Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery

This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for non-negativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images

In Situ Study of the Photodegradation of Carbofuran Deposited on TiO\u3csub\u3e2\u3c/sub\u3e Film under UV Light, Using ATR-FTIR Coupled to HS-MCR-ALS

The in situ study of the photodegradation of carbofuran deposited on a TiO2 catalyst film under UV light was carried out using the ATR-FTIR technique. The data were analyzed using a Hard–Soft Multivariate Curve Resolution-Alternating Least Squares (HS-MCR-ALS) methodology. Using S-MCR-ALS, four factors were deduced from the evolving factor analysis of the data, and their concentrations and spectra were determined. These results were used to draw qualitative and quantitative analyses of the major products of carbofuran photodegradation. The results of this analysis were in good agreement with GC-MS results and with reported mechanisms. Hard-MCR-ALS was then used to refine the spectra and concentrations, using a multistep kinetic model. The rate constant for the first step in the photodegradation of carbofuran was found to be 2.9 × 10–3 min–1. The higher magnitude of the correlation (96.87%), the explained variance (99.87%) and LOF (3.01), are good indicators of the reliability of the outcome of this approach. This method has been shown to be an efficient approach to study in situ photodegradation of pesticides on a solid surface

Bayesian Nonnegative Matrix Factorization with Volume Prior for Unmixing of Hyperspectral Images

In hyperspectral image analysis the objective is to unmix a set of acquired pixels into pure spectral signatures (endmembers) and corresponding fractional abundances. The Non-negative Matrix Factorization (NMF) methods have received a lot of attention for this unmixing process. Many of these NMF based unmixing algorithms are based on sparsity regularization encouraging pure spectral endmembers, but this is not optimal for certain applications, such as foods, where abundances are not sparse. The pixels will theoretically lie on a simplex and hence the endmembers can be estimated as the vertices of the smallest enclosing simplex. In this context we present a Bayesian framework employing a volume constraint for the NMF algorithm, where the posterior distribution is numerically sampled from using a Gibbs sampling procedure. We evaluate the method on synthetical and real hyperspectral data of wheat kernels. 1

An exploration into the sparse representation of spectra

Includes bibliographical references (leaves 73-76)This thesis describes an exploration in achieving sparse representations of object, with special focus on spectral data. Given a database of objects one would like to know the actual aspects of each class that distinguish it from any other class in the database. We explore the hypothesis that simple abstractions (descriptions) that humans normally make, especially based on the visual phenomenology or physics on the problem, can be helpful in extracting and formulating useful sparse representations of the observed objects. In this thesis we focus on the discovery of such underlying features, employing a number of recent methods from machine learning. Firstly we find that an approach to automatic feature discovery recently proposed in the literature (Non Negative Matrix Factorization) is not as it seems. We show the limitations of this approach and demonstrate a more efficient method on a synthetic problem. Secondly we explore a more empirical approach to extracting visually attractive features of spectra from which we formulate simple re-representation of spectral data and show that the identification and discovery of certain intuitive features at various scales can be sufficient to describe a spectrum profile. Finally we explore a more traditional and principled automatic method of analyzing a spectrum at different resolutions (Wavelets). We find that certain classes of spectra can easily be discriminated between by a simple approximation of the spectrum profile while in other cases only the finer profile details are important. Throughout this thesis we employ a measure called the separability index as our measure of how easy it is to discriminate objects in a database with the proposed representations

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin