New Hyperspectral Endmember Extraction Algorithms using Convex Geometry by Dharambhai Jayeshkumar Shah

Guided by: Dr. Y. N. Trivedi
16FTVPHDE18

ABSTRACT:
The decomposition of the mixed pixels into individual pure material (endmember) along with its
proposition is called spectral unfixing for hyperspectral images. Spectral unfixing is considered
a three-stage problem for the hyperspectral image. The first is the subspace dimension which finds
the number of pure materials in the image. The second one is endmember extraction which extracts
the pure material spectra from the image and the third one is abundance estimation which estimates
the proportions of each material in mixing. The endmember extraction is a very challenging stage
in spectral immixing as abundance mapping greatly depends on extracted endmembers. In the
literature, endmember extraction is addressed using a geometrical, statistical, sparse regression,
and deep learning approach. Due to simplicity and easy understanding, many researchers use the
geometrical approach. In our research work, we focus on the geometrical endmember extraction
approach which majorly uses the concept of convex geometry. In our work, we have developed
new eight algorithms that improve the endmember extraction accuracy and abundance estimation
accuracy. The first new algorithm explores entropy-based spatial information with convex set
optimization-based spectral information. The second algorithm uses K-medoids clustering with
convex geometry. The K-medoids clustering is used for removing redundant points that make us
second algorithm as noise-robust The third algorithm uses the area maximization approach instead
of conventional volume maximization. Surveyor’s formula is used for finding the area of a convex
polygon in this third algorithm. The fourth algorithm uses the Rank correlation coefficient to find
only effective bands for applying convex geometry. This fourth algorithm used Pearson’s correlation
coefficient. The fifth algorithm combines the geometrical features with statistical features. The
convex geometry is used as a geometrical feature and covariance of the band is used as a statistical
feature. The sixth algorithm uses the quality bands only for applying convex geometry. The high-quality
bands are selected before applying the convex geometry. The seventh proposed algorithm
uses an ensemble of all Winter’s belief-based algorithms for improving accuracy. The majority
voting-based ensemble is used to combine the performance of each Winter’s belief-based algorithm.
The eighth algorithm uses an integration framework of maximum simplex volume and extreme
projection on a subspace which are two major criteria of geometrical types of approaches. This
algorithm uses the newly defined score that is based on the convexity-based purity concept. All
the extracted endmembers of the proposed algorithms have been compared with the extracted
i endmembers of the prevailing algorithms on benchmark real and synthetic datasets using standard
evaluation parameters such as Spectral Angle Mapper (SAM), Spectral Information Divergence
(SID), and Normalized Cross-Correlation (NXC). The Root Mean Square Error (RMSE) is used
to test the efficacy of the extracted endmember for abundance mapping. The RMSE error is
calculated between FCLS-based abundance maps by the endmember of the proposed algorithm
and FCLS-based abundance maps by the Ground Truth. We have used Cuprite, Urban, Jasper,
Samson, Mangalore, and Ahmedabad as a real dataset. We have used the Hyperspectral Imagery
Synthesis Toolbox (HIST) for generating five types of synthetic images. The synthetic images are
added with Gaussian noise to test the noise robustness. The proposed algorithms in this thesis
can be used for a variety of hyperspectral applications, including classification, target detection,
and many others. We have also compared our eight proposed algorithms with the benchmark
geometrical algorithms.