|Ph.D Student||Kizel Fadi|
|Subject||Novel Methods for Stepwise Analytical and Spatially|
Adaptive Hyperspectral Unmixing
|Department||Department of Civil and Environmental Engineering||Supervisors||Professor Maxim Shoshany|
|Professor Gilad Even-Tzur|
|Full Thesis text|
Spectral mixture analysis (SMA) is highly important for hyper-spectral image analysis. During the spectral unmixing process, a vector of fraction abundances, corresponding to a set of constituent signatures' so-called endmembers (EMs), is estimated for each pixel in the image. One of the most commonly used methods for ordinary unmixing is the fully constrained least squares unmixing (FCLSU), which uses a least squares (LS) process for optimizing the minimum Euclidean distance (MED) objective function. Typically in this method the image is unmixed using the entire set of endmembers, whereas, in fact, most of the pixels contain only a subset of the entire endmembers. The use of nonparticipating endmembers may result in significant inaccuracy. In this dissertation there are two proposed strategies for improving the unmixing process. The first strategy involves a search in fraction-combination space based on three main components: 1) The gradient descent (GD) optimization technique; 2) the spectral angle mapper (SAM) objective function; and 3) analytical determination of the gradient and the step size employed in each iteration. Starting with an initial estimation of the endmembers’ fractions, an exact line search is carried out by employing closed-form analytical expressions derived for the objective function’s gradient and the optimal step size in each iteration. Taking advantage of the closed-form analytical expressions and the simplicity of the framework components', code vectorization for expediting the optimization was implemented, where the fractions for the entire image pixels are solved simultaneously, thus creating new vectorized code gradient descent unmixing (VCGDU). The second strategy, called Gaussian-based spatially adaptive unmixing (GBSAU), implements three main components: 1) Extraction of spatial core areas representing regional high fractions of certain endmembers; 2) fitting 2D Gaussians representing the spatial distribution of the potential endmembers' abundances around these core areas; and 3) solving the unmixing problem with potential endmembers defined for each pixel. A comprehensive assessment of these two new strategies was conducted by comparing them to the FCLSU and the sparse unmixing by variable splitting and augmented Lagrangian (SUnSAL) methods. Raw hyperspectral image and synthetic data sets served these comparisons. Implementing the stepwise-analytical VCGDU indicated that its accuracy is slightly better than that obtained by FCLSU and SUnSAL for a relatively large number of actual endmembers, and considerably better under the illumination change effect. The results obtained with the spatially adaptive method (GBSAU) indicated a significant improvement in the overall accuracy of the unmixing process compared with ordinary methods.