition. Seven experienced observers blindly graded image quality using a 5-point Likert scale and 2 Alternative Forced Choice software. Signal-to-Noise Ratio (SNR) was calculated for comparison. For each acquisition, femoral head diameter was also measured for magnification indication. Results - Results demonstrated that when increasing SID from 110 cm to 140 cm, both E and ESD reduced by 3.7% and 17.3% respectively when using AEC and 50.13% and 41.79% respectively, when the constant mAs was used. No significant statistical (T-test) difference (p = 0.967) between image quality was detected when increasing SID, with an intra-observer correlation of 0.77 (95% confidence level). SNR reduced slightly for both AEC (38%) and no AEC (36%) with increasing SID. Conclusion - For CR, increasing SID significantly reduces both E and ESD for AP pelvis imaging without adversely affecting image quality.

Espetroscopia (1H) por ressonância magnética do disco intervertebral lombar no adulto e sua aplicação na rotina imagiológica

Objetivos – Demonstrar o potencial da espetroscopia (1H) por ressonância magnética na doença degenerativa discal lombar e defender a integração desta técnica na rotina clínico‑imagiológica para a precisa classificação da involução vs degenerescência dos discos L4‑L5 e L5‑S1 em doentes com lombalgia não relacionável com causa mecânica. Material e métodos – O estudo incluiu 102 discos intervertebrais lombares de 123 doentes. Foram estudados 61 discos de L4‑L5, 41 discos de L5‑S1 e 34 discos de D12‑L1. Utilizou‑se um sistema de ressonância magnética de 1,5 T e técnica monovoxel. Obtiveram‑se os rácios [Lac/Nacetyl] e [Nacetyl/(Lac+Lípidos)] e aplicou‑se a ressonância de lípidos para avaliar a bioquímica do disco com o fim de conhecer o estado de involução vs degenerescência que o suscetibilizam para a instabilidade e sobrecarga. Avaliou‑se o comportamento dos rácios e do teor lipídico dos discos L4‑L5‑S1 e as diferenças apresentadas em relação a D12‑L1. Foi também realizada a comparação entre os discos L4‑L5, L5‑S1 e D12‑L1 na ponderação T2 (T2W), segundo a classificação ajustada (1‑4) de Pfirrmann. Resultados – Verificou‑se que os rácios e o valor dos lípidos dos discos L4‑L5‑S1 apresentaram diferenças estatisticamente significativas quando relacionados com os discos D12‑L1. O rácio [Lac/Nacetyl] em L4‑L5‑S1 mostrou‑se aumentado em relação a D12‑L1 (p=0,033 para os discos com grau de involução [1+2] e p=0,004 para os discos com grau [3+4]). Estes resultados sugerem que a involução vs degenerescência dos discos nos graus mais elevados condiciona um decréscimo do pico do Lactato. O rácio [Nacetyl/(Lac+Lip)] discrimina os graus de involução [1+2] do [3+4] no nível L4‑L5, apresentando os valores dos rácios (média 0,65 e 0,5 respetivamente com p=0,04). O rácio médio de [Nacetyl/(Lac+Lip)] dos discos L4‑L5 foi 1,8 vezes mais elevado do que em D12‑L1. O espetro lipídico em L4‑L5‑S1 nos graus mais elevados não mostrou ter uma prevalência constante quanto às frequências de ressonância. Conclusão – A espetroscopia (1H) dos discos intervertebrais poderá ter aplicação na discriminação dos graus de involução vs degenerescência e representar um contributo semiológico importante em suplemento à ponderação T2 convencional. As ressonâncias de lípidos dos discos L4‑L5 e L5‑S1, involuídos ou degenerados, devem ser avaliadas em relação a D12‑L1, utilizando este valor como referência, pois este último é o nível considerado estável e com baixa probabilidade de degenerescência.

PV system modeling by five parameters and in situ test

This paper focuses on a novel formalization for assessing the five parameter modeling of a photovoltaic cell. An optimization procedure is used as a feasibility problem to find the parameters tuned at the open circuit, maximum power, and short circuit points in order to assess the data needed for plotting the I-V curve. A comparison with experimental results is presented for two monocrystalline PV modules.

Does 6-minutes walk test predict functional capacity in elderly people?

Portugal has an accentuated aging tendency, presenting an elderly population (individuals with more than 65 years old) of 19.2%. The average life expectancy is 79.2 years. Thus, it’s important to maintain autonomy and independency as long as possible. Functional ability concept rises from the need to evaluate the capacity to conduct daily activities in an independent way. It can be estimated with the 6-minute walk test (6MWT) and other validated test. This test is simple, reliable, valid and consists in a daily activity (walk). The goals of this study was to verify associations between functional capacity measured with two different instruments (6MWT and Composite Physical Function (CPF) scale) and between those results and characterization variables.

PV system modeling by five parameters and in Situ test

This paper focuses on a novel formalization for assessing the five parameter modeling of a photovoltaic cell. An optimization procedure is used as a feasibility problem to find the parameters tuned at the open circuit, maximum power, and short circuit points in order to assess the data needed for plotting the I-V curve. A comparison with experimental results is presented for two monocrystalline PV modules.

Avaliação do gasto energético em amputados de membro inferior utilizando o Six-Minute Walk Test

A capacidade de deambulação apresenta um significado bastante importante para a população em geral, uma vez que contribui para a manutenção do estado de saúde e para a reabilitação e melhoria da condição física, de uma forma geral. A amputação de um membro inferior, com ou sem abordagem protésica, impõe, ao amputado, um aumento no gasto energético durante a deambulação. A medição do gasto energético durante a marcha em amputados serve, não só para quantificar o esforço requerido, mas também para comparar a eficácia de diferentes componentes protésicos. Objetivos do estudo - Determinação dos fatores que influenciam a capacidade funcional dos amputados do membro inferior. Perceção do impacto das características pessoais, quadro clínico, hábitos e fatores comportamentais, bem como componentes protésicos no consumo de oxigénio e capacidade de deambulação.

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.