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.

Usefulness of the detection of Toxoplasma gondii antigens in AIDS patients

Toxoplasmic encephalitis (TE) is a mayor cause of central nervous system infection in patients with acquired immunodeficiency syndrome (AIDS). Toxoplasma antibodies were detected in 56 of 79 patients with AIDS (71%), in the present study. Fourteen out of 57 seropositive patients developed TF (25%) and had Toxoplasma gondii antigen detected in their urine. For this, most of them received an effective therapy, with the subsequent disappearance of the symptoms and discontinuity of excretion of the T. gondii antigens. Our results suggest that the monitoring of T. gondii antigen in the urine of AIDS patients may be useful to decide on the proper time for therapy, as well as to avoid the beginning of neurologic signs in these patients.

Dot-enzyme-linked immunosorbent assay (Dot-ELISA) for detection of pneumococcal polysaccharide antigens in pleural fluid effusion samples.: Comparison with bacterial culture, counterimmunoelectrophoresis and latex agglutination

A dot-enzyme-linked immunosorbent assay (Dot-ELISA) for pneumococcal antigen detection was standardized in view of the need for a rapid and accurate immunodiagnosis of acute pneumococcal pneumonia. A total of 442 pleural fluid effusion samples (PFES) from children with clinical and laboratory diagnoses of acute bacterial pneumonia, plus 38 control PFES from tuberculosis patients and 20 negative control serum samples from healthy children were evaluated by Dot-ELISA. The samples were previously treated with 0.1 M EDTA pH 7.5 at 90°C for 10 min and dotted on nitrocellulose membrane. Pneumococcal omniserum diluted at 1:200 was employed in this assay for antigen detection. When compared with standard bacterial culture, counterimmunoelectrophoresis and latex agglutination techniques, the Dot-ELISA results showed relative indices of 0.940 to sensitivity, 0.830 to specificity and 0.760 to agreement. Pneumococcal omniserum proved to be an optimal polyvalent antiserum for the detection of pneumococcal antigen by Dot-ELISA. Dot-ELISA proved to be a practical alternative technique for the diagnosis of pneumococcal pneumonia.

Entamoeba histolytica: detection of coproantigens by purified antibody in the capture sandwich ELISA

A sensitive and specific Capture Sandwich ELISA (CSE) was developed using polyclonal purified rabbit antibodies against three different axenic strains of Entamoeba histolytica: CSP from Brazil and HM1 - IMSS from Mexico, for the detection of coproantigens in fecal samples. Immunoglobulin G (IgG) againstis E. histolytica was isolated from rabbits immunized with throphozoites whole extract in two stages: affinity chromatography in a column containing E. histolytica antigens bound to Sepharose 4B was followed by another chromatography in Sepharose antibodies 4B-Protein A. A Capture Sandwich ELISA using purified antibodies was able to detect 70ng of amebae protein, showing a sensitivity of 93% and specificity of 94%. The combination of microscopic examination and CSE gave a concordance and discordance of 93.25% and 6.75%, respectively. It was concluded that CSE is highly specific for the detection of coproantigens of E. histolytica in feces of infected patients, is quicker to perform, easier and more sensitive than microscopic examination.

Pattern of mycobacterial antigen detection in leprosy

Immunohistochemistry reaction (Peroxidase anti-peroxidase - PAP) was carried out on fifty-two skin biopsies from leprosy patients with the purpose to identify the antigenic pattern in mycobacteria and to study the sensitivity of this method. Five different patterns were found: bacillar, granular, vesicular, cytoplasmatic and deposits, classified according to the antigenic material characteristics. Deposits (thinely particulate material) appeared more frequently, confirming the immunohistochemistry sensitivity to detect small amounts of antigens even when this material is not detected by histochemical stainings.

Dot-ELISA for the detection of IgM and IgG antibodies to Schistosoma mansoni worm and egg antigens, associated with egg excretion by patients

Human schistosomiasis, caused by Schistosoma mansoni, is highly prevalent in Brazil and usually diagnosed by time consuming stool analysis. Serological tests are of limited use in this disease, mainly for epidemiological studies, showing no discrimination between previous contact with the parasite and active infections. In the present study, we standardized and compared a Dot-ELISA for IgM and IgG antibodies against S. mansoni antigens from eggs and worms with a routine IgG and IgM immunofluorescence assay using similar antigens, in the study of sera from 27 patients who had quantified egg stool excretion. The positivity obtained for IgG Dot-ELISA was 96.3% and 88.9% for IgM Dot-ELISA with worm antigen and 92.6% and 90.9% with egg antigen. The IFI presented similar positivities using worm antigen, 92.6% (IgG) and 96.3% (IgM),and lower results with egg antigen, 77.8% (IgG and IgM). The patients studied were divided into two groups according to their egg excretion, with greater positivity of serological tests in higher egg excreters. When comparing the quantitative egg excretion and the serological titers of the patients, we detected a correlation only with IgM Dot-ELISA, with r=0.552 (p=0.0127). These data show that Dot-ELISA can be used for the detection of specific antibodies against S. mansoni in sera from suspected patients or in epidemiological studies and, with further purification of egg antigen and larger samples, IgM Dot-ELISA could be a possible tool for rough estimates of parasite burden in epidemiological studies.

