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.

Modern techniques for constraint solving the CASPER experience

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Informática, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Identificação forense de ossadas por tomografia computorizada

A antropologia forense é uma disciplina das ciências forenses que trata da análise de restos cadavéricos humanos para fins legais. Uma das suas aplicações mais populares é a identificação forense que consiste em determinar o perfil biológico (idade, sexo, ancestralidade e estatura) de um indivíduo. No entanto, este processo muitas vezes é dificultado quando o corpo se encontra em avançado estado de decomposição apenas existindo restos esqueléticos. Neste caso, áreas médicas comummente utilizadas na identificação de cadáveres, como a patologia, tem de ser descartadas e surge a necessidade de aplicar outras técnicas. Neste contexto, muitos métodos antropométricos são propostos de forma a caracterizar uma pessoa através do seu esqueleto. Contudo, constata-se que a maioria dos procedimentos sugeridos é baseada em equipamentos básicos de medição, não usufruindo da tecnologia contemporânea. Assim, em parceria com a Delegação Norte do NMLCF, I. P., esta Tese teve na sua génese a criação de um sistema computacional baseado em imagens de Tomografia Computorizada (TC) de ossadas que, através de ferramentas open source, permita a realização de identificação forense. O trabalho apresentado baseia-se no processo de gestão de informação, aquisição, processamento e visualização de imagens TC. No decorrer da realização da presente Tese foi desenvolvida uma base de dados que permite organizar a informação de cada ossada e foram implementados algoritmos que levam a uma extracção de características muito mais vasta que a efetuada manualmente com os equipamentos de medição clássicos. O resultado final deste estudo consistiu num conjunto de técnicas que poderão ser englobadas num sistema computacional de identificação forense e deste modo criar uma aplicação com vantagens tecnológicas evidentes.

Using data mining techniques to support breast cancer diagnosis

More than ever, there is an increase of the number of decision support methods and computer aided diagnostic systems applied to various areas of medicine. In breast cancer research, many works have been done in order to reduce false-positives when used as a double reading method. In this study, we aimed to present a set of data mining techniques that were applied to approach a decision support system in the area of breast cancer diagnosis. This method is geared to assist clinical practice in identifying mammographic findings such as microcalcifications, masses and even normal tissues, in order to avoid misdiagnosis. In this work a reliable database was used, with 410 images from about 115 patients, containing previous reviews performed by radiologists as microcalcifications, masses and also normal tissue findings. Throughout this work, two feature extraction techniques were used: the gray level co-occurrence matrix and the gray level run length matrix. For classification purposes, we considered various scenarios according to different distinct patterns of injuries and several classifiers in order to distinguish the best performance in each case described. The many classifiers used were Naïve Bayes, Support Vector Machines, k-nearest Neighbors and Decision Trees (J48 and Random Forests). The results in distinguishing mammographic findings revealed great percentages of PPV and very good accuracy values. Furthermore, it also presented other related results of classification of breast density and BI-RADS® scale. The best predictive method found for all tested groups was the Random Forest classifier, and the best performance has been achieved through the distinction of microcalcifications. The conclusions based on the several tested scenarios represent a new perspective in breast cancer diagnosis using data mining techniques.

Detection of mycoplasmas in urethral swabs from HIV-1 infected patients and control individuals using culture techniques and polymerase chain reaction

The objective of the present study was to determine the prevalence of certain mycoplasma species, i.e., Mycoplasma hominis, Ureaplasma urealyticum and Mycoplasma penetrans, in urethral swabs from HIV-1 infected patients compared to swabs from a control group. Mycoplasmas were detected by routine culture techniques and by the Polymerase Chain Reaction (PCR) technique, using 16SrRNA generic primers of conserved region and Mycoplasma penetrans specific primers. The positivity rates obtained with the two methods were comparable. Nevertheless, PCR was more sensitive, while the culture techniques allowed the quantification of the isolates. The results showed no significant difference (p < 0.05) in positivity rates between the methods used for mycoplasma detection.

PALEOPARASITOLOGY: PERSPECTIVES WITH NEW TECHNIQUES

Paleoparasitology is the study of parasites found in archaeological material. The development of this field of research began with histological identification of helminth eggs in mummy tissues, analysis of coprolites, and recently through molecular biology. An approach to the history of paleoparasitology is reviewed in this paper, with special reference to the studies of ancient DNA identified in archaeological material.

Archaeological roman glasses: comparative characterisation by non-destructive analytical techniques

Dissertation presented in fulfilment of the requirements for the Master’s degree in Conservation and Restoration

Measurement of lead concentration in biological tissues by atomic spectroscopy techniques

Dissertation for the degree of Doctor of Philosophy in Physics

Immunoprecipitation techniques and Elisa in the detection of anti-Fonsecaea pedrosoi antibodies in chromoblastomycosis

Chromoblastomycosis (CBM) is a chronic subcutaneous infection caused by several dematiaceous fungi. The most commonly etiological agent found in Brazil is Fonsecaea pedrosoi, which appears as thick walled, brownish colored cells with transverse and longitudinal division in the lesions, called "muriform cells". This disease is found worldwide but countries like Madagascar and Brazil have highest incidence. Diagnosis is made by clinical, direct and histopathologic examination and culture of specimens. Serological tests have been used to identify specific antibodies against Fonsecaea pedrosoi antigens, as well as immunotechniques have been used for CBM serological identification and diagnosis. In the present study double immunodiffusion (DID), counterimmunoelectrophoresis (CIE) and immunoenzymatic test (ELISA) have been used to evaluate humoral immune response in patients with CBM caused by F. pedrosoi. Metabolic antigen was used for immunoprecipitation tests (DID and CIE) while somatic antigen for ELISA. Our results demonstrated 53% sensitivity and 96% specificity for DID, while CIE presented 68% sensitivity and 90.5% specificity. ELISA demonstrated 78% sensibility and 83% specificity. Serological tests can be a useful tool to study different aspects of CBM, such as helping differential diagnosis, when culture of the pathogenic agent is impossible.

Comparison between immunomagnetic separation, coupled with immunofluorescence, and the techniques of Faust et al. and of Lutz for the diagnosis of Giardia lamblia cysts in human feces

In the present study, the performance of Immunomagnetic Separation technique, coupled with Immunofluorescence (IMS-IFA), was compared with the FAUST et al. and Lutz parasitological techniques for the detection of Giardia lamblia cysts in human feces. One hundred and twenty-seven samples were evaluated by the three techniques at the same time showing a rate of cyst detection of 27.5% by IMS-IFA and 15.7% by both Faust et al. and Lutz techniques. Data analysis showed a higher sensitivity of IMS-IFA for the detection of G. lamblia cysts in comparison with the techniques of FAUST et al. and Lutz. The use of this methodology as a routine procedure enables the processing of many samples simultaneously, in order to increase recovery rate of G. lamblia cysts and reduce the time of sample storage.

Integer/fractional decomposition of the impulse response of fractional linear systems

The decomposition of a fractional linear system is discussed in this paper. It is shown that it can be decomposed into an integer order part, corresponding to possible existing poles, and a fractional part. The first and second parts are responsible for the short and long memory behaviors of the system, respectively, known as characteristic of fractional systems.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.