Abstruct-Most applications of hyperspectral imagery require processing techniques which achieve two fundamental goals: 1) detect and classify the constituent materials for each pixel in the scene; 2) reduce the data volumeldimensionality, without loss of critical information, so that it can be processed efficiently and assimilated by a human analyst. In this paper, we describe a technique which simultaneously reduces the data dimensionality, suppresses undesired or interfering spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel vector onto a subspace which is orthogonal to the undesired signatures. This operation is an optimal interference suppression process in the least squares sense. Once the interfering signatures have been nulled, projecting the residual onto the signature of interest maximizes the signal-to-noise ratio and results in a single component image that represents a classification for the signature of interest. The orthogonal subspace projection (OSP) operator can be extended to k signatures of interest, thus reducing the dimensionality of k and classifying the hyperspectral image simultaneously. The approach is applicable to both spectrally pure as well as mixed pixels. I. INTRODUCTION YPERSPECTRAL imaging spectrometer data pro-H vide a wealth of information which can be used to address a variety of earth remote sensing problems. A short list of applications includes environmental mapping, global change research, geological research, wetlands mapping, assessment of trafficability , plant and mineral identification and abundance estimation, crop analysis, and bathymetry. The common theme in all of these applications is the requirement for classification of each pixel in the scene, and reduction of data volume to tractable levels. Classification of a hyperspectral image sequence amounts to identifying which pixels contain various spectrally distinct materials that have been specified by the user. Several techniques for classification of multilhyperspectral pixels have been used from minimum distance and maximum likelihood classifiers [ 13 to correlation/ matched filter-based approaches such as spectral signature matching [2] and the spectral angle mapper [3]. The sta-Manuscript

Abstract-With very high spectral resolution, hyperspectral sensors can now uncover many unknown signal sources which cannot be identified by visual inspection or a priori. In order to account for such unknown signal sources, we introduce a new definition, referred to as virtual dimensionality (VD) in this paper. It is defined as the minimum number of spectrally distinct signal sources that characterize the hyperspectral data from the perspective view of target detection and classification. It is different from the commonly used intrinsic dimensionality (

A new growing method for simplex-based endmember extraction algorithms (EEAs), called simplex growing algorithm (SGA), is presented in this paper. It is a sequential algorithm to find a simplex with the maximum volume every time a new vertex is added. In order to terminate this algorithm a recently developed concept, virtual dimensionality (VD), is implemented as a stopping rule to determine the number of vertices required for the algorithm to generate. The SGA improves one commonly used EEA, the N-finder algorithm (N-FINDR) developed by Winter, by including a process of growing simplexes one vertex at a time until it reaches a desired number of vertices estimated by the VD, which results in a tremendous reduction of computational complexity. Additionally, it also judiciously selects an appropriate initial vector to avoid a dilemma caused by the use of random vectors as its initial condition in the N-FINDR where the N-FINDR generally produces different sets of final endmembers if different setsof randomly generated initial endmembers are used. In order to demonstrate the performance of the proposed SGA, the N-FINDR and two other EEAs, pixel purity index, and vertex component analysis are used for comparison. Index Terms-Endmember extraction, N-finder algorithm (N-FINDR), pixel purity index (PPI), sequential endmember extraction algorithm (SQEEA), simplex growing algorithm (SGA), simultaneous endmember extraction algorithm (SMEEA), vertex component analysis (VCA), virtual dimensionality (VD).

This paper proposes a hierarchical Bayesian model that can be used for semi-supervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data. Index Terms-Gibbs sampler, hierarchical Bayesian analysis, hyperspectral images, linear spectral unmixing, Markov chain Monte Carlo (MCMC) methods, reversible jumps. I. INTRODUCTIONS PECTRAL unmixing has been widely used in remote sensing signal processing for data analysis [1]. Its underlying assumption is based on the fact that all data sample vectors are mixed by a number of so-called endmembers assumed to be present in the data. By virtue of this assumption, two models have been investigated in the past to model how mixing activities take place. One is the macrospectral mixture that describes a mixed pixel as a linear mixture of endmembers opposed to the other model suggested by Hapke [2], referred to as intimate mixture that models a mixed pixel as a nonlinear mixture. Nonetheless, it has been shown in [3] that the intimate model could be linearized to simplify analysis. Accordingly, only linear spectral unmixing is considered in this paper. In