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.

Wavelength Selective a-SiC:H p-i-n/p-i-n Heterostructure for Fluorescent Proteins Detection

In this paper we present results on the optimization of multilayered a-SiC:H heterostructures that can be used as optical transducers for fluorescent proteins detection using the Fluorescence Resonance Energy Transfer approach. Double structures composed by pin based aSiC:H cells are analyzed. The color discrimination is achieved by ac photocurrent measurement under different externally applied bias. Experimental data on spectral response analysis, current-voltage characteristics and color and transmission rate discrimination are reported. An electrical model, supported by a numerical simulation gives insight into the device operation. Results show that the optimized a-SiC:H heterostructures act as voltage controlled optical filters in the visible spectrum. When the applied voltages are chosen appropriately those optical transducers can detect not only the selective excitation of specimen fluorophores, but also the subsequent weak acceptor fluorescent channel emission.

Field effect and light-assisted a-Si:H sensors for detection of ions in solution

In this paper we present an amorphous silicon device that can be used in two operation modes to measure the concentration of ions in solution. While crystalline devices present a higher sensitivity, their amorphous counterpart present a much lower fabrication cost, thus enabling the production of cheap disposable sensors for use, for example, in the food industry. The devices were fabricated on glass substrates by the PECVD technique in the top gate configuration, where the metallic gate is replaced by an electrolytic solution with an immersed Ag/AgCl reference electrode. Silicon nitride is used as gate dielectric enhancing the sensitivity and passivation layer used to avoid leakage and electrochemical reactions. In this article we report on the semiconductor unit, showing that the device can be operated in a light-assisted mode, where changes in the pH produce changes on the measured ac photocurrent. In alternative the device can be operated as a conventional ion selective field effect device where changes in the pH induce changes in the transistor's threshold voltage.

Design of a sea-level tsunami detection network for the Gulf of Cadiz

The devastating impact of the Sumatra tsunami of 26 December 2004, raised the question for scientists of how to forecast a tsunami threat. In 2005, the IOC-UNESCO XXIII assembly decided to implement a global tsunami warning system to cover the regions that were not yet protected, namely the Indian Ocean, the Caribbean and the North East Atlantic, the Mediterranean and connected seas (the NEAM region). Within NEAM, the Gulf of Cadiz is the more sensitive area, with an important record of devastating historical events. The objective of this paper is to present a preliminary design for a reliable tsunami detection network for the Gulf of Cadiz, based on a network of sea-level observatories. The tsunamigenic potential of this region has been revised in order to define the active tectonic structures. Tsunami hydrodynamic modeling and GIS technology have been used to identify the appropriate locations for the minimum number of sea-level stations. Results show that 3 tsunameters are required as the minimum number of stations necessary to assure an acceptable protection to the large coastal population in the Gulf of Cadiz. In addition, 29 tide gauge stations could be necessary to fully assess the effects of a tsunami along the affected coasts of Portugal, Spain and Morocco.

A non-pixel image reader for continuous image detection based on tandem heterostructures

An optically addressed read-write sensor based on two stacked p-i-n heterojunctions is analyzed. The device is a two terminal image sensing structure. The charge packets are injected optically into the p-i-n writer and confined at the illuminated regions changing locally the electrical field profile across the p-i-n reader. An optical scanner is used for charge readout. The design allows a continuous readout without the need for pixel-level patterning. The role of light pattern and scanner wavelengths on the readout parameters is analyzed. The optical-to-electrical transfer characteristics show high quantum efficiency, broad spectral response, and reciprocity between light and image signal. A numerical simulation supports the imaging process. A black and white image is acquired with a resolution around 20 mum showing the potentiality of these devices for imaging applications.

Tuning the spectral distribution of p-i-n a-SiC : H devices for colour detection

ZnO:Al/p (SiC:H)/i (Si:H)/n (SiC:H) large area image and colour sensor are analysed. Carrier transport and collection efficiency are investigated from dark and illuminated current-voltage (I-V) dependence and spectral response measurements under different optical and electrical bias conditions. Results show that the carrier collection depends on the optical bias and on the applied voltage. By changing the electrical bias around the open circuit voltage it is possible to filter the absorption at a given wavelength and so to tune the spectral sensitivity of the device. Transport and optical modelling give insight into the internal physical process and explain the bias control of the spectral response and the image and colour sensing properties of the devices.

Damage detection and quantification using transmissibility

Structures experience various types of loads along their lifetime, which can be either static or dynamic and may be associated to phenomena of corrosion and chemical attack, among others. As a consequence, different types of structural damage can be produced; the deteriorated structure may have its capacity affected, leading to excessive vibration problems or even possible failure. It is very important to develop methods that are able to simultaneously detect the existence of damage and to quantify its extent. In this paper the authors propose a method to detect and quantify structural damage, using response transmissibilities measured along the structure. Some numerical simulations are presented and a comparison is made with results using frequency response functions. Experimental tests are also undertaken to validate the proposed technique. (C) 2011 Elsevier Ltd. All rights reserved.

Detection of Change in Fluorescence Between Reactive Cyan and the Yellow Fluorophores Usinga-SiC:H Multilayer Transducers

Optical colour sensors based on multilayered a-SiC:H heterostructures can act as voltage controlled optical filters in the visible range. In this article we investigate the application of these structures for Fluorescence Resonance Energy Transfer (FRET) detection, The characteristics of a-SiC:H multilayered structure are studied both theoretically and experimentally in several wavelengths corresponding to different fluorophores. The tunable optical p-i'(a-SiC:H)-n/p-i(a-Si:H)-n heterostructures were produced by PECVD and tested for a proper fine tuning in the violet, cyan and yellow wavelengths. The devices were characterized through transmittance and spectral response measurements, under different electrical bias and frequencies. Violet, cyan and yellow signals were applied in simultaneous and results have shown that they can be recovered under suitable applied bias. A theoretical analysis supported by numerical simulation is presented.

