New Hyperspectral Endmember Extraction Algorithms using Convex Geometry

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.