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.

IOPT Petri Net State Space Generation Algorithm with Maximal-Step Execution Semantics

This paper presents an algorithm to efficiently generate the state-space of systems specified using the IOPT Petri-net modeling formalism. IOPT nets are a non-autonomous Petri-net class, based on Place-Transition nets with an extended set of features designed to allow the rapid prototyping and synthesis of system controllers through an existing hardware-software co-design framework. To obtain coherent and deterministic operation, IOPT nets use a maximal-step execution semantics where, in a single execution step, all enabled transitions will fire simultaneously. This fact increases the resulting state-space complexity and can cause an arc "explosion" effect. Real-world applications, with several million states, will reach a higher order of magnitude number of arcs, leading to the need for high performance state-space generator algorithms. The proposed algorithm applies a compilation approach to read a PNML file containing one IOPT model and automatically generate an optimized C program to calculate the corresponding state-space.

Comparação do cálculo de dose com os algoritmos Analytical Anisotropic Algorithm e Pencil Beam Convolution na patologia de pulmão

Mestrado em Radioterapia.

Comparação entre o pencil beam convolution algorithm e o analytical anisotropic algorithm em tumores de mama

Mestrado em Radioterapia

Dependent component analysis: a hyperspectral unmixing algorithm

Linear unmixing decomposes a hyperspectral image into a collection of reflectance spectra of the materials present in the scene, called endmember signatures, and the corresponding abundance fractions at each pixel in a spatial area of interest. This paper introduces a new unmixing method, called Dependent Component Analysis (DECA), which overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical properties of hyperspectral data. DECA models the abundance fractions as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum. The mixing matrix is inferred by a generalized expectation-maximization (GEM) type algorithm. The performance of the method is illustrated using simulated and real data.

Vertex component analysis: a fast algorithm to extract endmembers spectra from hyperspectral data

Chapter in Book Proceedings with Peer Review First Iberian Conference, IbPRIA 2003, Puerto de Andratx, Mallorca, Spain, JUne 4-6, 2003. Proceedings

Vertex component analysis: a fast algorithm to unmix hyperspectral data

Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

Comparison of the pencil beam convolution algorithm and the analytical anisotropic algorithm in breast tumors

The calculation of the dose is one of the key steps in radiotherapy planning1-5. This calculation should be as accurate as possible, and over the years it became feasible through the implementation of new algorithms to calculate the dose on the treatment planning systems applied in radiotherapy. When a breast tumour is irradiated, it is fundamental a precise dose distribution to ensure the planning target volume (PTV) coverage and prevent skin complications. Some investigations, using breast cases, showed that the pencil beam convolution algorithm (PBC) overestimates the dose in the PTV and in the proximal region of the ipsilateral lung. However, underestimates the dose in the distal region of the ipsilateral lung, when compared with analytical anisotropic algorithm (AAA). With this study we aim to compare the performance in breast tumors of the PBC and AAA algorithms.

A SON Enhanced Algorithm for Observed Time Differences Based Geolocation in Real 3G Networks

Conferência - 16th International Symposium on Wireless Personal Multimedia Communications (WPMC)- Jun 24-27, 2013

Comparação entre o pencil beam convolution algorithm e o analytical anisotropic algorithm em tumores de mama

Objectivo do estudo: comparar o desempenho dos algoritmos Pencil Beam Convolution (PBC) e do Analytical Anisotropic Algorithm (AAA) no planeamento do tratamento de tumores de mama com radioterapia conformacional a 3D.

Coding mode decision algorithm for binary descriptor coding

In visual sensor networks, local feature descriptors can be computed at the sensing nodes, which work collaboratively on the data obtained to make an efficient visual analysis. In fact, with a minimal amount of computational effort, the detection and extraction of local features, such as binary descriptors, can provide a reliable and compact image representation. In this paper, it is proposed to extract and code binary descriptors to meet the energy and bandwidth constraints at each sensing node. The major contribution is a binary descriptor coding technique that exploits the correlation using two different coding modes: Intra, which exploits the correlation between the elements that compose a descriptor; and Inter, which exploits the correlation between descriptors of the same image. The experimental results show bitrate savings up to 35% without any impact in the performance efficiency of the image retrieval task. © 2014 EURASIP.

Examination timetabling automation using hybrid meta-heuristics

Trabalho de projeto realizado para obtenção do grau de Mestre em Engenharia Informática e de Computadores

Algorithm-oriented design of efficient many-core architectures applied to dense matrix multiplication

Recent integrated circuit technologies have opened the possibility to design parallel architectures with hundreds of cores on a single chip. The design space of these parallel architectures is huge with many architectural options. Exploring the design space gets even more difficult if, beyond performance and area, we also consider extra metrics like performance and area efficiency, where the designer tries to design the architecture with the best performance per chip area and the best sustainable performance. In this paper we present an algorithm-oriented approach to design a many-core architecture. Instead of doing the design space exploration of the many core architecture based on the experimental execution results of a particular benchmark of algorithms, our approach is to make a formal analysis of the algorithms considering the main architectural aspects and to determine how each particular architectural aspect is related to the performance of the architecture when running an algorithm or set of algorithms. The architectural aspects considered include the number of cores, the local memory available in each core, the communication bandwidth between the many-core architecture and the external memory and the memory hierarchy. To exemplify the approach we did a theoretical analysis of a dense matrix multiplication algorithm and determined an equation that relates the number of execution cycles with the architectural parameters. Based on this equation a many-core architecture has been designed. The results obtained indicate that a 100 mm(2) integrated circuit design of the proposed architecture, using a 65 nm technology, is able to achieve 464 GFLOPs (double precision floating-point) for a memory bandwidth of 16 GB/s. This corresponds to a performance efficiency of 71 %. Considering a 45 nm technology, a 100 mm(2) chip attains 833 GFLOPs which corresponds to 84 % of peak performance These figures are better than those obtained by previous many-core architectures, except for the area efficiency which is limited by the lower memory bandwidth considered. The results achieved are also better than those of previous state-of-the-art many-cores architectures designed specifically to achieve high performance for matrix multiplication.

Detect and pointing algorithm's performance for a planar smart antenna array: a review

An adaptive antenna array combines the signal of each element, using some constraints to produce the radiation pattern of the antenna, while maximizing the performance of the system. Direction of arrival (DOA) algorithms are applied to determine the directions of impinging signals, whereas beamforming techniques are employed to determine the appropriate weights for the array elements, to create the desired pattern. In this paper, a detailed analysis of both categories of algorithms is made, when a planar antenna array is used. Several simulation results show that it is possible to point an antenna array in a desired direction based on the DOA estimation and on the beamforming algorithms. A comparison of the performance in terms of runtime and accuracy of the used algorithms is made. These characteristics are dependent on the SNR of the incoming signal.

GPU implementation of a hyperspectral coded aperture algorithm for compressive sensing

This paper presents a new parallel implementation of a previously hyperspectral coded aperture (HYCA) algorithm for compressive sensing on graphics processing units (GPUs). HYCA method combines the ideas of spectral unmixing and compressive sensing exploiting the high spatial correlation that can be observed in the data and the generally low number of endmembers needed in order to explain the data. The proposed implementation exploits the GPU architecture at low level, thus taking full advantage of the computational power of GPUs using shared memory and coalesced accesses to memory. The proposed algorithm is evaluated not only in terms of reconstruction error but also in terms of computational performance using two different GPU architectures by NVIDIA: GeForce GTX 590 and GeForce GTX TITAN. Experimental results using real data reveals signficant speedups up with regards to serial implementation.