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.