Gram-Schmidt orthogonal vector projection for hyperspectral unmixing

Orthogonal subspace projection (OSP) requires inverting a matrix to eliminate effect of unwanted signal sources on unmixing of desired signal sources. When the number of such wanted signals sources is large, which is indeed the case for hyperspectra data, OSP will become slow due to its matrix inversion. This paper develops a simple alternative approach to OSP without computing matrix inversion, called Gram Schmidt orthogonal vector projection (GSOVP) which is also based on orthogonal projection. Instead of annihilating all unwanted signal sources and then extracting the desired signal as OSP does, GSOVP accomplishes these two tasks by simple inner products. As a result, computational complexity is significantly reduced and hardware design is further simplified.