Minimum volume simplicial enclosure for spectral unmixing of remotely sensed hyperspectral data

Spectral unmixing is an important task for remotely sensed hyperspectral data exploitation. Linear spectral unmixing relies on two main steps: 1) identification of pure spectral constituents (endmembers), and 2) end member abundance estimation in mixed pixels. One of the main problems concerning the identification of spectral endmembers is the lack of pure spectral signatures in real hyperspectral data due to spatial resolution and mixture phenomena happening at different scales. In this paper, we present a new method for endmember estimation which does not assume the presence of pure pixels in the input data. The method minimizes the volume of an enclosing simplex in the reduced space while estimating the fractional abundance of vertices in simultaneous fashion, as opposed to other volume-based approaches such as N-FINDR which inflate the simplex of maximumvolume that can be formed using available image pixels. Our experimental results and comparisons to other endmember extraction algorithms indicate promising performance of the method in the task of extracting endmembers from real hyperspectral data. In our experiments, we use laboratory-simulated forest scenes with known endmembers and fractional abundances due to their acquisition in a controlled environment using a real hyperspectral imaging instrumen

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described