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.

Hyperspectral imagery framework for unmixing and dimensionality estimation

In hyperspectral imagery a pixel typically consists mixture of spectral signatures of reference substances, also called endmembers. Linear spectral mixture analysis, or linear unmixing, aims at estimating the number of endmembers, their spectral signatures, and their abundance fractions. This paper proposes a framework for hyperpsectral unmixing. A blind method (SISAL) is used for the estimation of the unknown endmember signature and their abundance fractions. This method solve a non-convex problem by a sequence of augmented Lagrangian optimizations, where the positivity constraints, forcing the spectral vectors to belong to the convex hull of the endmember signatures, are replaced by soft constraints. The proposed framework simultaneously estimates the number of endmembers present in the hyperspectral image by an algorithm based on the minimum description length (MDL) principle. Experimental results on both synthetic and real hyperspectral data demonstrate the effectiveness of the proposed algorithm.

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.

Parallel sparse unmixing of hyperspectral data

In this paper, a new parallel method for sparse spectral unmixing of remotely sensed hyperspectral data on commodity graphics processing units (GPUs) is presented. A semi-supervised approach is adopted, which relies on the increasing availability of spectral libraries of materials measured on the ground instead of resorting to endmember extraction methods. This method is based on the spectral unmixing by splitting and augmented Lagrangian (SUNSAL) that estimates the material's abundance fractions. The parallel method is performed in a pixel-by-pixel fashion and its implementation properly exploits the GPU architecture at low level, thus taking full advantage of the computational power of GPUs. Experimental results obtained for simulated and real hyperspectral datasets reveal significant speedup factors, up to 1 64 times, with regards to optimized serial implementation.

Biometric recognition system using low bandwidth ECG signals

Biometric recognition has recently emerged as part of applications where the privacy of the information is crucial, as in the health care field. This paper presents a biometric recognition system based on the Electrocardiographic signal (ECG). The proposed system is based on a state-of-the-art recognition method which extracts information from the frequency domain. In this paper we propose a new method to increase the spectral resolution of low bandwidth ECG signals due to the limited bandwidth of the acquisition sensor. Preliminary results show that the proposed scheme reveals a higher identification rate and lower equal error rate when compared to previous approaches.

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.

Comparison of Disposable Pipette Extraction and Dispersive Solid-Phase Extraction in the QuEChERS Method for Analysis of Pesticides in Strawberries

In this study, we sought to assess the applicability of GC–MS/MS for the identification and quantification of 36 pesticides in strawberry from integrated pest management (IPM) and organic farming (OF). Citrate versions of QuEChERS (quick, easy, cheap, effective, rugged and safe) using dispersive solid-phase extraction (d-SPE) and disposable pipette extraction (DPX) for cleanup were compared for pesticide extraction. For cleanup, a combination of MgSO4, primary secondary amine and C18 was used for both the versions. Significant differences were observed in recovery results between the two sample preparation versions (DPX and d-SPE). Overall, 86% of the pesticides achieved recoveries (three spiking levels 10, 50 and 200 µg/kg) in the range of 70–120%, with <13% RSD. The matrix effects were also evaluated in both the versions and in strawberries from different crop types. Although not evidencing significant differences between the two methodologies were observed, however, the DPX cleanup proved to be a faster technique and easy to execute. The results indicate that QuEChERS with d-SPE and DPX and GC–MS/MS analysis achieved reliable quantification and identification of 36 pesticide residues in strawberries from OF and IPM.

Enzyme linked immunosorbent assay for rubella antibodies: a simple method of antigen production. A preliminary report

A simple method of rubella antigen production by treatment with sodium desoxycholate for use in enzyme immunoassay (IMT-ELISA) is presented. When this assay was compared with a commercial test (Enzygnost-Rubella, Behring), in the study of 108 sera and 118 filter paper blood samples, 96.9% (219/226) overall agreement and correlation coefficient of 0.90 between absorbances were observed. Seven samples showed discordant results, negative by the commercial kit and positive by our test. Four of those 7 samples were available, being 3 positive by HI.