Central nervous system virion detection in acute measles: histopathological, ultrastructural and pathogenetic aspects

Histopathological and ultrastructural studies of 23 patients who died with clinical diagnosis of measles were carried out. In 12 cases viral nucleocapsids were searched by electron microscopy and detected in 100% of the cases in the lungs and in 50% of the cases in the central nervous system. They were mostly intranuclear. Histopathological changes associated to neurological alterations and the detection of virion are discussed in relation to acute and delayed clinical manifestations.

Bacterial antigen detection in cerebrospinal fluid by the latex agglutination test

Eighty purulent cerebrospinal fluid (CSF) samples from patients with clinical evidence of meningitis were studied using the Directigen latex agglutination (LA) kit to determine the presence of bacterial antigen in CSF. The results showed a better diagnostic performance of the LA test than bacterioscopy by Gram stain, culture and counterimmunoelectrophoresis (CIE), as far as Neisseria meningitidis groups B and C, and Haemophilus influenzae type b are concerned, and a better performance than bacterioscopy and culture considering Streptococcus pneumoniae. Comparison of the results with those of culture showed that the LA test had the highest sensitivity for the Neisseria meningitidis group C. Comparing the results with those of CIE, the highest levels of sensitivity were detected for N. meningitidis groups B and C. Regarding specificity, fair values were obtained for all organisms tested. The degree of K agreement when the LA test was compared with CIE exhibited better K indices of agreement for N. meningitidis groups B and C.

Detection of Cryptococcus neoformans capsular polysaccharide antigen in asymptomatic HIV-infected patients

Serum samples from 242 HIV-positive persons were studied for the detection of capsular polysaccha-ride antigen of Cryptococcus neoformans; 193 of these patients presented less than 300 CD4+ cells/µl of blood and 49 patients had more than 300 CD4+ cells/µl. None of them had symptoms or signs characteristic of cryptococcosis. The capsular antigen of C. neofarmans was detected by latex agglutination technique with pronase pre-treatment (IMMY, Crypto-Latex Antigen Detection System, Immunomycologics Inc., OK, USA); in 61% of the samples, ELISA technique was also used (Premier, Cryptococcal Antigen, Meridian Diagnostic Inc., Cincinatti, Oh, USA). The comparative study of both methods showed that the results obtained were similar in 96.9% of the cases. The capsular antigen was detected in 13 out of 193 (6.7%) patients with less than 300 CD4+ cells/µl. Cryptococcosis was confirmed mycologically in 3 of these 13 cases (23%) by the isolation of C. neoformans in CSF or blood cultures. Three patients, who had presented negative results of both tests for capsular antigen, suffered disseminated cryptococcosis 4 to 8 months later. The predictive diagnostic value of capsular antigen detection of C. neoformans seems tobe low and we believe that it should not be done routinely in asymptomatic HIV-positive persons.

New analytical methodologies for doping control – detection of anabolic androgenic steroids in human urine

Dissertation submitted to Faculdade de Ciências e Tecnologia - Universidade Nova de Lisboa in fulfilment of the requirements for the degree of Doctor of Philosophy (Biochemistry - Biotechnology)

Spatial metrics and Landsat data for urban landuse change detection: case of Addis Ababa, Ethiopia.

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies.

DNA nanoprobes for molecular detection

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Biológica – especialidade Engenharia Genética, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Immunoperoxidase for the detection for the detection of antibodies in cerebrospinal fluid in neurocysticercosis: use of Cysticercus cellulosae and Cysticercus longicollis particles fixed on microscopy slides

The ORF strain of Cysticercus longicollis represents an important model for the study of heterologous antigens in the immunodiagnosis of neurocysticercosis (NC). The immunoperoxidase (IP) technique was standardized using a particulate antigen suspension of Cysticercus longicollis (Cl) and Cysticercus cellulosae (Cc). Cerebrospinal fluid (CSF) samples were incubated on the antigen fixed to microscopy slides; the conjugate employed was anti-IgG-peroxidase and the enzymatic reaction was started by covering the slides with chromogen solution (diaminobenzidine/H2O2). After washing with distilled water, the slide was stained with 2% malachite green in water. Of the CSF samples from 21 patients with NC, 19 (90.5%) were positive, whereas the 8 CSF samples from the control group (100%) were negative. The results of the IP-Cl test applied to 127 CSF samples from patients with suspected NC showed 28.3% reactivity as opposed to 29.1 % for the IP-Cc test. The agreement index for the IP test (Cl x Cc) was 94.2%, with no significant difference between the two antigens.

Multilayer Perceptron Neural Networks Training Through Charged System Search and its Application for Non-Technical Losses Detection

The non-technical loss is not a problem with trivial solution or regional character and its minimization represents the guarantee of investments in product quality and maintenance of power systems, introduced by a competitive environment after the period of privatization in the national scene. In this paper, we show how to improve the training phase of a neural network-based classifier using a recently proposed meta-heuristic technique called Charged System Search, which is based on the interactions between electrically charged particles. The experiments were carried out in the context of non-technical loss in power distribution systems in a dataset obtained from a Brazilian electrical power company, and have demonstrated the robustness of the proposed technique against with several others natureinspired optimization techniques for training neural networks. Thus, it is possible to improve some applications on Smart Grids.