GROWING SIMPLEX VOLUME ANALYSIS FOR FINDING ENDMEMBERS IN HYPERSPECTRAL IMAGERY

Abstract

Finding endmembers is a fundamental task in hyperspectral data exploitation. Many Endmember Finding Algorithms (EFAs) have been proposed over the past years. Among all the algorithms, using maximal Simplex Volume (SV) as an optimal criterion for finding endmembers has been a major approach, which results in a well-known algorithm, N-finder algorithm (N-FINDR). As an alternative to N-FINDR, Simplex Growing Algorithm (SGA) was further proposed to reduce computational complexity to avoid an exhaustive search for endmembers required by N-FINDR. Nevertheless, both N-FINDR and SGA still suffer from an issue of numerical instability when it comes to SV calculation via matrix determinant. The research conducted in this dissertation converts Determinant-based SV calculation to Geometric SV (GSV) calculation by taking advantage of geometric structures of simplexes. As a result, there is no longer a need of using matrix determinant to calculate SV. Instead, GSV calculates the volume of a simplex by multiplying its base and height of a simplex. Many benefits can be gained from GSV, such as (1) no need of dimensionality reduction; (2) avoidance of numerical instability incurred by finding determinants of a non-square matrices; (3) no matrix inverses required; (4) significantly reduced computational complexity and computing cost; (5) easy implementation in hardware design. By virtue of GSV calculation several GSV-based EFAs can be re-derived to replace original Determinant SGA (DSGA), which include Orthogonal Projection-based SGA (OP-SGA), Geometric SGA (GSGA), and Geometric Convex Cone Volume Analysis (GCCVA). In order to facilitate real-time processing capability, these algorithms are further extended to their respective recursive counterparts which also result in Kalman filter-like EFAs.