Relationship exploration among PPI, ATGP and VCA via theoretical analysis

The principle of orthogonality using orthogonal projection (OP) is the key concept to develop mean squared error estimation theory in signal processing and communications. It has also found its way in a wide variety of applications in hyperspectral imaging. This paper explores close relationships among three OP-based algorithms, pixel purity index (PPI), vertex component analysis (VCA) in endmember extraction, automatic target generation process (ATGP) in mixed pixel classification and target detection, etc. and further shows that they indeed can be interpreted one way or another. Specifically, VCA and ATGP are essentially the same algorithm in the sense that they both extract targets via maximal OP from a nested sequence of successive orthogonal subspace projection spaces.