Hyperspectral Endmember Detection and Band Selection Using Bayesian Methods

Four methods for endmember detection and spectral unmixing which estimate endmember spectra and proportion values for each pixel are described. The first method simultaneously determines the number of endmembers in addition to estimating endmember spectra and proportion values. The second method treats endmembers as distributions and estimates each endmember distribution while simultaneously learning proportion values. The third endmember detection method autonomously partitions the input data set into convex regions for which endmember distributions and proportion values are simultaneously estimated. The fourth method which performs hyperspectral band selection in addition to endmember detection, spectral unmixing, and determinating of the number of endmembers is also described. Few endmember detection algorithms estimate the number of endmembers in addition to determining their spectral shape. Also, methods which treat endmembers as distributions or treat hyperspectral images as piece-wise convex data sets have not been previously developed. A hyperspectral image is a three-dimensional data cube containing radiance values collected over an area (or scene) in a range of wavelengths. Endmember detection and spectral unmixing attempt to decompose a hyperspectral image into the pure - separate and individual - spectral signatures of the materials in a scene, and the proportions of each material at every pixel location. Each spectral pixel in the image can then be approximated by a convex combination of proportions and endmember spectra. The first method described is the Sparsity Promoting Iterated Constrained Endmembers (SPICE) algorithm, which incorporates sparsity-promoting priors to estimate the number of endmembers. The algorithm is initialized with a large number of endmembers. The sparsity promotion process drives all proportions of some endmembers to zero. These endmembers can be removed by SPICE with no effect on the error incurred by representing the image with endmembers. The second method, the Endmember Distributions detection (ED) algorithm, models each endmember as a distribution rather than a single spectrum. This view can incorporate an endmember's spectral variation which may occur due to varying environmental conditions as well as inherent variability in a material. The third method is the Piece-wise Convex Endmember (PCE) detection algorithm which partitions the input hyperspectral data set into convex regions and determines endmembers for each of these regions. The number of convex regions are determined autonomously using the Dirichlet process while simultaneously estimating endmember distributions and proportion values for each pixel in the input data set. The SPICE, ED and PCE algorithms are effective at handling highly-mixed hyperspectral images where all of the pixels in the scene contain mixtures of multiple endmembers. These methods are capable of extracting endmember spectra from a scene that does not contain pure pixels composed of only a single endmember's material. Furthermore, the methods…