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.

Preparation and characterization of dye-sensitized TiO2 nanorod solar cells

TiO2 nanorodswere prepared by DC reactive magnetron sputtering technique and applied to dye-sensitized solar cells (DSSCs). The length of the TiO2 nanorods was varied from 1 μm to 6 μm. The scanning electronmicroscopy images showthat the nanorods are perpendicular to the substrate. Both the X-ray diffraction patterns and Raman scattering results show that the nanorods have an anatase phase; no other phase has been observed. (101) and the (220) diffraction peaks have been observed for the TiO2 nanorods. The (101) diffraction peak intensity remained constant despite the increase of nanorod length, while the intensity of the (220) diffraction peak increased almost linearly with the nanorod length. These nanorods were used as the working electrodes in DSSCs and the effect of the nanorod length on the conversion efficiency has been studied. An optimumphotoelectric conversion efficiency of 4.8% has been achieved for 4 μm length nanorods.

Controlo e optimização da perfuração em desmonte de maciços rochosos fracturados: avaliação preliminar

O presente trabalho tem por objectivo contribuir para aprofundar o conhecimento da temática que envolve a qualidade de execução da perfuração em maciços rochosos fracturados. A necessidade de conhecimento prévio sobre os resultados que podem ocorrer no desmonte de maciços rochosos após a realização da perfuração, leva a uma procura de indicadores que possibilitem obter mais conhecimento nessa matéria. No encadeamento do processo de análise de projecto, está o conhecimento adquirido, a caracterização do maciço rochoso, a implementação de correcções na componente da perfuração ajustadas ao maciço estudado e uma potencial previsão de granulometria final por emergência de um índice de qualidade, “Índice de Dispersão Volumétrica” que correlacione os elementos constituintes da geometria do diagrama de fogo e da envolvente intrínseca da matriz rochosa e aponte uma expectável granulometria final. Para atingir um nível de qualidade na operação global do processo de desmonte, a perfuração que está no topo da pirâmide assume papel de guia para as seguintes etapas, pelo que a qualidade dos equipamentos e acessórios e a sua correcta operação são fundamentais para obter o rigor da perfuração projectada, com vista a atingir uma determinada granulometria.

Dynamic and interaction of cytochrome c with Pf1 virus

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em BioOrgânica

Refractive index matching applied to fecal smear clearing

Thick smears of human feces can be made adequate for identification of helminth eggs by means of refractive index matching. Although this effect can be obtained by simply spreading a fleck of feces on a microscope slide, a glycerol solution has been routinely used to this end. Aiming at practicability, a new quantitative technique has been developed. To enhance both sharpness and contrast of the images, a sucrose solution (refractive index = 1.49) is used, which reduces the effect of light-scattering particulates. To each slide a template-measured (38.5 mm³) fecal sample is transferred. Thus, egg counts and sensitivity evaluations are easily made.

The characteristic time of glucose diffusion measured for muscle tissue at optical clearing

The study of agent diffusion in biological tissues is very important to understand and characterize the optical clearing effects and mechanisms involved: tissue dehydration and refractive index matching. From measurements made to study the optical clearing, it is obvious that light scattering is reduced and that the optical properties of the tissue are controlled in the process. On the other hand, optical measurements do not allow direct determination of the diffusion properties of the agent in the tissue and some calculations are necessary to estimate those properties. This fact is imposed by the occurrence of two fluxes at optical clearing: water typically directed out of and agent directed into the tissue. When the water content in the immersion solution is approximately the same as the free water content of the tissue, a balance is established for water and the agent flux dominates. To prove this concept experimentally, we have measured the collimated transmittance of skeletal muscle samples under treatment with aqueous solutions containing different concentrations of glucose. After estimating the mean diffusion time values for each of the treatments we have represented those values as a function of glucose concentration in solution. Such a representation presents a maximum diffusion time for a water content in solution equal to the tissue free water content. Such a maximum represents the real diffusion time of glucose in the muscle and with this value we could calculate the corresponding diffusion coefficient.

Rat muscle opacity decrease due to the osmosis of a simple mixture

It is known that the fibrous structure of muscle causes light scattering. This phenomenon occurs due to the refractive index discontinuities located between muscle fibers and interstitial fluid. To study the possibility of reducing light scattering inside muscle, we consider its spectral transmittance evolution during an immersion treatment with an optical clearing solution containing ethanol, glycerol, and distilled water. Our methodology consists of registering spectral transmittance of muscle samples while immersed in that solution. With the spectral data collected, we represent the transmittance evolution for some wavelengths during the treatment applied. Additionally, we study the variations that the treatment has caused on the samples regarding tissue refractive index and mass. By analyzing microscopic photographs of tissue cross section, we can also verify changes in the internal arrangement of muscle fibers caused by the immersion treatment. Due to a mathematical model that we develop, we can explain the variations observed in the studied parameters and estimate the amount of optical clearing agent that has diffused into the tissue samples during the immersion treatment. At the end of the study, we observe and explain the improvement in tissue spectral transmittance, which is approximately 65% after 20 min.

Selective synthesis under microwave irradiation of new monomers for potential applications in PDLC films

Dissertation to obtain the degree of master in Bioorganic

Using gold nanoparticles in protein crystallography: studies in crystal growth and derivatization

Dissertation for the Master Degree in Structural and Functional Biochemistry

Extracting temporal and spatial distributions information about marine mucilage phenomenon based on Modis satellite images; a case study of the Tyrrhenian and the Adriatic Sea, 2010-2012

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

Printed electronics for ubiquitous computing applications

Dissertação para obtenção do Grau de Doutor em Química

Caracterização estrutural de enzimas de molibdénio e suas chaperonas

Dissertação para obtenção do Grau de Mestre em Biotecnologia

Human ceruloplasmin and neurotransmitters: complex stabilization and crystallization

Dissertation to obtain a Master Degree in Molecular Genetics and Biomedicine at Faculty of Sciences and Technology,Universidade Nova de Lisboa

Role of surfactants in filtration and fouling of colloidal silica

The EM3E Master is an Education Programme supported by the European Commission, the European Membrane Society (EMS), the European Membrane House (EMH), and a large international network of industrial companies, research centres and universities

Structural and functional characterization of ModA and TupA proteins belonging to the molybdate and tungstate transport system from desulfovibrio alaskensis G20

Fundação para a Ciência e Tecnologia - EXPL/BBB-BEP/0274/2012