Linear Spectral Unmixing Using Least Squares Error, Orthogonal Projection and Simplex Volume for Hyperspectral Images

Linear spectral unmixing (LSU) and Simplex Volume (SV) are closely related. The link between these two has been recognized recently by the fact that simplex can be realized by two physical abundance constraints, Abundance Sum-to one Constraint (ASC) and Abundance Non-negativity Constraint (ANC). In other words, all data sample vectors are embraced by a simplex with vertices which are actually the set of signatures used to unmix data sample vectors where the data sample vectors outside the simplex are considered as unwanted sample vectors such as noisy samples, bad sample vectors. On the other hand, LSU is solved by Least Squares Error (LSE) which uses the principle of orthogonality to derive the solution. Therefore, LSU is also equivalent to being solved by Orthogonal Projection (OP). This paper explores applications of LSU using these criteria, simplex, LSE and OP in data unmixing.