A simple and inexprensive method to generate a microaerophilic atmosphere for the isolation of Campylobacter sp

Faeces of 138 chickens were inoculated on Blaser agar plates. One set of plates was incubated in jars with CampyPak envelopes. The others were incubated in "Zip-lock" plastic bags (7 x X in.) and a microaerophilic atmosphere was generated exhaling into the "Zip-lock" plastic bag, after holding the breath for 20 sec. Then, the bag was pressed to evacuate its atmosphere, inflated again, and pressed (4 times), and finally sealed. Campylobacter was isolated from 127 (96.2%) of samples incubated in jars with gas generator envelopes and from 129 (98%) of the specimens incubated into the bags. The proposed methodology offers good savings for cost-conscious laboratories.

Studies on prevalence of Strongyloides infection in Holambra and Maceió, Brazil, by the agar plate faecal culture method

Prevalence of Strongyloides stercoralis infection in three areas of Brazil was surveyed by a recently developed faecal culture method (an agar plate culture). The Strongyloides infection was confirmed in 11.3% of 432 subjects examined. The diagnostic efficacy of the agar plate culture was as high as 93.9% compared to only 28.5% and 26.5% by the Harada-Mori filter paper culture and faecal concentration methods, when faecal samples were examined simultaneously by these three methods. Among the 49 positive samples, about 60% were confirmed to be positive only by the agar plate culture. These results indicate that the agar plate culture is a sensitive new tool for the correct diagnosis of chronic Strongyloides infection.

A single method to stain Malassezia furfur and Corynebacterium minutissimum in scales

A single and practical method to slain Malassezia furfur and Corynebacterium minutissimum in lesions' scales is described. The scales are collected by pressing small pieces of scotch tape (about 4 cm lenght and 2 cm width) onto the lesions and following withdrawl the furfuraceous scales will remain on the glue side. These pieces are then immersed for some minutes in lactophenol-cotton blue stain. Following absorption of the stain the scales are washed in current water to remove the excess of blue stain, dried with filter paper, dehydrated via passage in two bottles containing absolute alcohol and then placed in xylene in a centrifugation tube. The xylene dissolves the scotch tape glue and the scales fall free in the tube. After centrifugation and decantation the scales concentrated on the bottom of the tube are collected with a platinum-loop, placed in Canada balsam on a microscopy slide and closed with a cover slip. The preparations are then ready to be submitted to microscopic examination. Other stains may also be used instead of lactophenol-cotton blue. This method is simple, easily performed, and offers good conditions to study these fungi as well as being useful for the diagnosis of the diseases that they cause.

Application of the EcoBlock method to eco-design - electric hand dryers versus paper towels

Sustainable Construction, Materials and Practice, p. 426-432

Detection and identification of dengue virus isolates from Brazil by a simplified reverse transcription - polymerase chain reaction (RT-PCR) method

We show here a simplified RT-PCR for identification of dengue virus types 1 and 2. Five dengue virus strains, isolated from Brazilian patients, and yellow fever vaccine 17DD as a negative control, were used in this study. C6/36 cells were infected and supernatants were collected after 7 days. The RT-PCR, done in a single reaction vessel, was carried out following a 1/10 dilution of virus in distilled water or in a detergent mixture containing Nonidet P40. The 50 µl assay reaction mixture included 50 pmol of specific primers amplifying a 482 base pair sequence for dengue type 1 and 210 base pair sequence for dengue type 2. In other assays, we used dengue virus consensus primers having maximum sequence similarity to the four serotypes, amplifying a 511 base pair sequence. The reaction mixture also contained 0.1 mM of the four deoxynucleoside triphosphates, 7.5 U of reverse transcriptase, 1U of thermostable Taq DNA polymerase. The mixture was incubated for 5 minutes at 37ºC for reverse transcription followed by 30 cycles of two-step PCR amplification (92ºC for 60 seconds, 53ºC for 60 seconds) with slow temperature increment. The PCR products were subjected to 1.7% agarose gel electrophoresis and visualized by UV light after staining with ethidium bromide solution. Low virus titer around 10 3, 6 TCID50/ml was detected by RT-PCR for dengue type 1. Specific DNA amplification was observed with all the Brazilian dengue strains by using dengue virus consensus primers. As compared to other RT-PCRs, this assay is less laborious, done in a shorter time, and has reduced risk of contamination

A study on parallel versus sequential relational fuzzy clustering methods

Dissertação para obtenção do Grau de Mestre em Engenharia Informática