Abstract
The simplex growing algorithm (SGA) has been widely used for finding endmembers. It can be considered as a sequential version of the well-known endmember finding algorithm, N-finder algorithm (N-FINDR), which finds endmembers one at a time by growing simplexes. However, one of the major hurdles for N-FINDR and SGA is the calculation of simplex volume (SV) which poses a great challenge in designing any algorithm using SV as a criterion for finding endmembers. This paper develops an orthogonal projection (OP)-based SGA (OP-SGA) which essentially resolves this computational issue. It converts the issue of calculating SV to calculating the OP on previously found simplexes without computing matrix determinants. Most importantly, a recursive Kalman filter-like OP-SGA, to be called recursive OP-SGA (ROP-SGA), can be also derived to ease computation. By virtue of ROP-SGA, several advantages and benefits in computational savings and hardware implementation can be gained for which N-FINDR and SGA do not have.
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