Linear Unmixing of Hyperspectral Signals via Wavelet

A pixel in remotely sensed hyperspectral imagery is typically a mixture of multiple electromagnetic radiances from various ground cover materials. Spectral unmixing is a quantitative analysis procedure used to recognize constituent ground cover materials (or endmembers) and obtain their mixing proportions (or abundances) from a mixed pixel. The abundances are typically estimated using the least squares estimation (LSE) method based on the linear mixture model (LMM). This dissertation provides a complete investigation on how the use of appropriate features can improve the LSE of endmember abundances using remotely sensed hyperspectral signals. The dissertation shows how features based on signal classification approaches, such as discrete wavelet transform (DWT), outperform features based on conventional signal representation methods for dimensionality reduction, such as principal component analysis (PCA), for the LSE of endmember abundances. Both experimental and theoretical analyses are reported in the dissertation. A DWT-based linear unmixing system is designed specially for the abundance estimation. The system utilizes the DWT as a pre-processing step for the feature extraction. Based on DWT-based features, the system utilizes the constrained LSE for the abundance estimation. Experimental results show that the use of DWT-based features reduces the abundance estimation deviation by 30-50% on average, as compared to the use of original hyperspectral signals or conventional PCA-based features. Based on the LMM and the LSE method, a series of theoretical analyses are derived to reveal the fundamental reasons why the use of the appropriate features, such as DWT-based features, can improve the LSE of endmember abundances. Under reasonable assumptions, the dissertation derives a generalized mathematical relationship between the abundance estimation error and the endmember separabilty. It is proven that the abundance estimation error can be reduced through increasing the endmember separability. The use of DWT-based features provides a potential to increase the endmember separability, and consequently improves the LSE of endmember abundances. The stability of the LSE of endmember abundances is also analyzed using the concept of the condition number. Analysis results show that the use of DWT-based features not only improves the LSE of endmember abundances, but also improves the LSE stability. ii DEDICATION To my wife and parents iii ACKNOWLEDGMENTS I would like to thank my major advisor, Dr. Lori Bruce, for her advising, support and help that finally lead to the successful completion of this dissertation. I would also like to thank my committee members, Dr. acknowledge all of the faculty and staff, working in …