Birsen Sirkeci

Total Least Squares Approaches for Spectral Unmixing of Hyperspectral Imagery

Date: May 29, 2001

Abstract: Spectral unmixing is a pixel-by-pixel approach to the detection and localization of features by spectral analysis techniques. Usually, partial knowledge about the feature, noise, and clutter spectra are provided, and the problem is to 'unmix' each pixel, or to estimate the relative concentrations of the reference spectra on a per pixel basis. A popular method of spectral unmixing for hyperspectral imagery is linear least squares. Linear least square approaches are appropriate when observational noise predominates and are inappropriate when significant modeling errors are present. The least squares approach has some disadvantages, especially in cases with few, poorly known references or significant reference variation throughout an image. In this thesis, total least squares approaches are presented and evaluated on experimental data. Feasible concentration estimates must account for non-negativity and sum-to-one constraints. Under the uniform light intensity assumption, restricted total least squares (RTLS) algorithm is proposed as a solution. This algorithm is an extention of classical total least squares approach with non-negativity and sum-to-one constraints. In case of light-intensity variation in the image, RTLS method is not applicable. To obtain consistent concentration estimates in such images, a new technique called non-negative total least squares (NNTLS) is developed. Performance of the proposed methods are compared to the existing least squared based methods using experimental (synthetic) and real data. Although total least squares based methods are computationally more demanding, simulation results show that they provide better concentration estimates in terms of Euclidean norm.

Defense Committee: Prof. David Brady (Advisor) Prof. Dana Brooks Prof. Eric Miller Prof. A. Bruce McDonald