Novel method using a laser scanning cytometer for detection of Mycobacteria in clinical samples

In order to evaluate the capacity of laser scanning cytometry (LSC) to detect acid-fast bacilli directly on clinical samples, a comparison between Kinyoun-stained smears analyzed under light microscopy and propidium iodide-auramine-stained smears analyzed by LSC was performed. The results were compared with those for culture on BACTEC MGIT 960. LSC is a new, reliable methodology to detect Mycobacteria.

Detection of Change in Fluorescence Between Reactive Cyan and the Yellow Fluorophores Using a-SiC:H Multilayer Transducers

The transducer consists of a semiconductor device based on two stacked -i-n heterostructures that were designed to detect the emissions of the fluorescence resonance energy transfer between fluorophores in the cyan (470 nm) and yellow (588 nm) range of the spectrum. This research represents a preliminary study on the use of such wavelength-sensitive devices as photodetectors for this kind of application. The device was characterized through optoelectronic measurements concerning spectral response measurements under different electrical and optical biasing conditions. To simulate the fluorescence resonance energy transfer (FRET) pairs, a chromatic time-dependent combination of cyan and yellow wavelengths was applied to the device. The generated photocurrent was measured under reverse and forward bias to read out the output photocurrent signal. A different wavelength-biasing light was also superimposed. Results show that under reverse bias, the photocurrent signal presents four separate levels, each one assigned to the different wavelength combinations of the FRET pairs. If a blue background is superimposed, the yellow channel is enhanced and the cyan suppressed, while under red irradiation, the opposite behavior occurs. So, under suitable biasing light, the transducer is able to detect separately the cyan and yellow fluorescence pairs. An electrical model, supported by a numerical simulation, supports the transduction mechanism of the device.

Detection of FRET signals with a wavelength sensitive device based on a-SiC:H

Glucose sensing is an issue with great interest in medical and biological applications. One possible approach to glucose detection takes advantage of measuring changes in fluorescence resonance energy transfer (FRET) between a fluorescent donor and an acceptor within a protein which undergoes glucose-induced changes in conformation. This demands the detection of fluorescent signals in the visible spectrum. In this paper we analyzed the emission spectrum obtained from fluorescent labels attached to a protein which changes its conformation in the presence of glucose using a commercial spectrofluorometer. Different glucose nanosensors were used to measure the output spectra with fluorescent signals located at the cyan and yellow bands of the spectrum. A new device is presented based on multilayered a-SiC:H heterostructures to detect identical transient visible signals. The transducer consists of a p-i'(a-SiC:H)-n/p-i(a-Si:H)-n heterostructure optimized for the detection of the fluorescence resonance energy transfer between fluorophores with excitation in the violet (400 nm) and emissions in the cyan (470 nm) and yellow (588 nm) range of the spectrum. Results show that the device photocurrent signal measured under reverse bias and using appropriate steady state optical bias, allows the separate detection of the cyan and yellow fluorescence signals. (C) 2013 Elsevier B.V. All rights reserved.

Molecular imaging agents for detection of β-amyloid plaques in Alzheimer’s disease

The formation of amyloid structures is a neuropathological feature that characterizes several neurodegenerative disorders, such as Alzheimer´s and Parkinson´s disease. Up to now, the definitive diagnosis of these diseases can only be accomplished by immunostaining of post mortem brain tissues with dyes such Thioflavin T and congo red. Aiming at early in vivo diagnosis of Alzheimer´s disease (AD), several amyloid-avid radioprobes have been developed for b-amyloid imaging by positron emission tomography (PET) and single-photon emission computed tomography (SPECT). The aim of this paper is to present a perspective of the available amyloid imaging agents, special those that have been selected for clinical trials and are at the different stages of the US Food and Drugs Administration (FDA) approval.

Analysis and simulation of a-Si Ha-SiC HPINIP structures for color image detection

It is presented in this paper a study on the photo-electronic properties of multi layer a-Si: H/a-SiC: H p-i-n-i-p structures. This study is aimed to give an insight into the internal electrical characteristics of such a structure in thermal equilibrium, under applied Was and under different illumination condition. Taking advantage of this insight it is possible to establish a relation among-the electrical behavior of the structure the structure geometry (i.e. thickness of the light absorbing intrinsic layers and of the internal n-layer) and the composition of the layers (i.e. optical bandgap controlled through percentage of carbon dilution in the a-Si1-xCx: H layers). Showing an optical gain for low incident light power controllable by means of externally applied bias or structure composition, these structures are quite attractive for photo-sensing device applications, like color sensors and large area color image detector. An analysis based on numerical ASCA simulations is presented for describing the behavior of different configurations of the device and compared with experimental measurements (spectral response and current-voltage characteristic). (c) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Automatic vehicle detection and classification

This paper presents a proposal for an automatic vehicle detection and classification (AVDC) system. The proposed AVDC should classify vehicles accordingly to the Portuguese legislation (vehicle height over the first axel and number of axels), and should also support profile based classification. The AVDC should also fulfill the needs of the Portuguese motorway operator, Brisa. For the classification based on the profile we propose:he use of Eigenprofiles, a technique based on Principal Components Analysis. The system should also support multi-lane free flow for future integration in this kind of environments.